diff --git a/.github/workflows/docs.yml b/.github/workflows/docs.yml
index 004acc8a..48f7e1f1 100644
--- a/.github/workflows/docs.yml
+++ b/.github/workflows/docs.yml
@@ -28,7 +28,7 @@ jobs:
- run: pip install pdoc
# ADJUST THIS: build your documentation into docs/.
# We use a custom build script for pdoc itself, ideally you just run `pdoc -o docs/ ...` here.
- - run: pdoc src/altk -d google --math -o ./docs
+ - run: pdoc src/ultk -d google --math -o ./docs
- uses: actions/upload-pages-artifact@v1
with:
diff --git a/.github/workflows/pypi-publish.yml b/.github/workflows/pypi-publish.yml
index fcbf28ef..b8fc563b 100644
--- a/.github/workflows/pypi-publish.yml
+++ b/.github/workflows/pypi-publish.yml
@@ -8,7 +8,7 @@ jobs:
runs-on: ubuntu-latest
environment:
name: testpypi
- url: https://test.pypi.org/project/clmbr-altk
+ url: https://test.pypi.org/project/ultk
permissions:
id-token: write # IMPORTANT: this permission is mandatory for trusted publishing
steps:
diff --git a/.gitignore b/.gitignore
index 5558b980..8d06e75d 100644
--- a/.gitignore
+++ b/.gitignore
@@ -8,4 +8,10 @@ src/altk.egg-info
dist/
*.egg-info/
.installed.cfg
-*.egg
\ No newline at end of file
+*.egg
+build/
+
+*.zip
+
+model/
+build/
diff --git a/README.md b/README.md
index a5ec4fbf..d71525ef 100644
--- a/README.md
+++ b/README.md
@@ -1,10 +1,10 @@
-# The Artificial Language ToolKit (ALTK)
+# The Unnatural Language ToolKit (ULTK)
-
Figures:
-> Kinship Categories Across Languages Reflect General Communicative Principles | Science. (n.d.). Retrieved February 27, 2023, from https://www.science.org/doi/10.1126/science.1218811
+> Kemp, C. & Regier, T. (2012) Kinship Categories Across Languages Reflect General Communicative Principles. Science. https://www.science.org/doi/10.1126/science.1218811
> Zaslavsky, N., Kemp, C., Regier, T., & Tishby, N. (2018). Efficient compression in color naming and its evolution. Proceedings of the National Academy of Sciences, 115(31), 7937–7942. https://doi.org/10.1073/pnas.1800521115
diff --git a/docs/altk/effcomm/information.html b/docs/altk/effcomm/information.html
deleted file mode 100644
index 372f8e3f..00000000
--- a/docs/altk/effcomm/information.html
+++ /dev/null
@@ -1,1385 +0,0 @@
-
-
-
- altk.effcomm.information API documentation
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
- Helper functions for Rate-Distortion based (including Information Bottleneck) efficient communication analyses.
-
View Source 1 """Helper functions for Rate-Distortion based (including Information Bottleneck) efficient communication analyses."""
- 2 3 import numpy as np
- 4 from altk.language.language import Language
- 5 from altk.language.semantics import Universe , Referent
- 6 from altk.effcomm.agent import LiteralSpeaker , BayesianListener
- 7 from altk.effcomm import util
- 8 from embo import InformationBottleneck
- 9 from typing import Callable
- 10 11 12 def information_rate ( source : np . ndarray , encoder : np . ndarray ) -> float :
- 13 """Compute the information rate / complexity of the encoder q(w|m) as $I[W:M]$."""
- 14 pXY = util . joint ( pY_X = encoder , pX = source )
- 15 return util . MI ( pXY = pXY )
- 16 17 18 ##############################################################################
- 19 # Rate-Distortion Theory
- 20 ##############################################################################
- 21 22 23 def get_rd_curve (
- 24 prior : np . ndarray ,
- 25 dist_mat : np . ndarray ,
- 26 betas : np . ndarray = np . linspace ( start = 0 , stop = 2 ** 7 , num = 1500 ),
- 27 ) -> list [ tuple [ float ]]:
- 28 """Use the Blahut Arimoto algorithm to obtain a list of (rate, distortion) points."""
- 29 rd = lambda beta : blahut_arimoto ( dist_mat , p_x = prior , beta = beta )[ "final" ]
- 30 pareto_points = [ rd ( beta ) for beta in betas ]
- 31 return pareto_points
- 32 33 34 def expected_distortion (
- 35 p_x : np . ndarray , p_xhat_x : np . ndarray , dist_mat : np . ndarray
- 36 ) -> float :
- 37 """$D[X, \hat{X}] = \sum_x p(x) \sum_{\hat{x}} p(\hat{x}|x) \cdot d(x, \hat{x})$"""
- 38 return np . sum ( p_x @ ( p_xhat_x * dist_mat ))
- 39 40 41 def compute_rate_distortion (
- 42 p_x ,
- 43 p_xhat_x ,
- 44 dist_mat ,
- 45 ) -> tuple [ np . ndarray ]:
- 46 """Compute the information rate $I(X;\hat{X})$ and total distortion $D[X, \hat{X}]$ of a joint distribution defind by $P(X)$ and $P(\hat{X}|X)$.
- 47 48 Args:
- 49 p_x: array of shape `|X|` the prior probability of an input symbol (i.e., the source)
- 50 51 p_xhat_x: array of shape `(|X|, |X_hat|)` the probability of an output symbol given the input
- 52 53 dist_mat: array of shape `(|X|, |X_hat|)` representing the distoriton matrix between the input alphabet and the reconstruction alphabet.
- 54 55 Returns:
- 56 a (rate, distortion) tuple containing the information rate (in bits) of compressing X into X_hat and the expected distortion between X, X_hat
- 57 """
- 58 return (
- 59 information_rate ( p_x , p_xhat_x ),
- 60 expected_distortion ( p_x , p_xhat_x , dist_mat ),
- 61 )
- 62 63 64 def blahut_arimoto (
- 65 dist_mat : np . ndarray ,
- 66 p_x : np . ndarray ,
- 67 beta : float ,
- 68 max_it : int = 200 ,
- 69 eps : float = 1e-5 ,
- 70 ignore_converge : bool = False ,
- 71 ) -> tuple [ float ]:
- 72 """Compute the rate-distortion function of an i.i.d distribution
- 73 74 Args:
- 75 dist_mat: array of shape `(|X|, |X_hat|)` representing the distortion matrix between the input alphabet and the reconstruction alphabet. dist_mat[i,j] = dist(x[i],x_hat[j]). In this context, X is a random variable representing the a speaker's meaning (target referent), and X_hat is a random variable representing a listener's meaning (guessed referent).
- 76 77 p_x: (1D array of shape `|X|`) representing the probability mass function of the source. In this context, the prior over states of nature.
- 78 79 beta: (scalar) the slope of the rate-distoriton function at the point where evaluation is required
- 80 81 max_it: max number of iterations
- 82 83 eps: accuracy required by the algorithm: the algorithm stops if there is no change in distoriton value of more than 'eps' between consequtive iterations
- 84 85 ignore_converge: whether to run the optimization until `max_it`, ignoring the stopping criterion specified by `eps`.
- 86 87 Returns:
- 88 a dict of the form
- 89 90 {
- 91 'final': a tuple of (rate, distortion) values. This is the rate (in bits) of compressing X into X_hat, and distortion between X, X_hat
- 92 93 'trajectory': a list of the (rate, distortion) points discovered during optimization
- 94 }
- 95 """
- 96 # start with iid conditional distribution, as p(x) may not be uniform
- 97 p_xhat_x = np . tile ( p_x , ( dist_mat . shape [ 1 ], 1 )) . T
- 98 99 # normalize
-100 p_x /= np . sum ( p_x )
-101 p_xhat_x /= np . sum ( p_xhat_x , 1 , keepdims = True )
-102 103 it = 0
-104 traj = []
-105 distortion = 2 * eps
-106 converged = False
-107 while not converged :
-108 it += 1
-109 distortion_prev = distortion
-110 111 # p(x_hat) = sum p(x) p(x_hat | x)
-112 p_xhat = p_x @ p_xhat_x
-113 114 # p(x_hat | x) = p(x_hat) exp(- beta * d(x_hat, x)) / Z
-115 p_xhat_x = np . exp ( - beta * dist_mat ) * p_xhat
-116 p_xhat_x /= np . expand_dims ( np . sum ( p_xhat_x , 1 ), 1 )
-117 118 # update for convergence check
-119 rate , distortion = compute_rate_distortion ( p_x , p_xhat_x , dist_mat )
-120 121 # collect point
-122 traj . append (( rate , distortion ))
-123 124 # convergence check
-125 if ignore_converge :
-126 converged = it == max_it
-127 else :
-128 converged = it == max_it or np . abs ( distortion - distortion_prev ) < eps
-129 130 return {
-131 "final" : ( rate , distortion ),
-132 "trajectory" : traj ,
-133 }
-134 135 136 ##############################################################################
-137 # Information Bottleneck
-138 ##############################################################################
-139 140 # === Main IB methods ===
-141 142 143 def get_ib_curve (
-144 prior : np . ndarray ,
-145 space : Universe ,
-146 decay : float ,
-147 cost : Callable [[ Referent , Referent ], float ],
-148 curve_type : str = "informativity" ,
-149 ) -> np . ndarray :
-150 """Compute the IB curve bound (I[M:W] vs. I[W:U]) for a given semantic space. We use the embo package, which does not allow one to specify the number of betas, which means some interpolation might be necessary later.
-151 152 Args:
-153 prior: array of shape `|meanings|`
-154 155 space: the ModalMeaningSpace on which meanings are defined
-156 157 decay: parameter for meaning distribution p(u|m) generation. See `generate_meaning_distributions`.
-158 159 cost: parameter for meaning distribution p(u|m) generation. See `generate_meaning_distributions`.
-160 161 curve_type: {'informativity', 'comm_cost'} specifies whether to return the (classic) IB axes of informativity vs. complexity, or the more Rate-Distortion Theory aligned axes of comm_cost vs. complexity. The latter can be obtained easily from the former by subtracting each informativity value from I[M:U], which is a constant for all languages in the same domain.
-162 163 Returns:
-164 an array of shape `(num_points, 2)` representing the list of (accuracy/comm_cost, complexity) points on the information plane.
-165 """
-166 conditional_pum = generate_meaning_distributions ( space , decay , cost )
-167 joint_pmu = util . joint ( conditional_pum , prior ) # P(u) = P(m)
-168 I_mu = util . MI ( joint_pmu )
-169 170 # I[M:W], I[W:U], H[W], beta
-171 I_mw , I_wu , _ , _ = InformationBottleneck ( pxy = joint_pmu ) . get_bottleneck ()
-172 173 if curve_type == "comm_cost" :
-174 points = np . array (
-175 list ( zip ( I_mu - I_wu , I_mw ))
-176 ) # expected kl divergence, complexity
-177 else :
-178 points = np . array ( list ( zip ( I_wu , I_mw ))) # informativity, complexity
-179 return points
-180 181 182 def ib_complexity (
-183 language : Language ,
-184 prior : np . ndarray ,
-185 ) -> float :
-186 """Compute the IB encoder complexity of a language $I[M:W]$."""
-187 return float (
-188 information_rate (
-189 source = prior ,
-190 encoder = language_to_ib_encoder_decoder (
-191 language ,
-192 prior ,
-193 )[ "encoder" ],
-194 )
-195 )
-196 197 198 def ib_informativity (
-199 language : Language ,
-200 prior : np . ndarray ,
-201 decay : float ,
-202 cost : Callable [[ Referent , Referent ], float ],
-203 ) -> float :
-204 """Compute the expected informativity (accuracy) $I[W:U]$ of a lexicon.
-205 206 Args:
-207 language: the Language to measure for informativity
-208 209 prior: communicative need distribution
-210 211 decay: parameter for meaning distribution p(u|m) generation. See `generate_meaning_distributions`.
-212 213 cost: parameter for meaning distribution p(u|m) generation. See `generate_meaning_distributions`.
-214 215 Returns:
-216 the informativity of the language I[W:U] in bits.
-217 """
-218 return float (
-219 util . MI (
-220 language_to_joint_distributions ( language , prior , decay , cost )[ "joint_pwu" ]
-221 )
-222 )
-223 224 225 def ib_comm_cost (
-226 language : Language ,
-227 prior : np . ndarray ,
-228 decay : float ,
-229 cost : Callable [[ Referent , Referent ], float ],
-230 ) -> float :
-231 """Compute the IB communicative cost, i.e. expected KL-divergence betweeen speaker and listener meanings, for a language.
-232 233 Args:
-234 language: the Language to measure for communicative cost
-235 236 prior: communicative need distribution
-237 238 decay: parameter for meaning distribution p(u|m) generation. See `generate_meaning_distributions`.
-239 240 cost: parameter for meaning distribution p(u|m) generation. See `generate_meaning_distributions`.
-241 242 Returns:
-243 the communicative cost, $\mathbb{E}[D_{KL}[M || \hat{M}]] = I[M:U] - I[W:U]$ in bits.
-244 """
-245 dists = language_to_joint_distributions ( language , prior , decay , cost )
-246 return float ( util . MI ( dists [ "joint_pmu" ]) - util . MI ( dists [ "joint_pwu" ]))
-247 248 249 def language_to_joint_distributions (
-250 language : Language ,
-251 prior : np . ndarray ,
-252 decay : float ,
-253 cost : Callable [[ Referent , Referent ], float ],
-254 ) -> float :
-255 """Given a Language, get P(M,U) the joint distribution over meanings and referents, and P(W,U) the joint distribution over words and referents.
-256 257 Args:
-258 language: the Language to convert to distributions
-259 260 prior: communicative need distribution
-261 262 decay: parameter for meaning distribution p(u|m) generation. See `generate_meaning_distributions`.
-263 264 cost: parameter for meaning distribution p(u|m) generation. See `generate_meaning_distributions`.
-265 266 Returns:
-267 a dict of the form
-268 269 {
-270 "joint_pmu": an array of shape `(|U|, |M|)` representing P(U, M)
-271 "joint_pwu": an array of shape `(|W|, |U|)` representing P(W, U)
-272 }
-273 274 """
-275 system = language_to_ib_encoder_decoder ( language , prior )
-276 encoder = system [ "encoder" ]
-277 decoder = system [ "decoder" ]
-278 space = language . universe
-279 280 conditional_pum = generate_meaning_distributions ( space , decay , cost )
-281 conditional_puw = deterministic_decoder ( decoder , conditional_pum )
-282 joint_pmu = util . joint ( conditional_pum , prior )
-283 p_w = util . marginalize ( encoder , prior )
-284 joint_pwu = util . joint ( conditional_puw , p_w )
-285 286 return {
-287 "joint_pmu" : joint_pmu ,
-288 "joint_pwu" : joint_pwu ,
-289 }
-290 291 292 # === IB Helpers ===
-293 294 295 def language_to_ib_encoder_decoder (
-296 language : Language ,
-297 prior : np . ndarray ,
-298 ) -> dict [ str , np . ndarray ]:
-299 """Convert a Language, a mapping of words to meanings, to IB encoder, q(w|m) and IB decoder q(m|w).
-300 301 Args:
-302 language: the lexicon from which to infer a speaker (encoder).
-303 304 prior: communicative need distribution
-305 306 Returns:
-307 a dict of the form
-308 {
-309 "encoder": np.ndarray of shape `(|meanings|, |words|)`,
-310 "decoder": np.ndarray of shape `(|words|, |meanings|)`,
-311 }
-312 """
-313 # In the IB framework, the encoder is _typically_ a literal speaker and the decoder is a bayes optimal listener. TODO: There are obviously other possible choices here.
-314 speaker = LiteralSpeaker ( language )
-315 speaker . weights = util . rows_zero_to_uniform ( speaker . normalized_weights ())
-316 listener = BayesianListener ( speaker , prior )
-317 return {
-318 "encoder" : speaker . normalized_weights (),
-319 "decoder" : listener . normalized_weights (),
-320 }
-321 322 323 def deterministic_decoder (
-324 decoder : np . ndarray , meaning_distributions : np . ndarray
-325 ) -> np . ndarray :
-326 """Compute $\hat{m}_{w}(u) = \sum_m p(m|w) \cdot m(u) $
-327 328 Args:
-329 decoder: array of shape `(|words|, |meanings|)`
-330 331 meaning_distributions: array of shape `(|meanings|, |meanings|)`
-332 333 Returns:
-334 array of shape `(|words|, |meanings|)` representing the 'optimal' deterministic decoder
-335 """
-336 return decoder @ meaning_distributions
-337 338 339 def generate_meaning_distributions (
-340 space : Universe ,
-341 decay : float ,
-342 cost : Callable [[ Referent , Referent ], float ],
-343 ) -> np . ndarray :
-344 """Generate a conditional distribution over world states given meanings, $p(u|m)$, for each meaning.
-345 346 Args:
-347 space: the ModalMeaningSpace on which meanings are defined
-348 349 decay: a float in [0,1]. controls informativity, by decaying how much probability mass is assigned to perfect recoveries. As decay approaches 0, only perfect recovery is rewarded (which overrides any partial credit structure built into the utility/cost function). As decay approaches 1, the worst guesses become most likely.
-350 351 cost: a cost function defining the pairwise communicative cost for confusing one Referent in the Universe with another. If you have a (scaled) communicative utility matrix, a natural choice for cost might be `lambda x, y: 1 - utility(x, y)`.
-352 353 Returns:
-354 p_u_m: an array of shape `(|space.referents|, |space.referents|)`
-355 """
-356 357 # construct p(u|m) for each meaning
-358 meaning_distributions = np . array (
-359 [[ decay ** cost ( m , u ) for u in space . referents ] for m in space . referents ]
-360 )
-361 # each row sums to 1.0
-362 np . seterr ( divide = "ignore" , invalid = "ignore" )
-363 meaning_distributions = np . nan_to_num (
-364 meaning_distributions / meaning_distributions . sum ( axis = 1 , keepdims = True )
-365 )
-366 367 return meaning_distributions
-
-
-
-
-
- def
- get_rd_curve ( prior : numpy . ndarray , dist_mat : numpy . ndarray , betas : numpy . ndarray = array ([ 0.00000000e+00 , 8.53902602e-02 , 1.70780520e-01 , ... ,
- 1.27829219e+02 , 1.27914610e+02 , 1.28000000e+02 ]) ) -> list [ tuple [ float ]] :
-
- View Source
-
- 24 def get_rd_curve (
-25 prior : np . ndarray ,
-26 dist_mat : np . ndarray ,
-27 betas : np . ndarray = np . linspace ( start = 0 , stop = 2 ** 7 , num = 1500 ),
-28 ) -> list [ tuple [ float ]]:
-29 """Use the Blahut Arimoto algorithm to obtain a list of (rate, distortion) points."""
-30 rd = lambda beta : blahut_arimoto ( dist_mat , p_x = prior , beta = beta )[ "final" ]
-31 pareto_points = [ rd ( beta ) for beta in betas ]
-32 return pareto_points
-Use the Blahut Arimoto algorithm to obtain a list of (rate, distortion) points.
-
-
-
-
- def
- expected_distortion ( p_x : numpy . ndarray , p_xhat_x : numpy . ndarray , dist_mat : numpy . ndarray ) -> float :
-
- View Source
-
- 35 def expected_distortion (
-36 p_x : np . ndarray , p_xhat_x : np . ndarray , dist_mat : np . ndarray
-37 ) -> float :
-38 """$D[X, \hat{X}] = \sum_x p(x) \sum_{\hat{x}} p(\hat{x}|x) \cdot d(x, \hat{x})$"""
-39 return np . sum ( p_x @ ( p_xhat_x * dist_mat ))
-$D[X, \hat{X}] = \sum_x p(x) \sum_{\hat{x}} p(\hat{x}|x) \cdot d(x, \hat{x})$
-
-
-
-
- def
- compute_rate_distortion (p_x , p_xhat_x , dist_mat ) -> tuple [ numpy . ndarray ] :
-
- View Source
-
- 42 def compute_rate_distortion (
-43 p_x ,
-44 p_xhat_x ,
-45 dist_mat ,
-46 ) -> tuple [ np . ndarray ]:
-47 """Compute the information rate $I(X;\hat{X})$ and total distortion $D[X, \hat{X}]$ of a joint distribution defind by $P(X)$ and $P(\hat{X}|X)$.
-48 49 Args:
-50 p_x: array of shape `|X|` the prior probability of an input symbol (i.e., the source)
-51 52 p_xhat_x: array of shape `(|X|, |X_hat|)` the probability of an output symbol given the input
-53 54 dist_mat: array of shape `(|X|, |X_hat|)` representing the distoriton matrix between the input alphabet and the reconstruction alphabet.
-55 56 Returns:
-57 a (rate, distortion) tuple containing the information rate (in bits) of compressing X into X_hat and the expected distortion between X, X_hat
-58 """
-59 return (
-60 information_rate ( p_x , p_xhat_x ),
-61 expected_distortion ( p_x , p_xhat_x , dist_mat ),
-62 )
-Compute the information rate $I(X;\hat{X})$ and total distortion $D[X, \hat{X}]$ of a joint distribution defind by $P(X)$ and $P(\hat{X}|X)$.
-
-
Arguments:
-
-
-p_x: array of shape |X| the prior probability of an input symbol (i.e., the source)p_xhat_x: array of shape (|X|, |X_hat|) the probability of an output symbol given the inputdist_mat: array of shape (|X|, |X_hat|) representing the distoriton matrix between the input alphabet and the reconstruction alphabet.
-
-
Returns:
-
-
- a (rate, distortion) tuple containing the information rate (in bits) of compressing X into X_hat and the expected distortion between X, X_hat
-
-
-
-
-
- def
- blahut_arimoto ( dist_mat : numpy . ndarray , p_x : numpy . ndarray , beta : float , max_it : int = 200 , eps : float = 1e-05 , ignore_converge : bool = False ) -> tuple [ float ] :
-
- View Source
-
- 65 def blahut_arimoto (
- 66 dist_mat : np . ndarray ,
- 67 p_x : np . ndarray ,
- 68 beta : float ,
- 69 max_it : int = 200 ,
- 70 eps : float = 1e-5 ,
- 71 ignore_converge : bool = False ,
- 72 ) -> tuple [ float ]:
- 73 """Compute the rate-distortion function of an i.i.d distribution
- 74 75 Args:
- 76 dist_mat: array of shape `(|X|, |X_hat|)` representing the distortion matrix between the input alphabet and the reconstruction alphabet. dist_mat[i,j] = dist(x[i],x_hat[j]). In this context, X is a random variable representing the a speaker's meaning (target referent), and X_hat is a random variable representing a listener's meaning (guessed referent).
- 77 78 p_x: (1D array of shape `|X|`) representing the probability mass function of the source. In this context, the prior over states of nature.
- 79 80 beta: (scalar) the slope of the rate-distoriton function at the point where evaluation is required
- 81 82 max_it: max number of iterations
- 83 84 eps: accuracy required by the algorithm: the algorithm stops if there is no change in distoriton value of more than 'eps' between consequtive iterations
- 85 86 ignore_converge: whether to run the optimization until `max_it`, ignoring the stopping criterion specified by `eps`.
- 87 88 Returns:
- 89 a dict of the form
- 90 91 {
- 92 'final': a tuple of (rate, distortion) values. This is the rate (in bits) of compressing X into X_hat, and distortion between X, X_hat
- 93 94 'trajectory': a list of the (rate, distortion) points discovered during optimization
- 95 }
- 96 """
- 97 # start with iid conditional distribution, as p(x) may not be uniform
- 98 p_xhat_x = np . tile ( p_x , ( dist_mat . shape [ 1 ], 1 )) . T
- 99 100 # normalize
-101 p_x /= np . sum ( p_x )
-102 p_xhat_x /= np . sum ( p_xhat_x , 1 , keepdims = True )
-103 104 it = 0
-105 traj = []
-106 distortion = 2 * eps
-107 converged = False
-108 while not converged :
-109 it += 1
-110 distortion_prev = distortion
-111 112 # p(x_hat) = sum p(x) p(x_hat | x)
-113 p_xhat = p_x @ p_xhat_x
-114 115 # p(x_hat | x) = p(x_hat) exp(- beta * d(x_hat, x)) / Z
-116 p_xhat_x = np . exp ( - beta * dist_mat ) * p_xhat
-117 p_xhat_x /= np . expand_dims ( np . sum ( p_xhat_x , 1 ), 1 )
-118 119 # update for convergence check
-120 rate , distortion = compute_rate_distortion ( p_x , p_xhat_x , dist_mat )
-121 122 # collect point
-123 traj . append (( rate , distortion ))
-124 125 # convergence check
-126 if ignore_converge :
-127 converged = it == max_it
-128 else :
-129 converged = it == max_it or np . abs ( distortion - distortion_prev ) < eps
-130 131 return {
-132 "final" : ( rate , distortion ),
-133 "trajectory" : traj ,
-134 }
-Compute the rate-distortion function of an i.i.d distribution
-
-
Arguments:
-
-
-dist_mat: array of shape (|X|, |X_hat|) representing the distortion matrix between the input alphabet and the reconstruction alphabet. dist_mat[i,j] = dist(x[i],x_hat[j]). In this context, X is a random variable representing the a speaker's meaning (target referent), and X_hat is a random variable representing a listener's meaning (guessed referent).p_x: (1D array of shape |X|) representing the probability mass function of the source. In this context, the prior over states of nature.beta: (scalar) the slope of the rate-distoriton function at the point where evaluation is requiredmax_it: max number of iterationseps: accuracy required by the algorithm: the algorithm stops if there is no change in distoriton value of more than 'eps' between consequtive iterationsignore_converge: whether to run the optimization until max_it, ignoring the stopping criterion specified by eps.
-
-
Returns:
-
-
- a dict of the form
-
-{
- 'final': a tuple of (rate, distortion) values. This is the rate (in bits) of compressing X into X_hat, and distortion between X, X_hat
-
- 'trajectory': a list of the (rate, distortion) points discovered during optimization
-}
-
-
-
- 144 def get_ib_curve (
-145 prior : np . ndarray ,
-146 space : Universe ,
-147 decay : float ,
-148 cost : Callable [[ Referent , Referent ], float ],
-149 curve_type : str = "informativity" ,
-150 ) -> np . ndarray :
-151 """Compute the IB curve bound (I[M:W] vs. I[W:U]) for a given semantic space. We use the embo package, which does not allow one to specify the number of betas, which means some interpolation might be necessary later.
-152 153 Args:
-154 prior: array of shape `|meanings|`
-155 156 space: the ModalMeaningSpace on which meanings are defined
-157 158 decay: parameter for meaning distribution p(u|m) generation. See `generate_meaning_distributions`.
-159 160 cost: parameter for meaning distribution p(u|m) generation. See `generate_meaning_distributions`.
-161 162 curve_type: {'informativity', 'comm_cost'} specifies whether to return the (classic) IB axes of informativity vs. complexity, or the more Rate-Distortion Theory aligned axes of comm_cost vs. complexity. The latter can be obtained easily from the former by subtracting each informativity value from I[M:U], which is a constant for all languages in the same domain.
-163 164 Returns:
-165 an array of shape `(num_points, 2)` representing the list of (accuracy/comm_cost, complexity) points on the information plane.
-166 """
-167 conditional_pum = generate_meaning_distributions ( space , decay , cost )
-168 joint_pmu = util . joint ( conditional_pum , prior ) # P(u) = P(m)
-169 I_mu = util . MI ( joint_pmu )
-170 171 # I[M:W], I[W:U], H[W], beta
-172 I_mw , I_wu , _ , _ = InformationBottleneck ( pxy = joint_pmu ) . get_bottleneck ()
-173 174 if curve_type == "comm_cost" :
-175 points = np . array (
-176 list ( zip ( I_mu - I_wu , I_mw ))
-177 ) # expected kl divergence, complexity
-178 else :
-179 points = np . array ( list ( zip ( I_wu , I_mw ))) # informativity, complexity
-180 return points
-Compute the IB curve bound (I[M:W] vs. I[W:U]) for a given semantic space. We use the embo package, which does not allow one to specify the number of betas, which means some interpolation might be necessary later.
-
-
Arguments:
-
-
-prior: array of shape |meanings|space: the ModalMeaningSpace on which meanings are defineddecay: parameter for meaning distribution p(u|m) generation. See generate_meaning_distributions cost: parameter for meaning distribution p(u|m) generation. See generate_meaning_distributions curve_type: {'informativity', 'comm_cost'} specifies whether to return the (classic) IB axes of informativity vs. complexity, or the more Rate-Distortion Theory aligned axes of comm_cost vs. complexity. The latter can be obtained easily from the former by subtracting each informativity value from I[M:U], which is a constant for all languages in the same domain.
-
-
Returns:
-
-
- an array of shape (num_points, 2) representing the list of (accuracy/comm_cost, complexity) points on the information plane.
-
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-
-
-
- 226 def ib_comm_cost (
-227 language : Language ,
-228 prior : np . ndarray ,
-229 decay : float ,
-230 cost : Callable [[ Referent , Referent ], float ],
-231 ) -> float :
-232 """Compute the IB communicative cost, i.e. expected KL-divergence betweeen speaker and listener meanings, for a language.
-233 234 Args:
-235 language: the Language to measure for communicative cost
-236 237 prior: communicative need distribution
-238 239 decay: parameter for meaning distribution p(u|m) generation. See `generate_meaning_distributions`.
-240 241 cost: parameter for meaning distribution p(u|m) generation. See `generate_meaning_distributions`.
-242 243 Returns:
-244 the communicative cost, $\mathbb{E}[D_{KL}[M || \hat{M}]] = I[M:U] - I[W:U]$ in bits.
-245 """
-246 dists = language_to_joint_distributions ( language , prior , decay , cost )
-247 return float ( util . MI ( dists [ "joint_pmu" ]) - util . MI ( dists [ "joint_pwu" ]))
-Compute the IB communicative cost, i.e. expected KL-divergence betweeen speaker and listener meanings, for a language.
-
-
Arguments:
-
-
-
-
Returns:
-
-
- the communicative cost, $\mathbb{E}[D_{KL}[M || \hat{M}]] = I[M:U] - I[W:U]$ in bits.
-
-
-
- 250 def language_to_joint_distributions (
-251 language : Language ,
-252 prior : np . ndarray ,
-253 decay : float ,
-254 cost : Callable [[ Referent , Referent ], float ],
-255 ) -> float :
-256 """Given a Language, get P(M,U) the joint distribution over meanings and referents, and P(W,U) the joint distribution over words and referents.
-257 258 Args:
-259 language: the Language to convert to distributions
-260 261 prior: communicative need distribution
-262 263 decay: parameter for meaning distribution p(u|m) generation. See `generate_meaning_distributions`.
-264 265 cost: parameter for meaning distribution p(u|m) generation. See `generate_meaning_distributions`.
-266 267 Returns:
-268 a dict of the form
-269 270 {
-271 "joint_pmu": an array of shape `(|U|, |M|)` representing P(U, M)
-272 "joint_pwu": an array of shape `(|W|, |U|)` representing P(W, U)
-273 }
-274 275 """
-276 system = language_to_ib_encoder_decoder ( language , prior )
-277 encoder = system [ "encoder" ]
-278 decoder = system [ "decoder" ]
-279 space = language . universe
-280 281 conditional_pum = generate_meaning_distributions ( space , decay , cost )
-282 conditional_puw = deterministic_decoder ( decoder , conditional_pum )
-283 joint_pmu = util . joint ( conditional_pum , prior )
-284 p_w = util . marginalize ( encoder , prior )
-285 joint_pwu = util . joint ( conditional_puw , p_w )
-286 287 return {
-288 "joint_pmu" : joint_pmu ,
-289 "joint_pwu" : joint_pwu ,
-290 }
-Given a Language, get P(M,U) the joint distribution over meanings and referents, and P(W,U) the joint distribution over words and referents.
-
-
Arguments:
-
-
-
-
Returns:
-
-
- a dict of the form
-
-{
-"joint_pmu": an array of shape `(|U|, |M|)` representing P(U, M)
-"joint_pwu": an array of shape `(|W|, |U|)` representing P(W, U)
-}
-
-
-
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-
def
-
language_to_ib_encoder_decoder ( language : altk.language.language.Language prior : numpy . ndarray ) -> dict [ str , numpy . ndarray ] :
-
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View Source
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-
296 def language_to_ib_encoder_decoder (
-297 language : Language ,
-298 prior : np . ndarray ,
-299 ) -> dict [ str , np . ndarray ]:
-300 """Convert a Language, a mapping of words to meanings, to IB encoder, q(w|m) and IB decoder q(m|w).
-301 302 Args:
-303 language: the lexicon from which to infer a speaker (encoder).
-304 305 prior: communicative need distribution
-306 307 Returns:
-308 a dict of the form
-309 {
-310 "encoder": np.ndarray of shape `(|meanings|, |words|)`,
-311 "decoder": np.ndarray of shape `(|words|, |meanings|)`,
-312 }
-313 """
-314 # In the IB framework, the encoder is _typically_ a literal speaker and the decoder is a bayes optimal listener. TODO: There are obviously other possible choices here.
-315 speaker = LiteralSpeaker ( language )
-316 speaker . weights = util . rows_zero_to_uniform ( speaker . normalized_weights ())
-317 listener = BayesianListener ( speaker , prior )
-318 return {
-319 "encoder" : speaker . normalized_weights (),
-320 "decoder" : listener . normalized_weights (),
-321 }
-Convert a Language, a mapping of words to meanings, to IB encoder, q(w|m) and IB decoder q(m|w).
-
-
Arguments:
-
-
-language: the lexicon from which to infer a speaker (encoder).prior: communicative need distribution
-
-
Returns:
-
-
- a dict of the form
- {
- "encoder": np.ndarray of shape (|meanings|, |words|),
- "decoder": np.ndarray of shape (|words|, |meanings|),
- }
-
-
-
-
-
- def
- deterministic_decoder ( decoder : numpy . ndarray , meaning_distributions : numpy . ndarray ) -> numpy . ndarray :
-
- View Source
-
- 324 def deterministic_decoder (
-325 decoder : np . ndarray , meaning_distributions : np . ndarray
-326 ) -> np . ndarray :
-327 """Compute $\hat{m}_{w}(u) = \sum_m p(m|w) \cdot m(u) $
-328 329 Args:
-330 decoder: array of shape `(|words|, |meanings|)`
-331 332 meaning_distributions: array of shape `(|meanings|, |meanings|)`
-333 334 Returns:
-335 array of shape `(|words|, |meanings|)` representing the 'optimal' deterministic decoder
-336 """
-337 return decoder @ meaning_distributions
-Compute $\hat{m}_{w}(u) = \sum_m p(m|w) \cdot m(u) $
-
-
Arguments:
-
-
-decoder: array of shape (|words|, |meanings|)meaning_distributions: array of shape (|meanings|, |meanings|)
-
-
Returns:
-
-
- array of shape (|words|, |meanings|) representing the 'optimal' deterministic decoder
-
-
-
- 340 def generate_meaning_distributions (
-341 space : Universe ,
-342 decay : float ,
-343 cost : Callable [[ Referent , Referent ], float ],
-344 ) -> np . ndarray :
-345 """Generate a conditional distribution over world states given meanings, $p(u|m)$, for each meaning.
-346 347 Args:
-348 space: the ModalMeaningSpace on which meanings are defined
-349 350 decay: a float in [0,1]. controls informativity, by decaying how much probability mass is assigned to perfect recoveries. As decay approaches 0, only perfect recovery is rewarded (which overrides any partial credit structure built into the utility/cost function). As decay approaches 1, the worst guesses become most likely.
-351 352 cost: a cost function defining the pairwise communicative cost for confusing one Referent in the Universe with another. If you have a (scaled) communicative utility matrix, a natural choice for cost might be `lambda x, y: 1 - utility(x, y)`.
-353 354 Returns:
-355 p_u_m: an array of shape `(|space.referents|, |space.referents|)`
-356 """
-357 358 # construct p(u|m) for each meaning
-359 meaning_distributions = np . array (
-360 [[ decay ** cost ( m , u ) for u in space . referents ] for m in space . referents ]
-361 )
-362 # each row sums to 1.0
-363 np . seterr ( divide = "ignore" , invalid = "ignore" )
-364 meaning_distributions = np . nan_to_num (
-365 meaning_distributions / meaning_distributions . sum ( axis = 1 , keepdims = True )
-366 )
-367 368 return meaning_distributions
-Generate a conditional distribution over world states given meanings, $p(u|m)$, for each meaning.
-
-
Arguments:
-
-
-space: the ModalMeaningSpace on which meanings are defineddecay: a float in [0,1]. controls informativity, by decaying how much probability mass is assigned to perfect recoveries. As decay approaches 0, only perfect recovery is rewarded (which overrides any partial credit structure built into the utility/cost function). As decay approaches 1, the worst guesses become most likely.cost: a cost function defining the pairwise communicative cost for confusing one Referent in the Universe with another. If you have a (scaled) communicative utility matrix, a natural choice for cost might be lambda x, y: 1 - utility(x, y).
-
-
Returns:
-
-
- p_u_m: an array of shape (|space.referents|, |space.referents|)
-
-
-
-
-
\ No newline at end of file
diff --git a/docs/altk/language/semantics.html b/docs/altk/language/semantics.html
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- altk.language.semantics API documentation
-
-
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-
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-
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-
-
- Classes for modeling the meanings of a language.
-
-
Meanings are modeled as things which map linguistic forms to objects of reference. The linguistic forms and objects of reference can in principle be very detailed, and future work may elaborate the meaning classes and implement a Form class.
-
-
In efficient communication analyses, simplicity and informativeness can be measured as properties of semantic aspects of a language. E.g., a meaning is simple if it is easy to represent, or to compress into some code; a meaning is informative if it is easy for a listener to recover a speaker's intended literal meaning.
-
-
Examples:
-
-
-
-
>>> from altk.language.semantics import Referent , Meaning , Universe
->>> from altk.language.language import Expression
->>> # construct the meaning space for numerals
->>> numerals_universe = NumeralUniverse ( referents = [ NumeralReferent ( str ( i )) for i in range ( 1 , 100 )])
->>> # construct a list of referents for the expression 'a few'
->>> a_few_refs = [ NumeralRefernt ( name = str ( i )) for i in range ( 2 , 6 )]
->>> a_few_meaning = NumeralMeaning ( referents = a_few_refs , universe = numerals_universe )
->>> # define the expression
->>> a_few = NumeralExpression ( form = "a few" , meaning = a_few_meaning )
-
-
-
View Source 1 """Classes for modeling the meanings of a language.
- 2 3 Meanings are modeled as things which map linguistic forms to objects of reference. The linguistic forms and objects of reference can in principle be very detailed, and future work may elaborate the meaning classes and implement a Form class.
- 4 5 In efficient communication analyses, simplicity and informativeness can be measured as properties of semantic aspects of a language. E.g., a meaning is simple if it is easy to represent, or to compress into some code; a meaning is informative if it is easy for a listener to recover a speaker's intended literal meaning.
- 6 7 Examples:
- 8 9 >>> from altk.language.semantics import Referent, Meaning, Universe
- 10 >>> from altk.language.language import Expression
- 11 >>> # construct the meaning space for numerals
- 12 >>> numerals_universe = NumeralUniverse(referents=[NumeralReferent(str(i)) for i in range(1, 100)])
- 13 >>> # construct a list of referents for the expression 'a few'
- 14 >>> a_few_refs = [NumeralRefernt(name=str(i)) for i in range(2, 6)]
- 15 >>> a_few_meaning = NumeralMeaning(referents=a_few_refs, universe=numerals_universe)
- 16 >>> # define the expression
- 17 >>> a_few = NumeralExpression(form="a few", meaning=a_few_meaning)
- 18 """
- 19 20 from typing import Iterable
- 21 22 23 class Referent :
- 24 """A referent is some object in the universe for a language."""
- 25 26 def __init__ ( self , name : str ) -> None :
- 27 """Initialize a referent.
- 28 29 Args:
- 30 name: a string representing the name of the referent
- 31 """
- 32 self . name = name
- 33 34 def __str__ ( self ) -> str :
- 35 raise NotImplementedError
- 36 37 def __hash__ ( self ) -> int :
- 38 raise NotImplementedError
- 39 40 41 class Universe :
- 42 43 """The universe is the set of possible referent objects for a meaning."""
- 44 45 def __init__ ( self , referents : Iterable [ Referent ]):
- 46 self . referents = referents
- 47 48 def __str__ ( self ):
- 49 referents_str = ", \n " . join ([ str ( point ) for point in self . referents ])
- 50 return f "Universe: { referents_str } "
- 51 52 def __eq__ ( self , __o : object ) -> bool :
- 53 """Returns true if the two universes are the same set."""
- 54 return self . referents == __o . referents
- 55 56 def __len__ ( self ) -> int :
- 57 return len ( self . referents )
- 58 59 60 class Meaning :
- 61 62 """A meaning picks out a set of objects from the universe.
- 63 64 On one tradition (from formal semantics), we might model an underspecified meaning as a subset of the universe. Sometimes these different referents are not equally likely, in which it can be helpful to define a meaning explicitly as a distribution over the universe.
- 65 """
- 66 67 def __init__ (
- 68 self ,
- 69 referents : Iterable [ Referent ],
- 70 universe : Universe ,
- 71 dist : dict [ str , float ] = None ,
- 72 ) -> None :
- 73 """A meaning is the set of things it refers to.
- 74 75 The objects of reference are a subset of the universe of discourse. Sometimes it is natural to construe the meaning as as a probability distribution over the universe, instead of just a binary predicate.
- 76 77 Args:
- 78 referents: a list of Referent objects, which must be a subset of the referents in `universe`.
- 79 80 universe: a Universe object that defines the probability space for a meaning.
- 81 82 dist: a dict of with Referent names as keys and weights or probabilities as values, representing the distribution over referents to associate with the meaning. By default is None, and the distribution will be uniform over the passed referents, and any remaining referents are assigned 0 probability.
- 83 """
- 84 if not set ( referents ) . issubset ( set ( universe . referents )):
- 85 print ( "referents:" )
- 86 print ([ str ( r ) for r in referents ])
- 87 print ( "universe:" )
- 88 print ([ str ( r ) for r in universe . referents ])
- 89 raise ValueError (
- 90 f "The set of referents for a meaning must be a subset of the universe of discourse."
- 91 )
- 92 93 self . referents = referents
- 94 self . universe = universe
- 95 96 zeros = { ref . name : 0.0 for ref in set ( self . universe . referents ) - set ( self . referents )}
- 97 if dist is not None :
- 98 # normalize weights to distribution
- 99 total_weight = sum ( dist . values ())
-100 self . dist = { ref . name : dist [ ref . name ] / total_weight for ref in self . referents } | zeros
-101 102 else :
-103 self . dist = { ref . name : 1 / len ( self . referents ) for ref in self . referents } | zeros
-
-
-
-
- class
- Referent :
-
- View Source
-
- 24 class Referent :
-25 """A referent is some object in the universe for a language."""
-26 27 def __init__ ( self , name : str ) -> None :
-28 """Initialize a referent.
-29 30 Args:
-31 name: a string representing the name of the referent
-32 """
-33 self . name = name
-34 35 def __str__ ( self ) -> str :
-36 raise NotImplementedError
-37 38 def __hash__ ( self ) -> int :
-39 raise NotImplementedError
-A referent is some object in the universe for a language.
-
-
-
-
- Referent (name : str
-
- View Source
-
-
27 def __init__ ( self , name : str ) -> None :
-28 """Initialize a referent.
-29 30 Args:
-31 name: a string representing the name of the referent
-32 """
-33 self . name = name
-
-
-
-
Initialize a referent.
-
-
Arguments:
-
-
-name: a string representing the name of the referent
-
-
-
-
-
-
-
- class
- Universe :
-
- View Source
-
- 42 class Universe :
-43 44 """The universe is the set of possible referent objects for a meaning."""
-45 46 def __init__ ( self , referents : Iterable [ Referent ]):
-47 self . referents = referents
-48 49 def __str__ ( self ):
-50 referents_str = ", \n " . join ([ str ( point ) for point in self . referents ])
-51 return f "Universe: { referents_str } "
-52 53 def __eq__ ( self , __o : object ) -> bool :
-54 """Returns true if the two universes are the same set."""
-55 return self . referents == __o . referents
-56 57 def __len__ ( self ) -> int :
-58 return len ( self . referents )
-The universe is the set of possible referent objects for a meaning.
-
-
-
-
-
46 def __init__ ( self , referents : Iterable [ Referent ]):
-47 self . referents = referents
-
-
-
-
-
-
-
-
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- class
- Meaning :
-
- View Source
-
- 61 class Meaning :
- 62 63 """A meaning picks out a set of objects from the universe.
- 64 65 On one tradition (from formal semantics), we might model an underspecified meaning as a subset of the universe. Sometimes these different referents are not equally likely, in which it can be helpful to define a meaning explicitly as a distribution over the universe.
- 66 """
- 67 68 def __init__ (
- 69 self ,
- 70 referents : Iterable [ Referent ],
- 71 universe : Universe ,
- 72 dist : dict [ str , float ] = None ,
- 73 ) -> None :
- 74 """A meaning is the set of things it refers to.
- 75 76 The objects of reference are a subset of the universe of discourse. Sometimes it is natural to construe the meaning as as a probability distribution over the universe, instead of just a binary predicate.
- 77 78 Args:
- 79 referents: a list of Referent objects, which must be a subset of the referents in `universe`.
- 80 81 universe: a Universe object that defines the probability space for a meaning.
- 82 83 dist: a dict of with Referent names as keys and weights or probabilities as values, representing the distribution over referents to associate with the meaning. By default is None, and the distribution will be uniform over the passed referents, and any remaining referents are assigned 0 probability.
- 84 """
- 85 if not set ( referents ) . issubset ( set ( universe . referents )):
- 86 print ( "referents:" )
- 87 print ([ str ( r ) for r in referents ])
- 88 print ( "universe:" )
- 89 print ([ str ( r ) for r in universe . referents ])
- 90 raise ValueError (
- 91 f "The set of referents for a meaning must be a subset of the universe of discourse."
- 92 )
- 93 94 self . referents = referents
- 95 self . universe = universe
- 96 97 zeros = { ref . name : 0.0 for ref in set ( self . universe . referents ) - set ( self . referents )}
- 98 if dist is not None :
- 99 # normalize weights to distribution
-100 total_weight = sum ( dist . values ())
-101 self . dist = { ref . name : dist [ ref . name ] / total_weight for ref in self . referents } | zeros
-102 103 else :
-104 self . dist = { ref . name : 1 / len ( self . referents ) for ref in self . referents } | zeros
-A meaning picks out a set of objects from the universe.
-
-
On one tradition (from formal semantics), we might model an underspecified meaning as a subset of the universe. Sometimes these different referents are not equally likely, in which it can be helpful to define a meaning explicitly as a distribution over the universe.
-
-
-
-
-
68 def __init__ (
- 69 self ,
- 70 referents : Iterable [ Referent ],
- 71 universe : Universe ,
- 72 dist : dict [ str , float ] = None ,
- 73 ) -> None :
- 74 """A meaning is the set of things it refers to.
- 75 76 The objects of reference are a subset of the universe of discourse. Sometimes it is natural to construe the meaning as as a probability distribution over the universe, instead of just a binary predicate.
- 77 78 Args:
- 79 referents: a list of Referent objects, which must be a subset of the referents in `universe`.
- 80 81 universe: a Universe object that defines the probability space for a meaning.
- 82 83 dist: a dict of with Referent names as keys and weights or probabilities as values, representing the distribution over referents to associate with the meaning. By default is None, and the distribution will be uniform over the passed referents, and any remaining referents are assigned 0 probability.
- 84 """
- 85 if not set ( referents ) . issubset ( set ( universe . referents )):
- 86 print ( "referents:" )
- 87 print ([ str ( r ) for r in referents ])
- 88 print ( "universe:" )
- 89 print ([ str ( r ) for r in universe . referents ])
- 90 raise ValueError (
- 91 f "The set of referents for a meaning must be a subset of the universe of discourse."
- 92 )
- 93 94 self . referents = referents
- 95 self . universe = universe
- 96 97 zeros = { ref . name : 0.0 for ref in set ( self . universe . referents ) - set ( self . referents )}
- 98 if dist is not None :
- 99 # normalize weights to distribution
-100 total_weight = sum ( dist . values ())
-101 self . dist = { ref . name : dist [ ref . name ] / total_weight for ref in self . referents } | zeros
-102 103 else :
-104 self . dist = { ref . name : 1 / len ( self . referents ) for ref in self . referents } | zeros
-
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A meaning is the set of things it refers to.
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The objects of reference are a subset of the universe of discourse. Sometimes it is natural to construe the meaning as as a probability distribution over the universe, instead of just a binary predicate.
-
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Arguments:
-
-
-referents: a list of Referent objects, which must be a subset of the referents in universe.universe: a Universe object that defines the probability space for a meaning.dist: a dict of with Referent names as keys and weights or probabilities as values, representing the distribution over referents to associate with the meaning. By default is None, and the distribution will be uniform over the passed referents, and any remaining referents are assigned 0 probability.
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\ No newline at end of file
diff --git a/docs/index.html b/docs/index.html
index a4318d13..73bb7418 100644
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+++ b/docs/index.html
@@ -2,6 +2,6 @@
0&&t.push(e);for(var i in n)"docs"!==i&&"df"!==i&&this.expandToken(e+i,t,n[i]);return t},t.InvertedIndex.prototype.toJSON=function(){return{root:this.root}},t.Configuration=function(e,n){var e=e||"";if(void 0==n||null==n)throw new Error("fields should not be null");this.config={};var i;try{i=JSON.parse(e),this.buildUserConfig(i,n)}catch(o){t.utils.warn("user configuration parse failed, will use default configuration"),this.buildDefaultConfig(n)}},t.Configuration.prototype.buildDefaultConfig=function(e){this.reset(),e.forEach(function(e){this.config[e]={boost:1,bool:"OR",expand:!1}},this)},t.Configuration.prototype.buildUserConfig=function(e,n){var i="OR",o=!1;if(this.reset(),"bool"in e&&(i=e.bool||i),"expand"in e&&(o=e.expand||o),"fields"in e)for(var r in e.fields)if(n.indexOf(r)>-1){var s=e.fields[r],u=o;void 0!=s.expand&&(u=s.expand),this.config[r]={boost:s.boost||0===s.boost?s.boost:1,bool:s.bool||i,expand:u}}else t.utils.warn("field name in user configuration not found in index instance fields");else this.addAllFields2UserConfig(i,o,n)},t.Configuration.prototype.addAllFields2UserConfig=function(e,t,n){n.forEach(function(n){this.config[n]={boost:1,bool:e,expand:t}},this)},t.Configuration.prototype.get=function(){return this.config},t.Configuration.prototype.reset=function(){this.config={}},lunr.SortedSet=function(){this.length=0,this.elements=[]},lunr.SortedSet.load=function(e){var t=new this;return t.elements=e,t.length=e.length,t},lunr.SortedSet.prototype.add=function(){var e,t;for(e=0;e1;){if(r===e)return o;e>r&&(t=o),r>e&&(n=o),i=n-t,o=t+Math.floor(i/2),r=this.elements[o]}return r===e?o:-1},lunr.SortedSet.prototype.locationFor=function(e){for(var t=0,n=this.elements.length,i=n-t,o=t+Math.floor(i/2),r=this.elements[o];i>1;)e>r&&(t=o),r>e&&(n=o),i=n-t,o=t+Math.floor(i/2),r=this.elements[o];return r>e?o:e>r?o+1:void 0},lunr.SortedSet.prototype.intersect=function(e){for(var t=new lunr.SortedSet,n=0,i=0,o=this.length,r=e.length,s=this.elements,u=e.elements;;){if(n>o-1||i>r-1)break;s[n]!==u[i]?s[n]u[i]&&i++:(t.add(s[n]),n++,i++)}return t},lunr.SortedSet.prototype.clone=function(){var e=new lunr.SortedSet;return e.elements=this.toArray(),e.length=e.elements.length,e},lunr.SortedSet.prototype.union=function(e){var t,n,i;this.length>=e.length?(t=this,n=e):(t=e,n=this),i=t.clone();for(var o=0,r=n.toArray();oThe Artificial Language ToolKit (ALTK)\n\n
\n\nIntroduction \n\nALTK is a software library that aims to support research in Unnatural Language Semantics -- a program in linguistics and cognitive science that tries to describe and explain the properties of natural languages by comparing them to the much larger set of mathematically possible languages.
\n\nA current focus is on efficient communication : determining whether linguistic meanings are optimized for a trade-off between cognitive complexity and communicative precision.
\n\nKey features:
\n\n\nPrimitives for constructing semantic spaces, expressions, and languages \nTools for measuring informativity of languages, communicative success of RSA speakers and listeners \nLanguage population sampling and optimization w.r.t Pareto fronts \nRate-Distortion and Information Bottleneck style analyses \n \n\nALTK is a long term project and it is currently in its early stages. It is intended to help lower the barrier to entry for certain research in computational semantics, and to unify methodologies. If you find something confusing, please open an issue. If you have a phenomena of interest in linguistic semantics that you want to run an efficient communication analysis on, please contact the contributors.
\n\nRead the documentation .
\n\nInstalling ALTK \n\n\nDownload or clone this repository and navigate to the root folder.
Create a fresh conda environment with the required packages by runing
\n\nconda env create --file environment.yml
Install ALTK
\n\npip install -e .
\n\nGetting started \n\n\n\nModules \n\nThere are two modules. The first is altk.effcomm , which includes methods for measuring informativity of languages and/or communicative success of Rational Speech Act agents, and for language population sampling and optimization w.r.t Pareto fronts.
\n\nThe second module is altk.language , which contains primitives for constructing semantic spaces, expressions, and languages.
\n\nThe source code is available on github here .
\n\nReferences \n\n\nFigures:
\n\n\n Kinship Categories Across Languages Reflect General Communicative Principles | Science. (n.d.). Retrieved February 27, 2023, from https://www.science.org/doi/10.1126/science.1218811
\n \n\n\n Zaslavsky, N., Kemp, C., Regier, T., & Tishby, N. (2018). Efficient compression in color naming and its evolution. Proceedings of the National Academy of Sciences, 115(31), 7937\u20137942. https://doi.org/10.1073/pnas.1800521115
\n \n\n\n Deni\u0107, M., Steinert-Threlkeld, S., & Szymanik, J. (2022). Indefinite Pronouns Optimize the Simplicity/Informativeness Trade-Off. Cognitive Science, 46(5), e13142. https://doi.org/10.1111/cogs.13142
\n \n\n\n Steinert-Threlkeld, S. (2021). Quantifiers in Natural Language: Efficient Communication and Degrees of Semantic Universals. Entropy, 23(10), Article 10. https://doi.org/10.3390/e23101335
\n \n\n
\n\n\nLinks:
\n\n\n Imel, N. (2023). The evolution of efficient compression in signaling games. PsyArXiv. https://doi.org/10.31234/osf.io/b62de
\n \n\n\n Imel, N., & Steinert-Threlkeld, S. (2022). Modal semantic universals optimize the simplicity/informativeness trade-off. Semantics and Linguistic Theory, 1(0), Article 0. https://doi.org/10.3765/salt.v1i0.5346
\n \n\n\n Kemp, C., Xu, Y., & Regier, T. (2018). Semantic Typology and Efficient Communication. Annual Review of Linguistics, 4(1), 109\u2013128. https://doi.org/10.1146/annurev-linguistics-011817-045406
\n \n\n
\n"}, {"fullname": "altk.effcomm", "modulename": "altk.effcomm", "kind": "module", "doc": "Tools for measuring languages for communicative efficiency.
\n\nSubmodules divide the labor of a computational experiment performing an efficiency analysis of a language into several parts: generating and sampling the space of possible languages, measuring their properties, and determining which languages optimize efficient trade-offs w.r.t these properties.
\n\nThe altk.effcomm.sampling submodule implements several methods for generating hypothetically possible languages of a given type, by sampling from a set of possible expressions, or permuting the expression-meaning mapping of an existing language.
\n\nThe altk.effcomm.optimization submodule contains a general implementation of an evolutionary algorithm, which can be used to estimate a Pareto frontier of optimal solutions to an efficiency trade-off. It can also be used as a technique for randomly exploring the space of possible languages.
\n\nThe altk.effcomm.tradeoff submodule contains tools for measuring a pool of languages for various properties, finding which languages are Pareto dominant with respect to two properties, and setting attributes of the language objects for further analysis.
\n\nThe altk.effcomm.analysis submodule contains tools for performing numerical analyses and producing paradigmatic plots of languages in 2D trade-off space.
\n\nThe altk.effcomm.information submodule contains tools for information theory based analyses of the communicative efficiency of languages. It includes methods for Rate-Distortion style (including the Information Bottleneck) analyses.
\n\nThe altk.effcomm.agent submodule implements classes for constructing various speakers and listeners of a language. These are typically used in static analyses of informativity of a language, and are unified abstractions from the Rational Speech Act framework. They can also be used for dynamic analyses, however (see the signaling game example ).
\n\nThe altk.effcomm.informativity submodule implements tools for computing the literal or pragmatic informativity of a language, based on speaker/listener abstractions described above.
\n\nThe altk.effcomm.util submodule contains various helper functions for working with the probability distributions associated with ALTK abstractions.
\n"}, {"fullname": "altk.effcomm.agent", "modulename": "altk.effcomm.agent", "kind": "module", "doc": "Classes for representing communicative agents, such as Senders and Receivers figuring in Lewis-Skyrms signaling games, literal and pragmatic agents in the Rational Speech Act framework, etc.
\n"}, {"fullname": "altk.effcomm.agent.CommunicativeAgent", "modulename": "altk.effcomm.agent", "qualname": "CommunicativeAgent", "kind": "class", "doc": "
\n"}, {"fullname": "altk.effcomm.agent.CommunicativeAgent.__init__", "modulename": "altk.effcomm.agent", "qualname": "CommunicativeAgent.__init__", "kind": "function", "doc": "An agent that uses a language to communicate, e.g. a RSA pragmatic agent or a Lewis-Skyrms signaler.
\n\nArguments: \n\n\nlanguage: a language to construct a agent to define the relation between meanings and expressions, which can be used to initialize the agent matrices (e.g. S or R).name: an optional string to name the communicative agent \n", "signature": "(language : altk . language . language . Language , ** kwargs "}, {"fullname": "altk.effcomm.agent.CommunicativeAgent.normalized_weights", "modulename": "altk.effcomm.agent", "qualname": "CommunicativeAgent.normalized_weights", "kind": "function", "doc": "Return the normalized weights of a CommunicativeAgent so that each row vector represents a probability distribution.
\n", "signature": "(self ) -> None : ", "funcdef": "def"}, {"fullname": "altk.effcomm.agent.CommunicativeAgent.initialize_weights", "modulename": "altk.effcomm.agent", "qualname": "CommunicativeAgent.initialize_weights", "kind": "function", "doc": "Initialize the agent's weight matrix.
\n\nArguments: \n\n\nweights: an np.ndarray representing the weights to initialize the agent with. By default None, and the agent's weights will be initialized uniformly.initial: {'ones', 'random'} a str reprsenting the initialization method to use. If 'ones' (default), initialize the weight matrix with np.ones. If 'random', initalize the weight matrix from np.random.uniform. \n", "signature": "(self , weights : numpy . ndarray = None , initial = 'ones' ) -> None : ", "funcdef": "def"}, {"fullname": "altk.effcomm.agent.CommunicativeAgent.referent_to_index", "modulename": "altk.effcomm.agent", "qualname": "CommunicativeAgent.referent_to_index", "kind": "function", "doc": "
\n", "signature": "(self , referent : altk . language . semantics . Referent ) -> int : ", "funcdef": "def"}, {"fullname": "altk.effcomm.agent.CommunicativeAgent.index_to_referent", "modulename": "altk.effcomm.agent", "qualname": "CommunicativeAgent.index_to_referent", "kind": "function", "doc": "
\n", "signature": "(self , index : int ) -> altk . language . semantics . Referent : ", "funcdef": "def"}, {"fullname": "altk.effcomm.agent.CommunicativeAgent.expression_to_index", "modulename": "altk.effcomm.agent", "qualname": "CommunicativeAgent.expression_to_index", "kind": "function", "doc": "
\n", "signature": "(self , expression : altk . language . language . Expression ) -> int : ", "funcdef": "def"}, {"fullname": "altk.effcomm.agent.CommunicativeAgent.index_to_expression", "modulename": "altk.effcomm.agent", "qualname": "CommunicativeAgent.index_to_expression", "kind": "function", "doc": "
\n", "signature": "(self , index : int ) -> altk . language . language . Expression : ", "funcdef": "def"}, {"fullname": "altk.effcomm.agent.CommunicativeAgent.policy_to_indices", "modulename": "altk.effcomm.agent", "qualname": "CommunicativeAgent.policy_to_indices", "kind": "function", "doc": "Maps communicative policies to weights.
\n\nGiven a expression and referent, access the corresponding weight coordinate.
\n\nArguments: \n\n\npolicy: a dict of the form {\"referent\": Referent, \"expression\": expression} representing an instance of communicative behavior, which we may call a communicative action policy for this agent. \n", "signature": "(self , policy : dict [ str , typing . Any ] ) -> tuple [ int ] : ", "funcdef": "def"}, {"fullname": "altk.effcomm.agent.CommunicativeAgent.sample_policy", "modulename": "altk.effcomm.agent", "qualname": "CommunicativeAgent.sample_policy", "kind": "function", "doc": "Sample a communicative policy by uniformly sampling from a row vector of the agent's weight matrix specified by the index.
\n\nArguments: \n\n\nindex: the integer index representing a row of the weight matrix. \n\nReturns: \n\n\n the integer index of the agent's choice
\n \n", "signature": "(self , index : int ) -> int : ", "funcdef": "def"}, {"fullname": "altk.effcomm.agent.CommunicativeAgent.to_language", "modulename": "altk.effcomm.agent", "qualname": "CommunicativeAgent.to_language", "kind": "function", "doc": "Get a language from the agent, representing its current (possibly learned) communicative behavior.
\n\nThis function uses: \n\n\n \n the agent's weight matrix, \n the set of expression forms, and \n the set of referents \n \n \n\nfrom the language the agent was initialized with to generate a new language accurately reflecting the new expression meanings, e.g. how the agent interprets expressions as meaning zero or more referents.
\n\nArguments: \n\n\nthreshold: a float in [0,1] representing the cutoff for determining if a meaning (referent) can be communicated by a expression. Because weights are not initialized to 0, it is a good idea to set nonzero values as the threshold. \n\nReturns: \n\n\n a Language corresponding to the form-meaning mapping defined by the communicative agent's weights.
\n \n", "signature": "(\tself , \tdata : dict = { 'complexity' : None , 'accuracy' : None } , \tthreshold : float = 0.1 ) -> altk . language . language . Language : ", "funcdef": "def"}, {"fullname": "altk.effcomm.agent.Speaker", "modulename": "altk.effcomm.agent", "qualname": "Speaker", "kind": "class", "doc": "
\n", "bases": "CommunicativeAgent"}, {"fullname": "altk.effcomm.agent.Speaker.__init__", "modulename": "altk.effcomm.agent", "qualname": "Speaker.__init__", "kind": "function", "doc": "An agent that uses a language to communicate, e.g. a RSA pragmatic agent or a Lewis-Skyrms signaler.
\n\nArguments: \n\n\nlanguage: a language to construct a agent to define the relation between meanings and expressions, which can be used to initialize the agent matrices (e.g. S or R).name: an optional string to name the communicative agent \n", "signature": "(language : altk . language . language . Language , ** kwargs "}, {"fullname": "altk.effcomm.agent.Speaker.normalized_weights", "modulename": "altk.effcomm.agent", "qualname": "Speaker.normalized_weights", "kind": "function", "doc": "Get the normalized weights of a Speaker.
\n\nEach row vector represents a conditional probability distribution over expressions, P(e | m).
\n", "signature": "(self ) -> numpy . ndarray : ", "funcdef": "def"}, {"fullname": "altk.effcomm.agent.Listener", "modulename": "altk.effcomm.agent", "qualname": "Listener", "kind": "class", "doc": "
\n", "bases": "CommunicativeAgent"}, {"fullname": "altk.effcomm.agent.Listener.__init__", "modulename": "altk.effcomm.agent", "qualname": "Listener.__init__", "kind": "function", "doc": "An agent that uses a language to communicate, e.g. a RSA pragmatic agent or a Lewis-Skyrms signaler.
\n\nArguments: \n\n\nlanguage: a language to construct a agent to define the relation between meanings and expressions, which can be used to initialize the agent matrices (e.g. S or R).name: an optional string to name the communicative agent \n", "signature": "(language : altk . language . language . Language , ** kwargs "}, {"fullname": "altk.effcomm.agent.Listener.normalized_weights", "modulename": "altk.effcomm.agent", "qualname": "Listener.normalized_weights", "kind": "function", "doc": "Normalize the weights of a Listener so that each row vector for the heard expression e represents a conditional probability distribution over referents P(m | e).
\n", "signature": "(self ) -> numpy . ndarray : ", "funcdef": "def"}, {"fullname": "altk.effcomm.agent.LiteralSpeaker", "modulename": "altk.effcomm.agent", "qualname": "LiteralSpeaker", "kind": "class", "doc": "A literal speaker chooses utterances without any reasoning about other agents. The literal speaker's conditional probability distribution P(e|m) is uniform over all expressions that can be used to communicate a particular meaning. This is in contrast to a pragmatic speaker, whose conditional distribution is not uniform in this way, but instead biased towards choosing expressions that are less likely to be misinterpreted by some listener.
\n", "bases": "Speaker"}, {"fullname": "altk.effcomm.agent.LiteralSpeaker.__init__", "modulename": "altk.effcomm.agent", "qualname": "LiteralSpeaker.__init__", "kind": "function", "doc": "An agent that uses a language to communicate, e.g. a RSA pragmatic agent or a Lewis-Skyrms signaler.
\n\nArguments: \n\n\nlanguage: a language to construct a agent to define the relation between meanings and expressions, which can be used to initialize the agent matrices (e.g. S or R).name: an optional string to name the communicative agent \n", "signature": "(language : altk . language . language . Language , ** kwargs "}, {"fullname": "altk.effcomm.agent.LiteralListener", "modulename": "altk.effcomm.agent", "qualname": "LiteralListener", "kind": "class", "doc": "A naive literal listener interprets utterances without any reasoning about other agents. Its conditional probability distribution P(m|e) for guessing meanings is uniform over all meanings that can be denoted by the particular expression heard. This is in contrast to a pragmatic listener, whose conditional distribution is biased to guess meanings that a pragmatic speaker most likely intended.
\n", "bases": "Listener"}, {"fullname": "altk.effcomm.agent.LiteralListener.__init__", "modulename": "altk.effcomm.agent", "qualname": "LiteralListener.__init__", "kind": "function", "doc": "An agent that uses a language to communicate, e.g. a RSA pragmatic agent or a Lewis-Skyrms signaler.
\n\nArguments: \n\n\nlanguage: a language to construct a agent to define the relation between meanings and expressions, which can be used to initialize the agent matrices (e.g. S or R).name: an optional string to name the communicative agent \n", "signature": "(language : altk . language . language . Language , ** kwargs "}, {"fullname": "altk.effcomm.agent.PragmaticSpeaker", "modulename": "altk.effcomm.agent", "qualname": "PragmaticSpeaker", "kind": "class", "doc": "A pragmatic speaker chooses utterances based on how a listener would interpret them. A pragmatic speaker may be initialized with any kind of listener, e.g. literal or pragmatic -- meaning the recursive reasoning can be modeled up to arbitrary depth.
\n", "bases": "Speaker"}, {"fullname": "altk.effcomm.agent.PragmaticSpeaker.__init__", "modulename": "altk.effcomm.agent", "qualname": "PragmaticSpeaker.__init__", "kind": "function", "doc": "Initialize the |M|-by-|E| matrix, S, corresponding to the pragmatic speaker's conditional probability distribution over expressions given meanings.
\n\nThe pragmatic speaker chooses expressions to communicate their intended meaning according to:
\n\n$P(e | m) \\propto \\exp(t * u(e,m))$
\n\nwhere $t \\in [0,1]$ is a temperature parameter and utility $u$ is defined
\n\n$u(e , m) := \\log(P_{\\text{Listener}}(m | e))$
\n\nArguments: \n\n\nlanguage: the language with |M| meanings and |E| expressions defining the size of S.listener: a communicative agent storing a matrix R representing the conditional distribution over expressions given meanings.temperature: a float \\in [0,1], representing how `optimally rational' the pragmatic speaker is; 1.0 is chosen when no particular assumptions about rationality are made. \n", "signature": "(\tlanguage : altk . language . language . Language , \tlistener : altk . effcomm . agent . Listener , \t** kwargs ) "}, {"fullname": "altk.effcomm.agent.PragmaticListener", "modulename": "altk.effcomm.agent", "qualname": "PragmaticListener", "kind": "class", "doc": "A pragmatic listener interprets utterances based on their expectations about a pragmatic speaker's decisions. A pragmatic listener may be initialized with any kind of speaker, e.g. literal or pragmatic -- meaning the recursive reasoning can be modeled up to arbitrary depth.
\n", "bases": "Listener"}, {"fullname": "altk.effcomm.agent.PragmaticListener.__init__", "modulename": "altk.effcomm.agent", "qualname": "PragmaticListener.__init__", "kind": "function", "doc": "Initialize the |E|-by-|M| matrix, R, corresponding to the pragmatic listener's conditional probability distribution over meanings given expressions.
\n\nThe pragmatic listener chooses meanings as their best guesses of the expression they heard according to:
\n\n$P(m | e) \\propto P_{\\text{PragmaticSpeaker}}(e | m)$
\n\nArguments: \n\n\nlanguage: the language with |M| meanings and |E| expressions defining the size of R.speaker: a communicative agent storing a matrix S representing the conditional distribution over expressions given meanings.prior: a diagonal matrix of size |M|-by-|M| representing the communicative need probabilities for meanings. \n", "signature": "(\tlanguage : altk . language . language . Language , \tspeaker : altk . effcomm . agent . Speaker , \tprior : numpy . ndarray , \t** kwargs ) "}, {"fullname": "altk.effcomm.agent.BayesianListener", "modulename": "altk.effcomm.agent", "qualname": "BayesianListener", "kind": "class", "doc": "A Bayesian reciever chooses an interpretation according to p(meaning | word), where
\n\n$P(m | w) = \\frac{P(M | W) \\cdot P(M)} { P(W) }$
\n\nFurthermore, we sometimes require that each word w is deterministically interpreted as meaning $\\hat{m}$ as follows:
\n\n$\\hat{m}_{w}(u) = \\sum_m p(m|w) \\cdot m(u)$
\n\nSee altk.effcomm.information for more details.
\n", "bases": "Listener"}, {"fullname": "altk.effcomm.agent.BayesianListener.__init__", "modulename": "altk.effcomm.agent", "qualname": "BayesianListener.__init__", "kind": "function", "doc": "An agent that uses a language to communicate, e.g. a RSA pragmatic agent or a Lewis-Skyrms signaler.
\n\nArguments: \n\n\nlanguage: a language to construct a agent to define the relation between meanings and expressions, which can be used to initialize the agent matrices (e.g. S or R).name: an optional string to name the communicative agent \n", "signature": "(\tspeaker : altk . effcomm . agent . Speaker , \tprior : numpy . ndarray , \tname : str = None ) "}, {"fullname": "altk.effcomm.analysis", "modulename": "altk.effcomm.analysis", "kind": "module", "doc": "Functions for analyzing and formatting the results of the simplicity/informativeness trade-off.
\n"}, {"fullname": "altk.effcomm.analysis.get_dataframe", "modulename": "altk.effcomm.analysis", "qualname": "get_dataframe", "kind": "function", "doc": "Get a pandas DataFrame for a list of languages containing efficient communication data.
\n\nArguments: \n\n\nlanguages: the list of languages to map into a dataframe.columns: the list of keys to a language's data dictionary attribute, which will comprise the columns of the resulting dataframe. By default will use all items of each language's data dictionary.subset: the columns to subset for duplicatesduplicates: {\"drop\", \"count\", \"leave\"} whether to drop, count, or do nothing with duplicates. By default is set to \"leave\" which will leave duplicates in the dataframe. \n\nReturns: \n\n\n \n data: a pandas DataFrame with rows as individual languages, with the columns specifying their data. \n \n \n", "signature": "(\tlanguages : list [ altk . language . language . Language ] , \tcolumns : list [ str ] = None , \tsubset : list [ str ] = [ 'complexity' , 'comm_cost' ] , \tduplicates : str = 'leave' ) -> pandas . core . frame . DataFrame : ", "funcdef": "def"}, {"fullname": "altk.effcomm.analysis.pearson_analysis", "modulename": "altk.effcomm.analysis", "qualname": "pearson_analysis", "kind": "function", "doc": "Measures pearson correlation coefficient for naturalness with a property.
\n\nUse nonparametric bootstrap for confidence intervals.
\n\nArguments: \n\n\ndata: a DataFrame representing the pool of measured languagespredictor: a string representing the column to measure pearson r withproperty: a string representing a column to measure pearson r with the predictor columnnum_bootstrap_samples: how many samples to bootstrap from the original data \n\nReturns: \n\n\n a dict of the pearson correlation coefficient for the predictor and the property, and bootstrapped confidence intervals for this coefficient, e.g.
\n\n{\n\"rho\": (a float between -1 and 1),\n\"confidence_intervals\": (a pandas Dataframe with the columns [\n 'bootstrap_sample_percent', 'low', 'high'\n])\n}\n \n", "signature": "(\tdata , \tpredictor : str , \tproperty : str , \tnum_bootstrap_samples = 100 ) -> dict [ str , typing . Any ] : ", "funcdef": "def"}, {"fullname": "altk.effcomm.analysis.trade_off_means", "modulename": "altk.effcomm.analysis", "qualname": "trade_off_means", "kind": "function", "doc": "Get a dataframe with the mean tradeoff data.
\n\nArguments: \n\n\nname: a str representing the subset of the population to observe mean properties for, e.g. \"natural\" or \"population\".df: a pandas DataFrame containing data of a language population to take the means of.prperties: the properties to take means of, corresponding to columns of df. \n\nExamples:
\n\n\n
>>> natural_means = trade_off_means ( "natural_means" , natural_data , properties ) \n>>> population_means = trade_off_means ( "population_means" , data , properties ) \n>>> means_df = pd . concat ([ natural_means , dlsav_means , population_means ]) . set_index ( "name" ) \n>>> means_df \n simplicity complexity informativity optimality \n name \n natural_means 0.772222 16.4000 0.746296 0.952280 \n population_means 0.681068 22.9631 0.525118 0.832010 \n\n
(\tname : str , \tdf : pandas . core . frame . DataFrame , \tproperties : list ) -> pandas . core . frame . DataFrame : ", "funcdef": "def"}, {"fullname": "altk.effcomm.analysis.trade_off_ttest", "modulename": "altk.effcomm.analysis", "qualname": "trade_off_ttest", "kind": "function", "doc": "Get a dataframe with a single-samples t-test results for a subpopulation against the full population.
\n\nThis is useful if we want to compare the optimality of natural languages to the full population of languages in an experiment. Because the property of 'being a natural language' is categorical, we use a single-samples T test.
\n\nArguments: \n\n\nsub_population: a pandas DataFrame representing a subset of the population to take ttests against the full language population for properties.population_means: a dict containing properties as keys and the mean value of the full language population for that property.properties: a list of strings corresponding to columns of the sub_population DataFrame and keys of the population_means dict. \n\nExamples: \n\n\n \n
>>> df = trade_off_ttest ( natural_data , population_means , properties ) \n>>> df \n simplicity complexity informativity optimality \n stat \n t-statistic 4.101937 -4.101937 3.126855 4.031027 \n Two-sided p-value 0.014830 0.014830 0.035292 0.015720 \n\n
\n", "signature": "(\tsub_population : pandas . core . frame . DataFrame , \tpopulation_means : dict , \tproperties : list ) -> pandas . core . frame . DataFrame : ", "funcdef": "def"}, {"fullname": "altk.effcomm.information", "modulename": "altk.effcomm.information", "kind": "module", "doc": "Helper functions for Rate-Distortion based (including Information Bottleneck) efficient communication analyses.
\n"}, {"fullname": "altk.effcomm.information.information_rate", "modulename": "altk.effcomm.information", "qualname": "information_rate", "kind": "function", "doc": "Compute the information rate / complexity of the encoder q(w|m) as $I[W:M]$.
\n", "signature": "(source : numpy . ndarray , encoder : numpy . ndarray ) -> float : ", "funcdef": "def"}, {"fullname": "altk.effcomm.information.get_rd_curve", "modulename": "altk.effcomm.information", "qualname": "get_rd_curve", "kind": "function", "doc": "Use the Blahut Arimoto algorithm to obtain a list of (rate, distortion) points.
\n", "signature": "(\tprior : numpy . ndarray , \tdist_mat : numpy . ndarray , \tbetas : numpy . ndarray = array ([ 0.00000000e+00 , 8.53902602e-02 , 1.70780520e-01 , ... , \n 1.27829219e+02 , 1.27914610e+02 , 1.28000000e+02 ]) ) -> list [ tuple [ float ]] : ", "funcdef": "def"}, {"fullname": "altk.effcomm.information.expected_distortion", "modulename": "altk.effcomm.information", "qualname": "expected_distortion", "kind": "function", "doc": "$D[X, \\hat{X}] = \\sum_x p(x) \\sum_{\\hat{x}} p(\\hat{x}|x) \\cdot d(x, \\hat{x})$
\n", "signature": "(\tp_x : numpy . ndarray , \tp_xhat_x : numpy . ndarray , \tdist_mat : numpy . ndarray ) -> float : ", "funcdef": "def"}, {"fullname": "altk.effcomm.information.compute_rate_distortion", "modulename": "altk.effcomm.information", "qualname": "compute_rate_distortion", "kind": "function", "doc": "Compute the information rate $I(X;\\hat{X})$ and total distortion $D[X, \\hat{X}]$ of a joint distribution defind by $P(X)$ and $P(\\hat{X}|X)$.
\n\nArguments: \n\n\np_x: array of shape |X| the prior probability of an input symbol (i.e., the source)p_xhat_x: array of shape (|X|, |X_hat|) the probability of an output symbol given the inputdist_mat: array of shape (|X|, |X_hat|) representing the distoriton matrix between the input alphabet and the reconstruction alphabet. \n\nReturns: \n\n\n a (rate, distortion) tuple containing the information rate (in bits) of compressing X into X_hat and the expected distortion between X, X_hat
\n \n", "signature": "(p_x , p_xhat_x , dist_mat ) -> tuple [ numpy . ndarray ] : ", "funcdef": "def"}, {"fullname": "altk.effcomm.information.blahut_arimoto", "modulename": "altk.effcomm.information", "qualname": "blahut_arimoto", "kind": "function", "doc": "Compute the rate-distortion function of an i.i.d distribution
\n\nArguments: \n\n\ndist_mat: array of shape (|X|, |X_hat|) representing the distortion matrix between the input alphabet and the reconstruction alphabet. dist_mat[i,j] = dist(x[i],x_hat[j]). In this context, X is a random variable representing the a speaker's meaning (target referent), and X_hat is a random variable representing a listener's meaning (guessed referent).p_x: (1D array of shape |X|) representing the probability mass function of the source. In this context, the prior over states of nature.beta: (scalar) the slope of the rate-distoriton function at the point where evaluation is requiredmax_it: max number of iterationseps: accuracy required by the algorithm: the algorithm stops if there is no change in distoriton value of more than 'eps' between consequtive iterationsignore_converge: whether to run the optimization until max_it, ignoring the stopping criterion specified by eps. \n\nReturns: \n\n\n a dict of the form
\n\n{\n 'final': a tuple of (rate, distortion) values. This is the rate (in bits) of compressing X into X_hat, and distortion between X, X_hat\n\n 'trajectory': a list of the (rate, distortion) points discovered during optimization\n}\n \n", "signature": "(\tdist_mat : numpy . ndarray , \tp_x : numpy . ndarray , \tbeta : float , \tmax_it : int = 200 , \teps : float = 1e-05 , \tignore_converge : bool = False ) -> tuple [ float ] : ", "funcdef": "def"}, {"fullname": "altk.effcomm.information.get_ib_curve", "modulename": "altk.effcomm.information", "qualname": "get_ib_curve", "kind": "function", "doc": "Compute the IB curve bound (I[M:W] vs. I[W:U]) for a given semantic space. We use the embo package, which does not allow one to specify the number of betas, which means some interpolation might be necessary later.
\n\nArguments: \n\n\nprior: array of shape |meanings|space: the ModalMeaningSpace on which meanings are defineddecay: parameter for meaning distribution p(u|m) generation. See generate_meaning_distributions.cost: parameter for meaning distribution p(u|m) generation. See generate_meaning_distributions.curve_type: {'informativity', 'comm_cost'} specifies whether to return the (classic) IB axes of informativity vs. complexity, or the more Rate-Distortion Theory aligned axes of comm_cost vs. complexity. The latter can be obtained easily from the former by subtracting each informativity value from I[M:U], which is a constant for all languages in the same domain. \n\nReturns: \n\n\n an array of shape (num_points, 2) representing the list of (accuracy/comm_cost, complexity) points on the information plane.
\n \n", "signature": "(\tprior : numpy . ndarray , \tspace : altk . language . semantics . Universe , \tdecay : float , \tcost : Callable [[ altk . language . semantics . Referent , altk . language . semantics . Referent ], float ] , \tcurve_type : str = 'informativity' ) -> numpy . ndarray : ", "funcdef": "def"}, {"fullname": "altk.effcomm.information.ib_complexity", "modulename": "altk.effcomm.information", "qualname": "ib_complexity", "kind": "function", "doc": "Compute the IB encoder complexity of a language $I[M:W]$.
\n", "signature": "(language : altk . language . language . Language , prior : numpy . ndarray ) -> float : ", "funcdef": "def"}, {"fullname": "altk.effcomm.information.ib_informativity", "modulename": "altk.effcomm.information", "qualname": "ib_informativity", "kind": "function", "doc": "Compute the expected informativity (accuracy) $I[W:U]$ of a lexicon.
\n\nArguments: \n\n\nlanguage: the Language to measure for informativityprior: communicative need distributiondecay: parameter for meaning distribution p(u|m) generation. See generate_meaning_distributions.cost: parameter for meaning distribution p(u|m) generation. See generate_meaning_distributions. \n\nReturns: \n\n\n the informativity of the language I[W:U] in bits.
\n \n", "signature": "(\tlanguage : altk . language . language . Language , \tprior : numpy . ndarray , \tdecay : float , \tcost : Callable [[ altk . language . semantics . Referent , altk . language . semantics . Referent ], float ] ) -> float : ", "funcdef": "def"}, {"fullname": "altk.effcomm.information.ib_comm_cost", "modulename": "altk.effcomm.information", "qualname": "ib_comm_cost", "kind": "function", "doc": "Compute the IB communicative cost, i.e. expected KL-divergence betweeen speaker and listener meanings, for a language.
\n\nArguments: \n\n\nlanguage: the Language to measure for communicative costprior: communicative need distributiondecay: parameter for meaning distribution p(u|m) generation. See generate_meaning_distributions.cost: parameter for meaning distribution p(u|m) generation. See generate_meaning_distributions. \n\nReturns: \n\n\n the communicative cost, $\\mathbb{E}[D_{KL}[M || \\hat{M}]] = I[M:U] - I[W:U]$ in bits.
\n \n", "signature": "(\tlanguage : altk . language . language . Language , \tprior : numpy . ndarray , \tdecay : float , \tcost : Callable [[ altk . language . semantics . Referent , altk . language . semantics . Referent ], float ] ) -> float : ", "funcdef": "def"}, {"fullname": "altk.effcomm.information.language_to_joint_distributions", "modulename": "altk.effcomm.information", "qualname": "language_to_joint_distributions", "kind": "function", "doc": "Given a Language, get P(M,U) the joint distribution over meanings and referents, and P(W,U) the joint distribution over words and referents.
\n\nArguments: \n\n\nlanguage: the Language to convert to distributionsprior: communicative need distributiondecay: parameter for meaning distribution p(u|m) generation. See generate_meaning_distributions.cost: parameter for meaning distribution p(u|m) generation. See generate_meaning_distributions. \n\nReturns: \n\n\n a dict of the form
\n\n{\n\"joint_pmu\": an array of shape `(|U|, |M|)` representing P(U, M)\n\"joint_pwu\": an array of shape `(|W|, |U|)` representing P(W, U)\n}\n \n", "signature": "(\tlanguage : altk . language . language . Language , \tprior : numpy . ndarray , \tdecay : float , \tcost : Callable [[ altk . language . semantics . Referent , altk . language . semantics . Referent ], float ] ) -> float : ", "funcdef": "def"}, {"fullname": "altk.effcomm.information.language_to_ib_encoder_decoder", "modulename": "altk.effcomm.information", "qualname": "language_to_ib_encoder_decoder", "kind": "function", "doc": "Convert a Language, a mapping of words to meanings, to IB encoder, q(w|m) and IB decoder q(m|w).
\n\nArguments: \n\n\nlanguage: the lexicon from which to infer a speaker (encoder).prior: communicative need distribution \n\nReturns: \n\n\n a dict of the form\n {\n \"encoder\": np.ndarray of shape (|meanings|, |words|),\n \"decoder\": np.ndarray of shape (|words|, |meanings|),\n }
\n \n", "signature": "(\tlanguage : altk . language . language . Language , \tprior : numpy . ndarray ) -> dict [ str , numpy . ndarray ] : ", "funcdef": "def"}, {"fullname": "altk.effcomm.information.deterministic_decoder", "modulename": "altk.effcomm.information", "qualname": "deterministic_decoder", "kind": "function", "doc": "Compute $\\hat{m}_{w}(u) = \\sum_m p(m|w) \\cdot m(u) $
\n\nArguments: \n\n\ndecoder: array of shape (|words|, |meanings|)meaning_distributions: array of shape (|meanings|, |meanings|) \n\nReturns: \n\n\n array of shape (|words|, |meanings|) representing the 'optimal' deterministic decoder
\n \n", "signature": "(\tdecoder : numpy . ndarray , \tmeaning_distributions : numpy . ndarray ) -> numpy . ndarray : ", "funcdef": "def"}, {"fullname": "altk.effcomm.information.generate_meaning_distributions", "modulename": "altk.effcomm.information", "qualname": "generate_meaning_distributions", "kind": "function", "doc": "Generate a conditional distribution over world states given meanings, $p(u|m)$, for each meaning.
\n\nArguments: \n\n\nspace: the ModalMeaningSpace on which meanings are defineddecay: a float in [0,1]. controls informativity, by decaying how much probability mass is assigned to perfect recoveries. As decay approaches 0, only perfect recovery is rewarded (which overrides any partial credit structure built into the utility/cost function). As decay approaches 1, the worst guesses become most likely.cost: a cost function defining the pairwise communicative cost for confusing one Referent in the Universe with another. If you have a (scaled) communicative utility matrix, a natural choice for cost might be lambda x, y: 1 - utility(x, y). \n\nReturns: \n\n\n p_u_m: an array of shape (|space.referents|, |space.referents|)
\n \n", "signature": "(\tspace : altk . language . semantics . Universe , \tdecay : float , \tcost : Callable [[ altk . language . semantics . Referent , altk . language . semantics . Referent ], float ] ) -> numpy . ndarray : ", "funcdef": "def"}, {"fullname": "altk.effcomm.informativity", "modulename": "altk.effcomm.informativity", "kind": "module", "doc": "Functions for measuring informativity in efficient communication analyses of languages.
\n"}, {"fullname": "altk.effcomm.informativity.informativity", "modulename": "altk.effcomm.informativity", "qualname": "informativity", "kind": "function", "doc": "The informativity of a language is identified with the successful communication between a speaker and a listener.
\n\nThis function is a wrapper for communicative_success.
\n\nArguments: \n\n\nlanguage: the language to compute informativity of.prior: a probability distribution representing communicative need (frequency) for meanings.utility: a function representing the usefulness of listener guesses about speaker meanings, e.g. meaning similarity. To reward only exact recovery of meanings, pass the an indicator function.kind: {\"literal, pragmatic\"} Whether to measure informativity using literal or pragmatic agents, as canonically described in the Rational Speech Act framework. The default is \"literal\". \n\nConcepts :\n The speaker can be thought of as a conditional distribution over expressions given meanings. The listener is likewise a conditional distribution over meanings given expressions. The communicative need, or cognitive source, is a prior probability over meanings representing how frequently agents need to use certain meanings in communication. The utility function represents the similarity, or appropriateness, of the listener's guess m' about the speaker's intended meaning m.
\n\nFormula :\n The informativity of a language $L$ with meaning space $M$ is defined:
\n\n$I(L) := \\sum_{m \\in M} p(m) \\sum_{i \\in L} p(i|m) \\sum_{\\hat{m} \\in i} p(\\hat{m}|i) \\cdot u(m, \\hat{m})$
\n\nBounds :\n A perfectly informative (=1.0) language can be constructed with a exactly one expression for each meaning.
\n\nFor u() = indicator(), every language has nonzero informativity because a language must contain at least one expression, and an expression must contain at least one meaning.\n(\tlanguage : altk . language . language . Language , \tprior : numpy . ndarray , \tutility : Callable [[ altk . language . semantics . Referent , altk . language . semantics . Referent ], float ] , \tagent_type : str = 'literal' ) -> float : ", "funcdef": "def"}, {"fullname": "altk.effcomm.informativity.communicative_success", "modulename": "altk.effcomm.informativity", "qualname": "communicative_success", "kind": "function", "doc": "Helper function to compute the literal informativity of a language.
\n\n$I(L) = \\sum_{m, \\hat{m}} P(m, \\hat{m}) \\cdot u(m, \\hat{m})$
\n\n$ = \\sum_{m \\in M} p(m) \\sum_{i \\in L} p(i|m) \\sum_{\\hat{m} \\in i} p(\\hat{m} |i) \\cdot u(m, m')$
\n\n$ = \\sum \\text{diag}(p)SR \\odot U $
\n\nFor more details, see docs/vectorized_informativity .
\n\nArguments: \n\n\nspeaker: a literal or pragmatic speaker, containing a matrix S for P(e | m)listener: a literal or pragmatic listener, containing a matrix R for P(m | e)prior: p(m), distribution over meanings representing communicative needutility: a function u(m, m') representing similarity of meanings, or pair-wise usefulness of listener guesses about speaker meanings. \n", "signature": "(\tspeaker : altk . effcomm . agent . Speaker , \tlistener : altk . effcomm . agent . Listener , \tprior : numpy . ndarray , \tutility : Callable [[ altk . language . semantics . Referent , altk . language . semantics . Referent ], float ] ) -> float : ", "funcdef": "def"}, {"fullname": "altk.effcomm.optimization", "modulename": "altk.effcomm.optimization", "kind": "module", "doc": "Classes and functions for generating languages that optimize the simplicity/informativeness trade-off, e.g. via an iterative evolutionary algorithm.
\n"}, {"fullname": "altk.effcomm.optimization.Mutation", "modulename": "altk.effcomm.optimization", "qualname": "Mutation", "kind": "class", "doc": "
\n"}, {"fullname": "altk.effcomm.optimization.Mutation.precondition", "modulename": "altk.effcomm.optimization", "qualname": "Mutation.precondition", "kind": "function", "doc": "Whether a mutation is allowed to apply to a language.
\n", "signature": "(self , language : altk . language . language . Language , ** kwargs ) -> bool : ", "funcdef": "def"}, {"fullname": "altk.effcomm.optimization.Mutation.mutate", "modulename": "altk.effcomm.optimization", "qualname": "Mutation.mutate", "kind": "function", "doc": "Mutate the language, possibly using a list of expressions.
\n", "signature": "(\tself , \tlanguage : altk . language . language . Language , \texpressions : list [ altk . language . language . Expression ] , \t** kwargs ) -> altk . language . language . Language : ", "funcdef": "def"}, {"fullname": "altk.effcomm.optimization.EvolutionaryOptimizer", "modulename": "altk.effcomm.optimization", "qualname": "EvolutionaryOptimizer", "kind": "class", "doc": "Class for approximating the Pareto frontier of languages optimizing the simplicity/informativity trade-off.
\n"}, {"fullname": "altk.effcomm.optimization.EvolutionaryOptimizer.__init__", "modulename": "altk.effcomm.optimization", "qualname": "EvolutionaryOptimizer.__init__", "kind": "function", "doc": "Initialize the evolutionary algorithm configurations.
\n\nThe measures of complexity and informativity, the expressions, and the mutations are all specific to the particular semantic domain.
\n\nArguments: \n\n\nobjectives: a dict of the two objectives to optimize for, e.g. simplicity and informativeness, of the form, e.g.\n{\n \"complexity\": comp_measure,\n \"comm_cost\": lambda l: 1 - inf_measure(l)\n}expressions: a list of expressions from which to apply mutations to languages.mutations: a list of Mutation objectssample_size: the size of the population at every generation.max_muatations: between 1 and this number of mutations will be applied to a subset of the population at the end of each generation.generations: how many iterations to run the evolutionary algorithm for.lang_size: between 1 and this number of expressions comprise a language.proceses: for multiprocessing.ProcessPool, e.g. 6. \n", "signature": "(\tobjectives : dict [ str , typing . Callable [[ altk . language . language . Language ], typing . Any ]] , \texpressions : list [ altk . language . language . Expression ] , \tmutations : list [ altk . effcomm . optimization . Mutation ] , \tsample_size : int , \tmax_mutations : int , \tgenerations : int , \tlang_size : int , \tx : str = 'comm_cost' , \ty : str = 'complexity' ) "}, {"fullname": "altk.effcomm.optimization.EvolutionaryOptimizer.fit", "modulename": "altk.effcomm.optimization", "qualname": "EvolutionaryOptimizer.fit", "kind": "function", "doc": "Computes the Pareto frontier, a set languages which cannot be both more simple and more informative.
\n\nUses pygmo's nondominated_front method for computing a population's best solutions to a multi-objective optimization problem.
\n\nArguments: \n\n\nseed_population: a list of languages representing the population at generation 0 of the algorithm.id_start: the number of languages generated in the experiment so far.explore: a float in [0,1] representing how much to optimize for fitness (optimality wrt pareto front of complexity and comm_cost), and how much to randomly explore. \n\nReturns: \n\n\n a dict of the estimated optimization solutions, as well as points explored along the way; of the form
\n\n{\n\"dominating_languages\": list of languages as estimated solutions,\n\"explored_languages\": list of all the languages explored during the evolutionary algorithm,\n\"id_start\": updated number of languages generated in the experiment.\n}\n \n", "signature": "(\tself , \tseed_population : list [ altk . language . language . Language ] , \tid_start : int , \texplore : float = 0.0 ) -> dict [ str , typing . Any ] : ", "funcdef": "def"}, {"fullname": "altk.effcomm.optimization.EvolutionaryOptimizer.sample_mutated", "modulename": "altk.effcomm.optimization", "qualname": "EvolutionaryOptimizer.sample_mutated", "kind": "function", "doc": "Arguments: \n\n\nlanguages: dominating languages of a generationamount: sample_size.expressions: the list of expressionsid_start: the number of languages generatd in the experiment so far. \n\nReturns: \n\n\n a dict of the new population of languages of size=sample_size, and the updated id_start, of the form
\n\n{\n\"languages\": (list of updated languages)\n\"id_start\": (updated length of languages)\n}\n \n", "signature": "(\tself , \tlanguages : list [ altk . language . language . Language ] , \tamount : int , \texpressions : list [ altk . language . language . Expression ] , \tid_start : int ) -> dict [ str , typing . Any ] : ", "funcdef": "def"}, {"fullname": "altk.effcomm.optimization.EvolutionaryOptimizer.mutate", "modulename": "altk.effcomm.optimization", "qualname": "EvolutionaryOptimizer.mutate", "kind": "function", "doc": "Randomly selects a mutation that is allowed to apply and applies it to a language.
\n\nArguments: \n\n\nlanguage: the Language to mutateexpressions: the list of all possible expressions. Some mutations need access to this list, so it is part of the mutation api. \n\nReturns: \n\n\n the mutated Language
\n \n", "signature": "(\tself , \tlanguage : altk . language . language . Language , \texpressions : list [ altk . language . language . Expression ] ) -> altk . language . language . Language : ", "funcdef": "def"}, {"fullname": "altk.effcomm.optimization.sample_parents", "modulename": "altk.effcomm.optimization", "qualname": "sample_parents", "kind": "function", "doc": "Use the explore parameter to explore possibly suboptimal areas of the language space.
\n\nArguments: \n\n\ndominating_languages: a list of the languages with current best fitness with respect to the objectives.explored_languages: a list of all languages encountered during the evolutionary algorithm.id_start: the number of languages generated in the experiment so far.explore: a float in [0,1] specifying how much to explore possibly suboptimal languages. If set to 0, parent_languages is just dominating_languages. \n\nReturns: \n\n\n a dict of the languages to serve as the next generation (after possible mutations) and updated id_start, of the form
\n\n{\n \"languages\": (list of updated languages)\n \"id_start\": (updated length of languages)\n}\n \n", "signature": "(\tdominating_languages : list [ altk . language . language . Language ] , \texplored_languages : list [ altk . language . language . Language ] , \tid_start : int , \texplore : float ) -> dict [ str , typing . Any ] : ", "funcdef": "def"}, {"fullname": "altk.effcomm.sampling", "modulename": "altk.effcomm.sampling", "kind": "module", "doc": "Functions for sampling expressions into languages.
\n"}, {"fullname": "altk.effcomm.sampling.get_hypothetical_variants", "modulename": "altk.effcomm.sampling", "qualname": "get_hypothetical_variants", "kind": "function", "doc": "For each system (parameterized by a language or else a speaker), generate num hypothetical variants by permuting the signals that the system assigns to states.
\n\nArguments: \n\n\nlanguages: a list of languages to permute, by constructing LiteralSpeakers and permuting their weights.speakers: a list of speakers of a language, whose weights can be directly permuted. Should be used instead of languages if possible, because it can be more finegrained (every language can be associated with multiple speakers).total: the total number of hypothetical variants to obtain \n\nReturns: \n\n\n hypothetical_variants: a list of type either Language or np.ndarray depending on whether languages or speakers was passed, representing hypothetical variants of the systems passed. If speakers was passed, a list of speakers is returned.
\n \n", "signature": "(\tlanguages : list [ altk . language . language . Language ] = None , \tspeakers : list [ altk . effcomm . agent . Speaker ] = None , \ttotal : int = 0 ) -> list [ typing . Any ] : ", "funcdef": "def"}, {"fullname": "altk.effcomm.sampling.generate_languages", "modulename": "altk.effcomm.sampling", "qualname": "generate_languages", "kind": "function", "doc": "Generate languages by randomly sampling vocabularies as bags of expressions.
\n\nA predicate (binary-valued property) of expressions may be supplied, which can be used to adjust the composition of vocabularies (e.g., by the percent of expressions satisfying the predicate).
\n\nIf sample size <= nCr, then take a random sample_size set of combinations. Otherwise, to prevent repeat languages, treat nCr as the sample size.
\n\nArguments: \n\n\nexpressions: a list of the possible expressions to sample from.lang_size: the maximum (or exact) number of expressions in each language.sample_size: the number of languages to generate.criterion: the predicate, (e.g. semantic universal) by which to split the expressions into those satisfying and those not, and then sample languages with degrees of naturalness based on the percentage from those satisfying. Must apply at the expression level. By default is a trivial criterion, so that all expressions are 'quasi-natural'.fixed_wordcount: whether to vary the language size from 1 to lang_size.verbose: How detailed the progress of sampling should be, printed to stdout.dummy_name: the default name to give to each sampled language, e.g. sampled_lang_42. These should not collide with any actual natural language names if the efficient communication experiment does use natural language data.id_start: an integer representing the number of languages already generated in an experiment. Languages sampled will be named according to this number. For example, if id_start is 0, the first language sampled will be named sampled_lang_0. Note that the largest id does not necessarily track the actual size of languages saved for the experiment, but it does track how many languages have been generated.exact_sample: a boolean representing whether to sample until the exact sample size is filled. If True, the resulting pool of languages may not be unique.verbose: a boolean representing how verbose output should be during sampling. \n\nReturns: \n\n\n a dict representing the generated pool of languages and the updated id_start, of the form
\n\n{\n \"languages\": (list of updated languages)\n \"id_start\": (updated length of languages)\n}\n \n\nExamples: \n\n\n \n
>>> # Turn the knob on a universal property for modals \n>>> expressions = load_expressions ( expressions_file ) \n>>> universal_property = iff \n>>> result = generate_languages ( \n... ModalLanguage , \n... expressions , \n... lang_size , \n... sample_size , \n... universal_property , \n...) \n>>> languages = result [ "languages" ] \n>>> id_start = result [ "id_start" ] \n\n
\n", "signature": "(\tlanguage_class : Type [ altk . language . language . Language ] , \texpressions : list [ altk . language . language . Expression ] , \tlang_size : int , \tsample_size : int , \tcriterion : Callable [[ altk . language . language . Expression ], bool ] = < function < lambda >> , \tfixed_wordcount = False , \tdummy_name = 'sampled_lang_' , \tid_start : int = 0 , \texact_sample = False , \tverbose = False ) -> dict [ str , typing . Any ] : ", "funcdef": "def"}, {"fullname": "altk.effcomm.sampling.sample_lang_size", "modulename": "altk.effcomm.sampling", "qualname": "sample_lang_size", "kind": "function", "doc": "Get a sample of languages each of exactly lang_size.
\n\nArguments: \n\n\nlanguage_class: a subclass of altk.Languageexpressions: a list of Expressions to sample fromlang_size: int representing the maximum language size to samplesample_size: int representing the number of total languages to returnid_start: an int representing the number of languages already generated in an experiment. \n\nReturns: \n\n\n a dict containing the randomly sampled languages and the updated id_start, of the form
\n\n{\n \"languages\": (list of updated languages)\n \"id_start\": (updated length of languages)\n}\n \n", "signature": "(\tlanguage_class : Type [ altk . language . language . Language ] , \texpressions : list [ altk . language . language . Expression ] , \tlang_size : int , \tsample_size : int , \tid_start : int = 0 , \tverbose = False , \tdummy_name = 'sampled_lang_id' ) -> list [ altk . language . language . Language ] : ", "funcdef": "def"}, {"fullname": "altk.effcomm.sampling.sample_quasi_natural", "modulename": "altk.effcomm.sampling", "qualname": "sample_quasi_natural", "kind": "function", "doc": "Turn the knob on degree quasi-naturalness for a sample of languages, either by enumerating or randomly sampling unique subsets of all possible combinations.
\n\nArguments: \n\n\nnatural_terms: expressions satisfying some criteria of quasi-naturalness, e.g, a semantic universal.unnatural_terms: expressions not satisfying the criteria.lang_size: the exact number of expressions a language must have.sample_size: how many languages to sample. \n\nReturns: \n\n\n a dict containing the randomly sampled quasi-natural languages and the updated id_start, of the form
\n\n{\n \"languages\": (list of updated languages)\n \"id_start\": (updated length of languages)\n}\n \n", "signature": "(\tlanguage_class : Type [ altk . language . language . Language ] , \tnatural_terms : list [ altk . language . language . Expression ] , \tunnatural_terms : list [ altk . language . language . Expression ] , \tlang_size : int , \tsample_size : int , \tid_start : int , \tdummy_name = 'sampled_lang_id' , \tverbose = False ) -> dict [ str , typing . Any ] : ", "funcdef": "def"}, {"fullname": "altk.effcomm.sampling.rename_id", "modulename": "altk.effcomm.sampling", "qualname": "rename_id", "kind": "function", "doc": "Updates a string of form sampled_lang_X with a new id for X.
\n", "signature": "(name : str , id : int ) -> str : ", "funcdef": "def"}, {"fullname": "altk.effcomm.sampling.enumerate_all_languages", "modulename": "altk.effcomm.sampling", "qualname": "enumerate_all_languages", "kind": "function", "doc": "When the sample size requested is greater than the size of all possible languages, just enumerate all the possible languages.
\n\nArguments: \n\n\nlanguage_class: the kind of Language to constructid_start: a number to start counting from for assigning names with numerical ids to languages.natural_indices: the indices of quasi-natural languages already seennum_natural: the number of quasi-natural languages to samplenatural_terms: the list of quasi-natural terms to sample fromunnatural_indices: the indices of non-quasi-natural languages already seennum_unnatural: the number of non-quasi-natural languages to sample; 0 by defaultunnatural_terms: the list of non-quasi-natural terms to sample from; empty by default.dummy_name: the format of the string to name each language constructed. \n\nReturns: \n\n\n a dict containing a set of languages and the updated id_start, of the form
\n\n{\n \"languages\": (list of updated languages)\n \"id_start\": (updated length of languages)\n}\n \n", "signature": "(\tlanguage_class : Type [ altk . language . language . Language ] , \tid_start : int , \tnatural_terms : list [ altk . language . language . Expression ] , \tnatural_indices : list [ int ] , \tnum_natural : int = 0 , \tunnatural_terms : list [ altk . language . language . Expression ] = [] , \tunnatural_indices : list [ int ] = [] , \tnum_unnatural : int = 0 , \tdummy_name = 'sampled_lang_id' , \tverbose = False ) -> dict [ str , typing . Any ] : ", "funcdef": "def"}, {"fullname": "altk.effcomm.sampling.random_combination_vocabulary", "modulename": "altk.effcomm.sampling", "qualname": "random_combination_vocabulary", "kind": "function", "doc": "Get a single vocabulary for a specific language size by choosing a random combination of natural and unnatural terms.
\n\nArguments: \n\n\nseen: the list of language indices already seennum_natural: intnatural_terms: list[Expression]num_unnatural: int=0unnatural_terms: list[Expression]=[] \n\nReturns: \n\n\n languages: the extended list of input languages.
\n \n", "signature": "(\tseen : set , \tnum_natural : int , \tnatural_terms : list [ altk . language . language . Expression ] , \tnum_unnatural : int = 0 , \tunnatural_terms : list [ altk . language . language . Expression ] = [] ) -> list [ altk . language . language . Language ] : ", "funcdef": "def"}, {"fullname": "altk.effcomm.tradeoff", "modulename": "altk.effcomm.tradeoff", "kind": "module", "doc": "Functions for constructing an efficient communication analysis by measuring the simplicity/informativeness trade-off languages and formatting results as a dataframe or a plot.
\n"}, {"fullname": "altk.effcomm.tradeoff.pareto_optimal_languages", "modulename": "altk.effcomm.tradeoff", "qualname": "pareto_optimal_languages", "kind": "function", "doc": "Use pygmo.non_dominated_front_2d to compute the Pareto languages.
\n", "signature": "(\tlanguages : list [ altk . language . language . Language ] , \tx : str = 'comm_cost' , \ty : str = 'complexity' , \tunique : bool = False ) -> list [ altk . language . language . Language ] : ", "funcdef": "def"}, {"fullname": "altk.effcomm.tradeoff.pareto_min_distances", "modulename": "altk.effcomm.tradeoff", "qualname": "pareto_min_distances", "kind": "function", "doc": "Measure the Pareto optimality of each language by measuring its Euclidean closeness to the frontier. The frontier is a line (list of points) interpolated from the pareto points.
\n\nArguments: \n\n\npoints: the list of all language (x, y) pairs, where x and y are usually communicative cost and complexity.pareto_points: the list of all dominant language (x, y) pairs to constitute the Pareto frontier. The points should have been measured by pygmo's non_dominated_front_2d function. \n\nReturns: \n\n\n min_distances: an array of shape len(points) Euclidean distances for each language to the closest point on the Pareto frontier.
\n \n", "signature": "(points : list [ tuple ] , pareto_points : list [ tuple ] ) -> numpy . ndarray : ", "funcdef": "def"}, {"fullname": "altk.effcomm.tradeoff.interpolate_data", "modulename": "altk.effcomm.tradeoff", "qualname": "interpolate_data", "kind": "function", "doc": "Interpolate the points yielded by the pareto optimal languages into a continuous (though not necessarily smooth) curve.
\n\nArguments: \n\n\npoints: an list of (comm_cost, complexity) pairs of size [dominating_languages], a possibly non-smooth set of solutions to the trade-off.min_cost: the minimum communicative cost value possible to interpolate from.max_cost: the maximum communicative cost value possible to interpolate from. A natural assumption is to let complexity=0.0 if max_cost=1.0, which will result in a Pareto curve that spans the entire 2d space, and consequently the plot with x and y limits both ranging [0.0, 1.0].num: the number of x-axis points (cost) to interpolate. Controls smoothness of curve. \n\nReturns: \n\n\n interpolated_points: an array of size (num, num)
\n \n", "signature": "(\tpoints : list [ tuple [ float ]] , \tmin_cost : float = 0.0 , \tmax_cost : float = 1.0 , \tnum = 5000 ) -> numpy . ndarray : ", "funcdef": "def"}, {"fullname": "altk.effcomm.tradeoff.tradeoff", "modulename": "altk.effcomm.tradeoff", "qualname": "tradeoff", "kind": "function", "doc": "Builds a final efficient communication analysis by measuring a list of languages, updating their internal data, and returning the results.
\n\nThis function measures possibly many graded or categorical properties of each language, but minimally the properties of commmunicative cost and complexity. These two measures fully define the results of an efficiency analysis, in the sense they define the optimal solutions.
\n\nArguments: \n\n\nlanguages: A list representing the pool of all languages to be measured for an efficient communication analysis.x: the first pressure to measure, e.g. communicative cost.y: the second pressure to measure, e.g. cognitive complexity.frontier: a list of (comm_cost, complexity) points representing a Pareto frontier to measure optimality w.r.t. \n\nReturns: \n\n\n a dictionary of the population and the pareto front, of the form
\n\n{\n \"languages\": the list of languages, with their internal efficient communication data updated,\n\n \"dominating_languages\": the list of the languages dominating the population w.r.t. comm_cost and complexity. If no `frontier` is none, this can be considered the Pareto frontier.\n}\n \n", "signature": "(\tlanguages : list [ altk . language . language . Language ] , \tproperties : dict [ str , typing . Callable [[ altk . language . language . Language ], typing . Any ]] , \tx : str = 'comm_cost' , \ty : str = 'complexity' , \tfrontier : list [ tuple ] = None ) -> dict [ str , list [ altk . language . language . Language ]] : ", "funcdef": "def"}, {"fullname": "altk.effcomm.util", "modulename": "altk.effcomm.util", "kind": "module", "doc": "Various helper functions for computing complexity and informativity.
\n"}, {"fullname": "altk.effcomm.util.rows_zero_to_uniform", "modulename": "altk.effcomm.util", "qualname": "rows_zero_to_uniform", "kind": "function", "doc": "Ensure that mat encodes a probability distribution, i.e. each row (indexed by a meaning) is a distribution over expressions: sums to exactly 1.0.
\n\nThis is necessary when exploring mathematically possible languages (including natural languages, like Hausa in the case of modals) which sometimes have that a row of the matrix p(word|meaning) is a vector of 0s.
\n\nArguments: \n\n\nmat: a 2D numpy array that should be normalized so that each row is a probability distribution. \n", "signature": "(mat : numpy . ndarray ) -> numpy . ndarray : ", "funcdef": "def"}, {"fullname": "altk.effcomm.util.build_utility_matrix", "modulename": "altk.effcomm.util", "qualname": "build_utility_matrix", "kind": "function", "doc": "Construct the square matrix specifying the utility function defined for pairs of meanings, used for computing communicative success.
\n", "signature": "(\tuniverse : altk . language . semantics . Universe , \tutility : Callable [[ altk . language . semantics . Meaning , altk . language . semantics . Meaning ], float ] ) -> numpy . ndarray : ", "funcdef": "def"}, {"fullname": "altk.effcomm.util.marginal", "modulename": "altk.effcomm.util", "qualname": "marginal", "kind": "function", "doc": "Compute $p(x) = \\sum_x p(x,y)$
\n\nArguments: \n\n\npXY: a numpy array of shape (|X|, |Y|) \n\nReturns: \n\n\n pY: (axis = 0) or pX (default, axis = 1)
\n \n", "signature": "(pXY , axis = 1 ): ", "funcdef": "def"}, {"fullname": "altk.effcomm.util.conditional", "modulename": "altk.effcomm.util", "qualname": "conditional", "kind": "function", "doc": "Compute $p(y|x) = \\frac{p(x,y)}{p(x)}$
\n\nArguments: \n\n\npXY: a numpy array of shape (|X|, |Y|) \n\nReturns: \n\n\n pY_X: a numpy array of shape (|X|, |Y|)
\n \n", "signature": "(pXY ): ", "funcdef": "def"}, {"fullname": "altk.effcomm.util.joint", "modulename": "altk.effcomm.util", "qualname": "joint", "kind": "function", "doc": "Compute $p(x,y) = p(y|x) \\cdot p(x) $
\n\nArguments: \n\n\npY_X: a numpy array of shape (|X|, |Y|)pX: a numpy array |X| \n\nReturns: \n\n\n pXY: a numpy array of the shape (|X|, |Y|)
\n \n", "signature": "(pY_X , pX ): ", "funcdef": "def"}, {"fullname": "altk.effcomm.util.marginalize", "modulename": "altk.effcomm.util", "qualname": "marginalize", "kind": "function", "doc": "Compute $p(y) = \\sum_x p(y|x) \\cdot p(x)$
\n\nArguments: \n\n\npY_X: a numpy array of shape (|X|, |Y|)pX: a numpy array of shape |X| \n\nReturns: \n\n\n pY: a numpy array of shape |Y|
\n \n", "signature": "(pY_X , pX ): ", "funcdef": "def"}, {"fullname": "altk.effcomm.util.bayes", "modulename": "altk.effcomm.util", "qualname": "bayes", "kind": "function", "doc": "Compute $p(x|y) = \\frac{p(y|x) \\cdot p(x)}{p(y)}$
\n\nArguments: \n\n\npY_X: a numpy array of shape (|X|, |Y|) \n", "signature": "(pY_X , pX ): ", "funcdef": "def"}, {"fullname": "altk.effcomm.util.xlogx", "modulename": "altk.effcomm.util", "qualname": "xlogx", "kind": "function", "doc": "Compute $x \\log p(x)$
\n", "signature": "(p ): ", "funcdef": "def"}, {"fullname": "altk.effcomm.util.H", "modulename": "altk.effcomm.util", "qualname": "H", "kind": "function", "doc": "Compute the entropy of p, $H(X) = - \\sum_x x \\log p(x)$
\n", "signature": "(p , axis = None ): ", "funcdef": "def"}, {"fullname": "altk.effcomm.util.MI", "modulename": "altk.effcomm.util", "qualname": "MI", "kind": "function", "doc": "Compute mutual information, $I[X:Y]$
\n", "signature": "(pXY ): ", "funcdef": "def"}, {"fullname": "altk.effcomm.util.DKL", "modulename": "altk.effcomm.util", "qualname": "DKL", "kind": "function", "doc": "Compute KL divergences, $D_{KL}[p~||~q]$
\n", "signature": "(p , q , axis = None ): ", "funcdef": "def"}, {"fullname": "altk.language", "modulename": "altk.language", "kind": "module", "doc": "Classes for modeling (natural or hypothetical) languagese.
\n\nAt the current stage of development, ALTK focuses on supporting abstractions to model the mapping between expressions and meanings of a language. So far, we leave almost everything besides this basic mapping (morphosyntax, phonology, phonetic inventories, among other features of human languages) to future work.
\n\nThe altk.language.language submodule contains classes for constructing a language, which can contain one or more expressions.
\n\nThe altk.language.semantics submodule contains classes for defining a universe (meaning space) of referents (denotations) and meanings (categories).
\n"}, {"fullname": "altk.language.language", "modulename": "altk.language.language", "kind": "module", "doc": "Classes for modeling languages as form-meaning mappings, most important among them the Language and Expression classes.
\n\nExample usage: \n\n\n \n
>>> from altk.language.language import Expression , Language \n>>> # assuming the meaning `a_few_meaning` has already been constructed \n>>> # define the expression \n>>> a_few = NumeralExpression ( form = "a few" , meaning = a_few_meaning ) \n>>> # define a very small language \n>>> lang_1 = Language ([ a_few ]) \n>>> # or a slightly larger one with synonymy \n>>> lang_2 = Language ([ a_few ] * 3 ) \n\n
\n"}, {"fullname": "altk.language.language.Expression", "modulename": "altk.language.language", "qualname": "Expression", "kind": "class", "doc": "Minimally contains a form and a meaning.
\n"}, {"fullname": "altk.language.language.Expression.__init__", "modulename": "altk.language.language", "qualname": "Expression.__init__", "kind": "function", "doc": "
\n", "signature": "(form : str = None , meaning : altk . language . semantics . Meaning = None "}, {"fullname": "altk.language.language.Expression.can_express", "modulename": "altk.language.language", "qualname": "Expression.can_express", "kind": "function", "doc": "Return True if the expression can express the input single meaning point and false otherwise.
\n", "signature": "(self , m : altk . language . semantics . Meaning ) -> bool : ", "funcdef": "def"}, {"fullname": "altk.language.language.Expression.yaml_rep", "modulename": "altk.language.language", "qualname": "Expression.yaml_rep", "kind": "function", "doc": "
\n", "signature": "(self ): ", "funcdef": "def"}, {"fullname": "altk.language.language.Language", "modulename": "altk.language.language", "qualname": "Language", "kind": "class", "doc": "Minimally contains Expression objects.
\n"}, {"fullname": "altk.language.language.Language.__init__", "modulename": "altk.language.language", "qualname": "Language.__init__", "kind": "function", "doc": "
\n", "signature": "(expressions : list [ altk . language . language . Expression ] , ** kwargs "}, {"fullname": "altk.language.language.Language.add_expression", "modulename": "altk.language.language", "qualname": "Language.add_expression", "kind": "function", "doc": "Add an expression to the list of expressions in a language.
\n", "signature": "(self , e : altk . language . language . Expression ): ", "funcdef": "def"}, {"fullname": "altk.language.language.Language.pop", "modulename": "altk.language.language", "qualname": "Language.pop", "kind": "function", "doc": "Removes an expression at the specified index of the list of expressions, and returns it.
\n", "signature": "(self , index : int ) -> altk . language . language . Expression : ", "funcdef": "def"}, {"fullname": "altk.language.language.Language.is_natural", "modulename": "altk.language.language", "qualname": "Language.is_natural", "kind": "function", "doc": "Whether a language represents a human natural language.
\n", "signature": "(self ) -> bool : ", "funcdef": "def"}, {"fullname": "altk.language.language.Language.degree_property", "modulename": "altk.language.language", "qualname": "Language.degree_property", "kind": "function", "doc": "Count what percentage of expressions in a language have a given property.
\n", "signature": "(\tself , \tproperty : Callable [[ altk . language . language . Expression ], bool ] ) -> float : ", "funcdef": "def"}, {"fullname": "altk.language.language.Language.binary_matrix", "modulename": "altk.language.language", "qualname": "Language.binary_matrix", "kind": "function", "doc": "Get a binary matrix of shape (num_meanings, num_expressions)\nspecifying which expressions can express which meanings.
\n", "signature": "(self ) -> numpy . ndarray : ", "funcdef": "def"}, {"fullname": "altk.language.semantics", "modulename": "altk.language.semantics", "kind": "module", "doc": "Classes for modeling the meanings of a language.
\n\nMeanings are modeled as things which map linguistic forms to objects of reference. The linguistic forms and objects of reference can in principle be very detailed, and future work may elaborate the meaning classes and implement a Form class.
\n\nIn efficient communication analyses, simplicity and informativeness can be measured as properties of semantic aspects of a language. E.g., a meaning is simple if it is easy to represent, or to compress into some code; a meaning is informative if it is easy for a listener to recover a speaker's intended literal meaning.
\n\nExamples: \n\n\n \n
>>> from altk.language.semantics import Referent , Meaning , Universe \n>>> from altk.language.language import Expression \n>>> # construct the meaning space for numerals \n>>> numerals_universe = NumeralUniverse ( referents = [ NumeralReferent ( str ( i )) for i in range ( 1 , 100 )]) \n>>> # construct a list of referents for the expression 'a few' \n>>> a_few_refs = [ NumeralRefernt ( name = str ( i )) for i in range ( 2 , 6 )] \n>>> a_few_meaning = NumeralMeaning ( referents = a_few_refs , universe = numerals_universe ) \n>>> # define the expression \n>>> a_few = NumeralExpression ( form = "a few" , meaning = a_few_meaning ) \n\n
\n"}, {"fullname": "altk.language.semantics.Referent", "modulename": "altk.language.semantics", "qualname": "Referent", "kind": "class", "doc": "A referent is some object in the universe for a language.
\n"}, {"fullname": "altk.language.semantics.Referent.__init__", "modulename": "altk.language.semantics", "qualname": "Referent.__init__", "kind": "function", "doc": "Initialize a referent.
\n\nArguments: \n\n\nname: a string representing the name of the referent \n", "signature": "(name : str "}, {"fullname": "altk.language.semantics.Universe", "modulename": "altk.language.semantics", "qualname": "Universe", "kind": "class", "doc": "The universe is the set of possible referent objects for a meaning.
\n"}, {"fullname": "altk.language.semantics.Universe.__init__", "modulename": "altk.language.semantics", "qualname": "Universe.__init__", "kind": "function", "doc": "
\n", "signature": "(referents : Iterable [ altk . language . semantics . Referent ] "}, {"fullname": "altk.language.semantics.Meaning", "modulename": "altk.language.semantics", "qualname": "Meaning", "kind": "class", "doc": "A meaning picks out a set of objects from the universe.
\n\nOn one tradition (from formal semantics), we might model an underspecified meaning as a subset of the universe. Sometimes these different referents are not equally likely, in which it can be helpful to define a meaning explicitly as a distribution over the universe.
\n"}, {"fullname": "altk.language.semantics.Meaning.__init__", "modulename": "altk.language.semantics", "qualname": "Meaning.__init__", "kind": "function", "doc": "A meaning is the set of things it refers to.
\n\nThe objects of reference are a subset of the universe of discourse. Sometimes it is natural to construe the meaning as as a probability distribution over the universe, instead of just a binary predicate.
\n\nArguments: \n\n\nreferents: a list of Referent objects, which must be a subset of the referents in universe.universe: a Universe object that defines the probability space for a meaning.dist: a dict of with Referent names as keys and weights or probabilities as values, representing the distribution over referents to associate with the meaning. By default is None, and the distribution will be uniform over the passed referents, and any remaining referents are assigned 0 probability. \n", "signature": "(\treferents : Iterable [ altk . language . semantics . Referent ] , \tuniverse : altk . language . semantics . Universe , \tdist : dict [ str , float ] = None ) "}];
+ /** pdoc search index */const docs = {"version": "0.9.5", "fields": ["qualname", "fullname", "annotation", "default_value", "signature", "bases", "doc"], "ref": "fullname", "documentStore": {"docs": {"ultk": {"fullname": "ultk", "modulename": "ultk", "kind": "module", "doc": "\n\n
\n\nIntroduction \n\nULTK is a software library that aims to support efficient communication analyses of natural language. This is a line of research that aims to explain why natural languages have the structure that they do in terms competing pressures to minimize cognitive complexity and maximize communicative accuracy.
\n\nKey features:
\n\n\nPrimitives for constructing semantic spaces, expressions, and languages \nTools for measuring informativity of languages, communicative success of RSA speakers and listeners \nLanguage population sampling and optimization w.r.t Pareto fronts \nRate-Distortion and Information Bottleneck style analyses \n \n\nULTK is a long term project and it is currently in its early stages. It is intended to help lower the barrier to entry for certain research in computational semantics, and to unify methodologies. If you find something confusing, please open an issue. If you have a phenomena of interest in linguistic semantics that you want to run an efficient communication analysis on, please contact the contributors.
\n\nRead the documentation .
\n\nInstalling ULTK \n\nFirst, set up a virtual environment (e.g. via miniconda , conda create -n ultk python=3.11, and conda activate ultk).
\n\n\nDownload or clone this repository and navigate to the root folder.
Install ULTK (We recommend doing this inside a virtual environment)
\n\npip install -e .
\n\nGetting started \n\n\nCheck out the examples , starting with a basic signaling game. The examples folder also contains a simiple efficient communication analysis of indefinites . \nTo see more scaled up usage examples, visit the codebase for an efficient communication analysis of modals or sim-max games . \nFor an introduction to efficient communication research, here is a survey paper of the field. \nFor an introduction to the RSA framework, see this online textbook . \n \n\nModules \n\nThere are two modules. The first is ultk.effcomm , which includes methods for measuring informativity of languages and/or communicative success of Rational Speech Act agents, and for language population sampling and optimization w.r.t Pareto fronts.
\n\nThe second module is ultk.language , which contains primitives for constructing semantic spaces, expressions, and languages. It also has a grammar module which can be used for building expressions in a Language of Thought and measuring complexity in terms of minimum description length, as well as for natural language syntax.
\n\nThe source code is available on github here .
\n\nTesting \n\nUnit tests are written in pytest and executed via running pytest in the src/tests folder.
\n\nReferences \n\n\nFigures:
\n\n\n Kinship Categories Across Languages Reflect General Communicative Principles | Science. (n.d.). Retrieved February 27, 2023, from https://www.science.org/doi/10.1126/science.1218811
\n \n\n\n Zaslavsky, N., Kemp, C., Regier, T., & Tishby, N. (2018). Efficient compression in color naming and its evolution. Proceedings of the National Academy of Sciences, 115(31), 7937\u20137942. https://doi.org/10.1073/pnas.1800521115
\n \n\n\n Deni\u0107, M., Steinert-Threlkeld, S., & Szymanik, J. (2022). Indefinite Pronouns Optimize the Simplicity/Informativeness Trade-Off. Cognitive Science, 46(5), e13142. https://doi.org/10.1111/cogs.13142
\n \n\n\n Steinert-Threlkeld, S. (2021). Quantifiers in Natural Language: Efficient Communication and Degrees of Semantic Universals. Entropy, 23(10), Article 10. https://doi.org/10.3390/e23101335
\n \n\n
\n\n\nLinks:
\n\n\n Imel, N. (2023). The evolution of efficient compression in signaling games. PsyArXiv. https://doi.org/10.31234/osf.io/b62de
\n \n\n\n Imel, N., & Steinert-Threlkeld, S. (2022). Modal semantic universals optimize the simplicity/informativeness trade-off. Semantics and Linguistic Theory, 1(0), Article 0. https://doi.org/10.3765/salt.v1i0.5346
\n \n\n\n Kemp, C., Xu, Y., & Regier, T. (2018). Semantic Typology and Efficient Communication. Annual Review of Linguistics, 4(1), 109\u2013128. https://doi.org/10.1146/annurev-linguistics-011817-045406
\n \n\n
\n"}, "ultk.effcomm": {"fullname": "ultk.effcomm", "modulename": "ultk.effcomm", "kind": "module", "doc": "Tools for measuring languages for communicative efficiency.
\n\nSubmodules divide the labor of a computational experiment performing an efficiency analysis of a language into several parts: generating and sampling the space of possible languages, measuring their properties, and determining which languages optimize efficient trade-offs w.r.t these properties.
\n\nThe altk.effcomm.sampling submodule implements several methods for generating hypothetically possible languages of a given type, by sampling from a set of possible expressions, or permuting the expression-meaning mapping of an existing language.
\n\nThe altk.effcomm.optimization submodule contains a general implementation of an evolutionary algorithm, which can be used to estimate a Pareto frontier of optimal solutions to an efficiency trade-off. It can also be used as a technique for randomly exploring the space of possible languages.
\n\nThe altk.effcomm.tradeoff submodule contains tools for measuring a pool of languages for various properties, finding which languages are Pareto dominant with respect to two properties, and setting attributes of the language objects for further analysis.
\n\nThe altk.effcomm.analysis submodule contains tools for performing numerical analyses and producing paradigmatic plots of languages in 2D trade-off space.
\n\nThe altk.effcomm.information submodule contains tools for information theory based analyses of the communicative efficiency of languages. It includes methods for Rate-Distortion style (including the Information Bottleneck) analyses.
\n\nThe altk.effcomm.agent submodule implements classes for constructing various speakers and listeners of a language. These are typically used in static analyses of informativity of a language, and are unified abstractions from the Rational Speech Act framework. They can also be used for dynamic analyses, however (see the signaling game example ).
\n\nThe altk.effcomm.informativity submodule implements tools for computing the literal or pragmatic informativity of a language, based on speaker/listener abstractions described above.
\n\nThe altk.effcomm.util submodule contains various helper functions for working with the probability distributions associated with ALTK abstractions.
\n"}, "ultk.effcomm.agent": {"fullname": "ultk.effcomm.agent", "modulename": "ultk.effcomm.agent", "kind": "module", "doc": "Classes for representing communicative agents, such as Senders and Receivers figuring in Lewis-Skyrms signaling games, literal and pragmatic agents in the Rational Speech Act framework, etc.
\n"}, "ultk.effcomm.agent.CommunicativeAgent": {"fullname": "ultk.effcomm.agent.CommunicativeAgent", "modulename": "ultk.effcomm.agent", "qualname": "CommunicativeAgent", "kind": "class", "doc": "
\n"}, "ultk.effcomm.agent.CommunicativeAgent.__init__": {"fullname": "ultk.effcomm.agent.CommunicativeAgent.__init__", "modulename": "ultk.effcomm.agent", "qualname": "CommunicativeAgent.__init__", "kind": "function", "doc": "An agent that uses a language to communicate, e.g. a RSA pragmatic agent or a Lewis-Skyrms signaler.
\n\nArguments: \n\n\nlanguage: a language to construct a agent to define the relation between meanings and expressions, which can be used to initialize the agent matrices (e.g. S or R).name: an optional string to name the communicative agent \n", "signature": "(language : ultk . language . language . Language , ** kwargs "}, "ultk.effcomm.agent.CommunicativeAgent.language": {"fullname": "ultk.effcomm.agent.CommunicativeAgent.language", "modulename": "ultk.effcomm.agent", "qualname": "CommunicativeAgent.language", "kind": "variable", "doc": "
\n"}, "ultk.effcomm.agent.CommunicativeAgent.shape": {"fullname": "ultk.effcomm.agent.CommunicativeAgent.shape", "modulename": "ultk.effcomm.agent", "qualname": "CommunicativeAgent.shape", "kind": "variable", "doc": "
\n"}, "ultk.effcomm.agent.CommunicativeAgent.weights": {"fullname": "ultk.effcomm.agent.CommunicativeAgent.weights", "modulename": "ultk.effcomm.agent", "qualname": "CommunicativeAgent.weights", "kind": "variable", "doc": "
\n", "annotation": ": numpy.ndarray"}, "ultk.effcomm.agent.CommunicativeAgent.normalized_weights": {"fullname": "ultk.effcomm.agent.CommunicativeAgent.normalized_weights", "modulename": "ultk.effcomm.agent", "qualname": "CommunicativeAgent.normalized_weights", "kind": "function", "doc": "Return the normalized weights of a CommunicativeAgent so that each row vector represents a probability distribution.
\n", "signature": "(self ) -> None : ", "funcdef": "def"}, "ultk.effcomm.agent.CommunicativeAgent.initialize_weights": {"fullname": "ultk.effcomm.agent.CommunicativeAgent.initialize_weights", "modulename": "ultk.effcomm.agent", "qualname": "CommunicativeAgent.initialize_weights", "kind": "function", "doc": "Initialize the agent's weight matrix.
\n\nArguments: \n\n\nweights: an np.ndarray representing the weights to initialize the agent with. By default None, and the agent's weights will be initialized uniformly.initial: {'ones', 'random'} a str reprsenting the initialization method to use. If 'ones' (default), initialize the weight matrix with np.ones. If 'random', initalize the weight matrix from np.random.uniform. \n", "signature": "(self , weights : numpy . ndarray = None , initial = 'ones' ) -> None : ", "funcdef": "def"}, "ultk.effcomm.agent.CommunicativeAgent.referent_to_index": {"fullname": "ultk.effcomm.agent.CommunicativeAgent.referent_to_index", "modulename": "ultk.effcomm.agent", "qualname": "CommunicativeAgent.referent_to_index", "kind": "function", "doc": "
\n", "signature": "(self , referent : ultk . language . semantics . Referent ) -> int : ", "funcdef": "def"}, "ultk.effcomm.agent.CommunicativeAgent.index_to_referent": {"fullname": "ultk.effcomm.agent.CommunicativeAgent.index_to_referent", "modulename": "ultk.effcomm.agent", "qualname": "CommunicativeAgent.index_to_referent", "kind": "function", "doc": "
\n", "signature": "(self , index : int ) -> ultk . language . semantics . Referent : ", "funcdef": "def"}, "ultk.effcomm.agent.CommunicativeAgent.expression_to_index": {"fullname": "ultk.effcomm.agent.CommunicativeAgent.expression_to_index", "modulename": "ultk.effcomm.agent", "qualname": "CommunicativeAgent.expression_to_index", "kind": "function", "doc": "
\n", "signature": "(self , expression : ultk . language . language . Expression ) -> int : ", "funcdef": "def"}, "ultk.effcomm.agent.CommunicativeAgent.index_to_expression": {"fullname": "ultk.effcomm.agent.CommunicativeAgent.index_to_expression", "modulename": "ultk.effcomm.agent", "qualname": "CommunicativeAgent.index_to_expression", "kind": "function", "doc": "
\n", "signature": "(self , index : int ) -> ultk . language . language . Expression : ", "funcdef": "def"}, "ultk.effcomm.agent.CommunicativeAgent.strategy_to_indices": {"fullname": "ultk.effcomm.agent.CommunicativeAgent.strategy_to_indices", "modulename": "ultk.effcomm.agent", "qualname": "CommunicativeAgent.strategy_to_indices", "kind": "function", "doc": "Maps communicative strategies to weights.
\n\nGiven a expression and referent, access the corresponding weight coordinate.
\n\nArguments: \n\n\nstrategy: a dict of the form {\"referent\": Referent, \"expression\": expression} representing an instance of communicative behavior, which we may call a communicative strategy for this agent. \n", "signature": "(self , strategy : dict [ str , typing . Any ] ) -> tuple [ int ] : ", "funcdef": "def"}, "ultk.effcomm.agent.CommunicativeAgent.sample_strategy": {"fullname": "ultk.effcomm.agent.CommunicativeAgent.sample_strategy", "modulename": "ultk.effcomm.agent", "qualname": "CommunicativeAgent.sample_strategy", "kind": "function", "doc": "Sample a communicative strategy (e.g., a word for Speaker's intended referent, or interpretation for Listener's heard word) by uniformly sampling from a row vector of the agent's weight matrix specified by the index.
\n\nArguments: \n\n\nindex: the integer index representing a row of the weight matrix. \n\nReturns: \n\n\n the integer index of the agent's choice
\n \n", "signature": "(self , index : int ) -> int : ", "funcdef": "def"}, "ultk.effcomm.agent.CommunicativeAgent.to_language": {"fullname": "ultk.effcomm.agent.CommunicativeAgent.to_language", "modulename": "ultk.effcomm.agent", "qualname": "CommunicativeAgent.to_language", "kind": "function", "doc": "Get a language from the agent, representing its current (possibly learned) communicative behavior.
\n\nThis function uses: \n\n\n \n the agent's weight matrix, \n the set of expression forms, and \n the set of referents \n \n \n\nfrom the language the agent was initialized with to generate a new language accurately reflecting the new expression meanings, e.g. how the agent interprets expressions as meaning zero or more referents.
\n\nArguments: \n\n\nthreshold: a float in [0,1] representing the cutoff for determining if a meaning (referent) can be communicated by a expression. Because weights are not initialized to 0, it is a good idea to set nonzero values as the threshold. \n\nReturns: \n\n\n a Language corresponding to the form-meaning mapping defined by the communicative agent's weights.
\n \n", "signature": "(\tself , \tdata : dict = { 'complexity' : None , 'accuracy' : None } , \tthreshold : float = 0.1 ) -> ultk . language . language . Language : ", "funcdef": "def"}, "ultk.effcomm.agent.Speaker": {"fullname": "ultk.effcomm.agent.Speaker", "modulename": "ultk.effcomm.agent", "qualname": "Speaker", "kind": "class", "doc": "
\n", "bases": "CommunicativeAgent"}, "ultk.effcomm.agent.Speaker.__init__": {"fullname": "ultk.effcomm.agent.Speaker.__init__", "modulename": "ultk.effcomm.agent", "qualname": "Speaker.__init__", "kind": "function", "doc": "An agent that uses a language to communicate, e.g. a RSA pragmatic agent or a Lewis-Skyrms signaler.
\n\nArguments: \n\n\nlanguage: a language to construct a agent to define the relation between meanings and expressions, which can be used to initialize the agent matrices (e.g. S or R).name: an optional string to name the communicative agent \n", "signature": "(language : ultk . language . language . Language , ** kwargs "}, "ultk.effcomm.agent.Speaker.S": {"fullname": "ultk.effcomm.agent.Speaker.S", "modulename": "ultk.effcomm.agent", "qualname": "Speaker.S", "kind": "variable", "doc": "
\n", "annotation": ": numpy.ndarray"}, "ultk.effcomm.agent.Speaker.normalized_weights": {"fullname": "ultk.effcomm.agent.Speaker.normalized_weights", "modulename": "ultk.effcomm.agent", "qualname": "Speaker.normalized_weights", "kind": "function", "doc": "Get the normalized weights of a Speaker.
\n\nEach row vector represents a conditional probability distribution over expressions, P(e | m).
\n", "signature": "(self ) -> numpy . ndarray : ", "funcdef": "def"}, "ultk.effcomm.agent.Listener": {"fullname": "ultk.effcomm.agent.Listener", "modulename": "ultk.effcomm.agent", "qualname": "Listener", "kind": "class", "doc": "
\n", "bases": "CommunicativeAgent"}, "ultk.effcomm.agent.Listener.__init__": {"fullname": "ultk.effcomm.agent.Listener.__init__", "modulename": "ultk.effcomm.agent", "qualname": "Listener.__init__", "kind": "function", "doc": "An agent that uses a language to communicate, e.g. a RSA pragmatic agent or a Lewis-Skyrms signaler.
\n\nArguments: \n\n\nlanguage: a language to construct a agent to define the relation between meanings and expressions, which can be used to initialize the agent matrices (e.g. S or R).name: an optional string to name the communicative agent \n", "signature": "(language : ultk . language . language . Language , ** kwargs "}, "ultk.effcomm.agent.Listener.R": {"fullname": "ultk.effcomm.agent.Listener.R", "modulename": "ultk.effcomm.agent", "qualname": "Listener.R", "kind": "variable", "doc": "
\n", "annotation": ": numpy.ndarray"}, "ultk.effcomm.agent.Listener.normalized_weights": {"fullname": "ultk.effcomm.agent.Listener.normalized_weights", "modulename": "ultk.effcomm.agent", "qualname": "Listener.normalized_weights", "kind": "function", "doc": "Normalize the weights of a Listener so that each row vector for the heard expression e represents a conditional probability distribution over referents P(m | e).
\n", "signature": "(self ) -> numpy . ndarray : ", "funcdef": "def"}, "ultk.effcomm.agent.LiteralSpeaker": {"fullname": "ultk.effcomm.agent.LiteralSpeaker", "modulename": "ultk.effcomm.agent", "qualname": "LiteralSpeaker", "kind": "class", "doc": "A literal speaker chooses utterances without any reasoning about other agents. The literal speaker's conditional probability distribution P(e|m) is uniform over all expressions that can be used to communicate a particular meaning. This is in contrast to a pragmatic speaker, whose conditional distribution is not uniform in this way, but instead biased towards choosing expressions that are less likely to be misinterpreted by some listener.
\n", "bases": "Speaker"}, "ultk.effcomm.agent.LiteralSpeaker.__init__": {"fullname": "ultk.effcomm.agent.LiteralSpeaker.__init__", "modulename": "ultk.effcomm.agent", "qualname": "LiteralSpeaker.__init__", "kind": "function", "doc": "An agent that uses a language to communicate, e.g. a RSA pragmatic agent or a Lewis-Skyrms signaler.
\n\nArguments: \n\n\nlanguage: a language to construct a agent to define the relation between meanings and expressions, which can be used to initialize the agent matrices (e.g. S or R).name: an optional string to name the communicative agent \n", "signature": "(language : ultk . language . language . Language , ** kwargs "}, "ultk.effcomm.agent.LiteralSpeaker.S": {"fullname": "ultk.effcomm.agent.LiteralSpeaker.S", "modulename": "ultk.effcomm.agent", "qualname": "LiteralSpeaker.S", "kind": "variable", "doc": "
\n", "annotation": ": numpy.ndarray"}, "ultk.effcomm.agent.LiteralListener": {"fullname": "ultk.effcomm.agent.LiteralListener", "modulename": "ultk.effcomm.agent", "qualname": "LiteralListener", "kind": "class", "doc": "A naive literal listener interprets utterances without any reasoning about other agents. Its conditional probability distribution P(m|e) for guessing meanings is uniform over all meanings that can be denoted by the particular expression heard. This is in contrast to a pragmatic listener, whose conditional distribution is biased to guess meanings that a pragmatic speaker most likely intended.
\n", "bases": "Listener"}, "ultk.effcomm.agent.LiteralListener.__init__": {"fullname": "ultk.effcomm.agent.LiteralListener.__init__", "modulename": "ultk.effcomm.agent", "qualname": "LiteralListener.__init__", "kind": "function", "doc": "An agent that uses a language to communicate, e.g. a RSA pragmatic agent or a Lewis-Skyrms signaler.
\n\nArguments: \n\n\nlanguage: a language to construct a agent to define the relation between meanings and expressions, which can be used to initialize the agent matrices (e.g. S or R).name: an optional string to name the communicative agent \n", "signature": "(language : ultk . language . language . Language , ** kwargs "}, "ultk.effcomm.agent.LiteralListener.R": {"fullname": "ultk.effcomm.agent.LiteralListener.R", "modulename": "ultk.effcomm.agent", "qualname": "LiteralListener.R", "kind": "variable", "doc": "
\n", "annotation": ": numpy.ndarray"}, "ultk.effcomm.agent.PragmaticSpeaker": {"fullname": "ultk.effcomm.agent.PragmaticSpeaker", "modulename": "ultk.effcomm.agent", "qualname": "PragmaticSpeaker", "kind": "class", "doc": "A pragmatic speaker chooses utterances based on how a listener would interpret them. A pragmatic speaker may be initialized with any kind of listener, e.g. literal or pragmatic -- meaning the recursive reasoning can be modeled up to arbitrary depth.
\n", "bases": "Speaker"}, "ultk.effcomm.agent.PragmaticSpeaker.__init__": {"fullname": "ultk.effcomm.agent.PragmaticSpeaker.__init__", "modulename": "ultk.effcomm.agent", "qualname": "PragmaticSpeaker.__init__", "kind": "function", "doc": "Initialize the |M|-by-|E| matrix, S, corresponding to the pragmatic speaker's conditional probability distribution over expressions given meanings.
\n\nThe pragmatic speaker chooses expressions to communicate their intended meaning according to:
\n\n$P(e | m) \\propto \\exp(t * u(e,m))$
\n\nwhere $t \\in [0,1]$ is a temperature parameter and utility $u$ is defined
\n\n$u(e , m) := \\log(P_{\\text{Listener}}(m | e))$
\n\nArguments: \n\n\nlanguage: the language with |M| meanings and |E| expressions defining the size of S.listener: a communicative agent storing a matrix R representing the conditional distribution over expressions given meanings.temperature: a float \\in [0,1], representing how `optimally rational' the pragmatic speaker is; 1.0 is chosen when no particular assumptions about rationality are made. \n", "signature": "(\tlanguage : ultk . language . language . Language , \tlistener : ultk . effcomm . agent . Listener , \ttemperature : float = 1.0 , \t** kwargs ) "}, "ultk.effcomm.agent.PragmaticSpeaker.S": {"fullname": "ultk.effcomm.agent.PragmaticSpeaker.S", "modulename": "ultk.effcomm.agent", "qualname": "PragmaticSpeaker.S", "kind": "variable", "doc": "
\n", "annotation": ": numpy.ndarray"}, "ultk.effcomm.agent.PragmaticListener": {"fullname": "ultk.effcomm.agent.PragmaticListener", "modulename": "ultk.effcomm.agent", "qualname": "PragmaticListener", "kind": "class", "doc": "A pragmatic listener interprets utterances based on their expectations about a pragmatic speaker's decisions. A pragmatic listener may be initialized with any kind of speaker, e.g. literal or pragmatic -- meaning the recursive reasoning can be modeled up to arbitrary depth.
\n", "bases": "Listener"}, "ultk.effcomm.agent.PragmaticListener.__init__": {"fullname": "ultk.effcomm.agent.PragmaticListener.__init__", "modulename": "ultk.effcomm.agent", "qualname": "PragmaticListener.__init__", "kind": "function", "doc": "Initialize the |E|-by-|M| matrix, R, corresponding to the pragmatic listener's conditional probability distribution over meanings given expressions.
\n\nThe pragmatic listener chooses meanings as their best guesses of the expression they heard according to:
\n\n$P(m | e) \\propto P_{\\text{PragmaticSpeaker}}(e | m)$
\n\nArguments: \n\n\nlanguage: the language with |M| meanings and |E| expressions defining the size of R.speaker: a communicative agent storing a matrix S representing the conditional distribution over expressions given meanings.prior: a diagonal matrix of size |M|-by-|M| representing the communicative need probabilities for meanings. \n", "signature": "(\tlanguage : ultk . language . language . Language , \tspeaker : ultk . effcomm . agent . Speaker , \tprior : numpy . ndarray , \t** kwargs ) "}, "ultk.effcomm.agent.PragmaticListener.R": {"fullname": "ultk.effcomm.agent.PragmaticListener.R", "modulename": "ultk.effcomm.agent", "qualname": "PragmaticListener.R", "kind": "variable", "doc": "
\n", "annotation": ": numpy.ndarray"}, "ultk.effcomm.agent.BayesianListener": {"fullname": "ultk.effcomm.agent.BayesianListener", "modulename": "ultk.effcomm.agent", "qualname": "BayesianListener", "kind": "class", "doc": "A Bayesian reciever chooses an interpretation according to p(meaning | word), where
\n\nBUG: This is extremely misleading since we basically only use this function for IB, and IB assumes a DETERMINISTIC bayes-derived listener. \n\n$P(m | w) = \\frac{P(M | W) \\cdot P(M)} { P(W) }$
\n\nFurthermore, we sometimes require that each word w is deterministically interpreted as meaning $\\hat{m}$ as follows:
\n\nBUG: This says nothing about determinism. \n\n$\\hat{m}_{w}(u) = \\sum_m p(m|w) \\cdot m(u)$
\n\nSee ultk.effcomm.information for more details.
\n", "bases": "Listener"}, "ultk.effcomm.agent.BayesianListener.__init__": {"fullname": "ultk.effcomm.agent.BayesianListener.__init__", "modulename": "ultk.effcomm.agent", "qualname": "BayesianListener.__init__", "kind": "function", "doc": "An agent that uses a language to communicate, e.g. a RSA pragmatic agent or a Lewis-Skyrms signaler.
\n\nArguments: \n\n\nlanguage: a language to construct a agent to define the relation between meanings and expressions, which can be used to initialize the agent matrices (e.g. S or R).name: an optional string to name the communicative agent \n", "signature": "(\tspeaker : ultk . effcomm . agent . Speaker , \tprior : numpy . ndarray , \tname : str = None ) "}, "ultk.effcomm.analysis": {"fullname": "ultk.effcomm.analysis", "modulename": "ultk.effcomm.analysis", "kind": "module", "doc": "Functions for analyzing and formatting the results of the simplicity/informativeness trade-off.
\n"}, "ultk.effcomm.analysis.get_dataframe": {"fullname": "ultk.effcomm.analysis.get_dataframe", "modulename": "ultk.effcomm.analysis", "qualname": "get_dataframe", "kind": "function", "doc": "Get a pandas DataFrame for a list of languages containing efficient communication data.
\n\nArguments: \n\n\nlanguages: the list of languages to map into a dataframe.columns: the list of keys to a language's data dictionary attribute, which will comprise the columns of the resulting dataframe. By default will use all items of each language's data dictionary.subset: the columns to subset for duplicatesduplicates: {\"drop\", \"count\", \"leave\"} whether to drop, count, or do nothing with duplicates. By default is set to \"leave\" which will leave duplicates in the dataframe. \n\nReturns: \n\n\n \n data: a pandas DataFrame with rows as individual languages, with the columns specifying their data. \n \n \n", "signature": "(\tlanguages : list [ ultk . language . language . Language ] , \tcolumns : list [ str ] = None , \tsubset : list [ str ] = [ 'complexity' , 'comm_cost' ] , \tduplicates : str = 'leave' ) -> pandas . core . frame . DataFrame : ", "funcdef": "def"}, "ultk.effcomm.analysis.pearson_analysis": {"fullname": "ultk.effcomm.analysis.pearson_analysis", "modulename": "ultk.effcomm.analysis", "qualname": "pearson_analysis", "kind": "function", "doc": "Measures pearson correlation coefficient for naturalness with a property.
\n\nUse nonparametric bootstrap for confidence intervals.
\n\nArguments: \n\n\ndata: a DataFrame representing the pool of measured languagespredictor: a string representing the column to measure pearson r withproperty: a string representing a column to measure pearson r with the predictor columnnum_bootstrap_samples: how many samples to bootstrap from the original data \n\nReturns: \n\n\n a dict of the pearson correlation coefficient for the predictor and the property, and bootstrapped confidence intervals for this coefficient, e.g.
\n\n{\n\"rho\": (a float between -1 and 1),\n\"confidence_intervals\": (a pandas Dataframe with the columns [\n 'bootstrap_sample_percent', 'low', 'high'\n])\n}\n \n", "signature": "(\tdata , \tpredictor : str , \tproperty : str , \tnum_bootstrap_samples = 100 ) -> dict [ str , typing . Any ] : ", "funcdef": "def"}, "ultk.effcomm.analysis.trade_off_means": {"fullname": "ultk.effcomm.analysis.trade_off_means", "modulename": "ultk.effcomm.analysis", "qualname": "trade_off_means", "kind": "function", "doc": "Get a dataframe with the mean tradeoff data.
\n\nArguments: \n\n\nname: a str representing the subset of the population to observe mean properties for, e.g. \"natural\" or \"population\".df: a pandas DataFrame containing data of a language population to take the means of.prperties: the properties to take means of, corresponding to columns of df. \n\nExamples:
\n\n\n
>>> natural_means = trade_off_means ( "natural_means" , natural_data , properties ) \n>>> population_means = trade_off_means ( "population_means" , data , properties ) \n>>> means_df = pd . concat ([ natural_means , dlsav_means , population_means ]) . set_index ( "name" ) \n>>> means_df \n simplicity complexity informativity optimality \n name \n natural_means 0.772222 16.4000 0.746296 0.952280 \n population_means 0.681068 22.9631 0.525118 0.832010 \n\n
(\tname : str , \tdf : pandas . core . frame . DataFrame , \tproperties : list ) -> pandas . core . frame . DataFrame : ", "funcdef": "def"}, "ultk.effcomm.analysis.trade_off_ttest": {"fullname": "ultk.effcomm.analysis.trade_off_ttest", "modulename": "ultk.effcomm.analysis", "qualname": "trade_off_ttest", "kind": "function", "doc": "Get a dataframe with a single-samples t-test results for a subpopulation against the full population.
\n\nThis is useful if we want to compare the optimality of natural languages to the full population of languages in an experiment. Because the property of 'being a natural language' is categorical, we use a single-samples T test.
\n\nArguments: \n\n\nsub_population: a pandas DataFrame representing a subset of the population to take ttests against the full language population for properties.population_means: a dict containing properties as keys and the mean value of the full language population for that property.properties: a list of strings corresponding to columns of the sub_population DataFrame and keys of the population_means dict. \n\nExamples: \n\n\n \n
>>> df = trade_off_ttest ( natural_data , population_means , properties ) \n>>> df \n simplicity complexity informativity optimality \n stat \n t-statistic 4.101937 -4.101937 3.126855 4.031027 \n Two-sided p-value 0.014830 0.014830 0.035292 0.015720 \n\n
\n", "signature": "(\tsub_population : pandas . core . frame . DataFrame , \tpopulation_means : dict , \tproperties : list ) -> pandas . core . frame . DataFrame : ", "funcdef": "def"}, "ultk.effcomm.information": {"fullname": "ultk.effcomm.information", "modulename": "ultk.effcomm.information", "kind": "module", "doc": "Helper functions for Rate-Distortion based (including Information Bottleneck) efficient communication analyses.
\n"}, "ultk.effcomm.information.information_rate": {"fullname": "ultk.effcomm.information.information_rate", "modulename": "ultk.effcomm.information", "qualname": "information_rate", "kind": "function", "doc": "Compute the information rate / complexity of the encoder q(w|m) as $I[W:M]$.
\n", "signature": "(source : numpy . ndarray , encoder : numpy . ndarray ) -> float : ", "funcdef": "def"}, "ultk.effcomm.information.get_rd_curve": {"fullname": "ultk.effcomm.information.get_rd_curve", "modulename": "ultk.effcomm.information", "qualname": "get_rd_curve", "kind": "function", "doc": "Use the Blahut Arimoto algorithm to obtain a list of (rate, distortion) points.
\n", "signature": "(\tprior : numpy . ndarray , \tdist_mat : numpy . ndarray , \tbetas : numpy . ndarray = None ) -> list [ tuple [ float ]] : ", "funcdef": "def"}, "ultk.effcomm.information.expected_distortion": {"fullname": "ultk.effcomm.information.expected_distortion", "modulename": "ultk.effcomm.information", "qualname": "expected_distortion", "kind": "function", "doc": "$D[X, \\hat{X}] = \\sum_x p(x) \\sum_{\\hat{x}} p(\\hat{x}|x) \\cdot d(x, \\hat{x})$
\n", "signature": "(\tp_x : numpy . ndarray , \tp_xhat_x : numpy . ndarray , \tdist_mat : numpy . ndarray ) -> float : ", "funcdef": "def"}, "ultk.effcomm.information.compute_rate_distortion": {"fullname": "ultk.effcomm.information.compute_rate_distortion", "modulename": "ultk.effcomm.information", "qualname": "compute_rate_distortion", "kind": "function", "doc": "Compute the information rate $I(X;\\hat{X})$ and total distortion $D[X, \\hat{X}]$ of a joint distribution defind by $P(X)$ and $P(\\hat{X}|X)$.
\n\nArguments: \n\n\np_x: array of shape |X| the prior probability of an input symbol (i.e., the source)p_xhat_x: array of shape (|X|, |X_hat|) the probability of an output symbol given the inputdist_mat: array of shape (|X|, |X_hat|) representing the distoriton matrix between the input alphabet and the reconstruction alphabet. \n\nReturns: \n\n\n a (rate, distortion) tuple containing the information rate (in bits) of compressing X into X_hat and the expected distortion between X, X_hat
\n \n", "signature": "(p_x , p_xhat_x , dist_mat ) -> tuple [ numpy . ndarray ] : ", "funcdef": "def"}, "ultk.effcomm.information.blahut_arimoto": {"fullname": "ultk.effcomm.information.blahut_arimoto", "modulename": "ultk.effcomm.information", "qualname": "blahut_arimoto", "kind": "function", "doc": "Compute the rate-distortion function of an i.i.d distribution
\n\nArguments: \n\n\ndist_mat: array of shape (|X|, |X_hat|) representing the distortion matrix between the input alphabet and the reconstruction alphabet. dist_mat[i,j] = dist(x[i],x_hat[j]). In this context, X is a random variable representing the a speaker's meaning (target referent), and X_hat is a random variable representing a listener's meaning (guessed referent).p_x: (1D array of shape |X|) representing the probability mass function of the source. In this context, the prior over states of nature.beta: (scalar) the slope of the rate-distoriton function at the point where evaluation is requiredmax_it: max number of iterationseps: accuracy required by the algorithm: the algorithm stops if there is no change in distoriton value of more than 'eps' between consequtive iterationsignore_converge: whether to run the optimization until max_it, ignoring the stopping criterion specified by eps. \n\nReturns: \n\n\n a dict of the form
\n\n{\n 'final': a tuple of (rate, distortion) values. This is the rate (in bits) of compressing X into X_hat, and distortion between X, X_hat\n\n 'trajectory': a list of the (rate, distortion) points discovered during optimization\n}\n \n", "signature": "(\tdist_mat : numpy . ndarray , \tp_x : numpy . ndarray , \tbeta : float , \tmax_it : int = 200 , \teps : float = 1e-05 , \tignore_converge : bool = False ) -> tuple [ float ] : ", "funcdef": "def"}, "ultk.effcomm.information.get_ib_curve": {"fullname": "ultk.effcomm.information.get_ib_curve", "modulename": "ultk.effcomm.information", "qualname": "get_ib_curve", "kind": "function", "doc": "Get a list of (complexity, accuracy) or (complexity, distortion) points. A minimal wrapper of get_bottleneck.
\n\nArguments: \n\n\nprior: array of shape |meanings|meaning_dists: array of shape (|meanings|, |meanings|) representing the distribution over world states given meanings.curve_type: {'informativity', 'comm_cost'} specifies whether to return the (classic) IB axes of informativity vs. complexity, or the more Rate-Distortion Theory aligned axes of comm_cost vs. complexity. The latter can be obtained easily from the former by subtracting each informativity value from I[M:U], which is a constant for all languages in the same domain.maxbeta: the maximum value of beta to use to compute the curve.minbeta: the minimum value of beta to use.numbeta: the number of (equally-spaced) beta values to consider to compute the curve.processes: number of cpu threads to run in parallel (default = 1) \n\nReturns: \n\n\n an array of shape (num_points, 2) representing the list of (accuracy/comm_cost, complexity) points on the information plane.
\n \n", "signature": "(\tprior : numpy . ndarray , \tmeaning_dists : numpy . ndarray , \tmaxbeta : float , \tminbeta : float , \tnumbeta : float , \tprocesses : int = 1 , \tcurve_type : str = 'informativity' ) -> tuple [ float ] : ", "funcdef": "def"}, "ultk.effcomm.information.get_bottleneck": {"fullname": "ultk.effcomm.information.get_bottleneck", "modulename": "ultk.effcomm.information", "qualname": "get_bottleneck", "kind": "function", "doc": "Compute the IB curve bound (I[M:W] vs. I[W:U]). We use the embo package, which has support for smoothing any non-monotonicity in the bound resulting from BA optimization getting stuck in local minima.
\n\nArguments: \n\n\nprior: array of shape |meanings|meaning_dists: array of shape (|meanings|, |meanings|) representing the distribution over world states given meanings.curve_type: {'informativity', 'comm_cost'} specifies whether to return the (classic) IB axes of informativity vs. complexity, or the more Rate-Distortion Theory aligned axes of comm_cost vs. complexity. The comm_cost can be obtained easily from informativity by subtracting each informativity value from I[M:U], which is a constant for all languages in the same domain.maxbeta: the maximum value of beta to use to compute the curve.minbeta: the minimum value of beta to use.numbeta: the number of (equally-spaced) beta values to consider to compute the curve.processes: number of cpu threads to run in parallel (default = 1) \n\nReturns: \n\n\n a dict containing the coordinates and encoders corresponding to IB optima, of the form
\n\n{\n\"encoders\": an array of shape `(num_meanings, num_words)`,\n\n\"coordinates\": a tuple of arrays `(complexity, accuracy, comm_cost)` each of shape (`numbeta`,)\n\"beta\": an array of shape (`numbeta`,) corresponding to the actually used betas after non-monotonicity corrections.\n}\n \n", "signature": "(\tprior : numpy . ndarray , \tmeaning_dists : numpy . ndarray , \tmaxbeta : float , \tminbeta : float , \tnumbeta : float , \tprocesses : int = 1 ) -> numpy . ndarray : ", "funcdef": "def"}, "ultk.effcomm.information.ib_complexity": {"fullname": "ultk.effcomm.information.ib_complexity", "modulename": "ultk.effcomm.information", "qualname": "ib_complexity", "kind": "function", "doc": "Compute the IB encoder complexity of a language $I[M:W]$.
\n", "signature": "(language : ultk . language . language . Language , prior : numpy . ndarray ) -> float : ", "funcdef": "def"}, "ultk.effcomm.information.ib_informativity": {"fullname": "ultk.effcomm.information.ib_informativity", "modulename": "ultk.effcomm.information", "qualname": "ib_informativity", "kind": "function", "doc": "Compute the expected informativity (accuracy) $I[W:U]$ of a lexicon.
\n\nArguments: \n\n\nlanguage: the Language to measure for informativityprior: communicative need distributionmeaning_dists: array of shape (|meanings|, |meanings|) representing the distribution over world states given meanings. \n\nReturns: \n\n\n the informativity of the language I[W:U] in bits.
\n \n", "signature": "(\tlanguage : ultk . language . language . Language , \tprior : numpy . ndarray , \tmeaning_dists : numpy . ndarray ) -> float : ", "funcdef": "def"}, "ultk.effcomm.information.ib_comm_cost": {"fullname": "ultk.effcomm.information.ib_comm_cost", "modulename": "ultk.effcomm.information", "qualname": "ib_comm_cost", "kind": "function", "doc": "Compute the IB communicative cost, i.e. expected KL-divergence betweeen speaker and listener meanings, for a language.
\n\nArguments: \n\n\nlanguage: the Language to measure for communicative costprior: communicative need distributionmeaning_dists: array of shape (|meanings|, |meanings|) representing the distribution over world states given meanings. \n\nReturns: \n\n\n the communicative cost, $\\mathbb{E}[D_{KL}[M || \\hat{M}]] = I[M:U] - I[W:U]$ in bits.
\n \n", "signature": "(\tlanguage : ultk . language . language . Language , \tprior : numpy . ndarray , \tmeaning_dists : numpy . ndarray ) -> float : ", "funcdef": "def"}, "ultk.effcomm.information.language_to_ib_encoder_decoder": {"fullname": "ultk.effcomm.information.language_to_ib_encoder_decoder", "modulename": "ultk.effcomm.information", "qualname": "language_to_ib_encoder_decoder", "kind": "function", "doc": "Convert a Language, a mapping of words to meanings, to IB encoder, q(w|m) and IB decoder q(m|w).
\n\nArguments: \n\n\nlanguage: the lexicon from which to infer a speaker (encoder).prior: communicative need distribution \n\nReturns: \n\n\n a dict of the form\n {\n \"encoder\": np.ndarray of shape (|meanings|, |words|),\n \"decoder\": np.ndarray of shape (|words|, |meanings|),\n }
\n \n", "signature": "(\tlanguage : ultk . language . language . Language , \tprior : numpy . ndarray ) -> dict [ str , numpy . ndarray ] : ", "funcdef": "def"}, "ultk.effcomm.information.ib_accuracy": {"fullname": "ultk.effcomm.information.ib_accuracy", "modulename": "ultk.effcomm.information", "qualname": "ib_accuracy", "kind": "function", "doc": "Return the accuracy of the lexicon I[W:U]
\n\nArguments: \n\n\nencoder: array of shape (|M|, |W|) representing P(W | M)decoder: array of shape (|W|, |M|) representing P(M | W)meaning_dists: array of shape (|M|, |U|) representing P(U | M)prior: array of shape |M| representing P(M) \n\nReturns: \n\n\n the accuracy of the lexicon I[W:U]
\n \n", "signature": "(\tencoder : numpy . ndarray , \tprior : numpy . ndarray , \tmeaning_dists : numpy . ndarray ) -> float : ", "funcdef": "def"}, "ultk.effcomm.information.ib_distortion": {"fullname": "ultk.effcomm.information.ib_distortion", "modulename": "ultk.effcomm.information", "qualname": "ib_distortion", "kind": "function", "doc": "Return the IB distortion measure E[DKL[ M || M_hat ]]
\n\nArguments: \n\n\nencoder: array of shape (|M|, |W|) representing P(W | M)decoder: array of shape (|W|, |M|) representing P(M | W)meaning_dists: array of shape (|M|, |U|) representing P(U | M)prior: array of shape |M| representing P(M) \n\nReturns: \n\n\n the distortion E[DKL[ M || M_hat ]] = I[M:U] - I[W:U]
\n \n", "signature": "(\tencoder : numpy . ndarray , \tprior : numpy . ndarray , \tmeaning_dists : numpy . ndarray ) -> float : ", "funcdef": "def"}, "ultk.effcomm.information.ib_encoder_to_point": {"fullname": "ultk.effcomm.information.ib_encoder_to_point", "modulename": "ultk.effcomm.information", "qualname": "ib_encoder_to_point", "kind": "function", "doc": "Return (complexity, accuracy, comm_cost) IB coordinates.
\n\nArguments: \n\n\nmeaning_dists: array of shape (|meanings|, |meanings|) representing the distribution over world states given meanings.prior: array of shape |M| representing the cognitive sourceencoder: array of shape (|M|, |W|) representing P(W | M)decoder: array of shape (|W|, |M|) representing P(M | W). By default is None, and the Bayesian optimal decoder will be inferred. \n", "signature": "(\tmeaning_dists : numpy . ndarray , \tprior : numpy . ndarray , \tencoder : numpy . ndarray , \tdecoder : numpy . ndarray = None ) -> tuple [ float ] : ", "funcdef": "def"}, "ultk.effcomm.information.ib_optimal_decoder": {"fullname": "ultk.effcomm.information.ib_optimal_decoder", "modulename": "ultk.effcomm.information", "qualname": "ib_optimal_decoder", "kind": "function", "doc": "Compute the bayesian optimal decoder. See https://github.com/nogazs/ib-color-naming/blob/master/src/ib_naming_model.py#L40
\n\nArguments: \n\n\nencoder: array of shape (|words|, |meanings|)prior: array of shape (|meanings|,)meaning_dists: array of shape (|meanings|, |meanings|) \n\nReturns: \n\n\n array of shape (|words|, |meanings|) representing the 'optimal' deterministic decoder
\n \n", "signature": "(\tencoder : numpy . ndarray , \tprior : numpy . ndarray , \tmeaning_dists : numpy . ndarray ) -> numpy . ndarray : ", "funcdef": "def"}, "ultk.effcomm.informativity": {"fullname": "ultk.effcomm.informativity", "modulename": "ultk.effcomm.informativity", "kind": "module", "doc": "Functions for measuring informativity in efficient communication analyses of languages.
\n"}, "ultk.effcomm.informativity.indicator_utility": {"fullname": "ultk.effcomm.informativity.indicator_utility", "modulename": "ultk.effcomm.informativity", "qualname": "indicator_utility", "kind": "function", "doc": "Indicator utility function, i.e. delta. Returns 1.0 iff ref1 equals ref2.
\n", "signature": "(\tref1 : ultk . language . semantics . Referent , \tref2 : ultk . language . semantics . Referent ) -> float : ", "funcdef": "def"}, "ultk.effcomm.informativity.informativity": {"fullname": "ultk.effcomm.informativity.informativity", "modulename": "ultk.effcomm.informativity", "qualname": "informativity", "kind": "function", "doc": "The informativity of a language is identified with the successful communication between a speaker and a listener.
\n\nThis function is a wrapper for communicative_success.
\n\nArguments: \n\n\nlanguage: the language to compute informativity of.prior: a probability distribution representing communicative need (frequency) for Referents.utility: a function representing the usefulness of listener guesses about speaker Referents, e.g. Referent similarity. To reward only exact recovery of meanings, use the indicator function (default).kind: {\"literal, pragmatic\"} Whether to measure informativity using literal or pragmatic agents, as canonically described in the Rational Speech Act framework. The default is \"literal\". \n\nConcepts :\n The speaker can be thought of as a conditional distribution over expressions given meanings. The listener is likewise a conditional distribution over meanings given expressions. The communicative need, or cognitive source, is a prior probability over meanings representing how frequently agents need to use certain meanings in communication. The utility function represents the similarity, or appropriateness, of the listener's guess m' about the speaker's intended meaning m.
\n\nFormula :\n The informativity of a language $L$ with meaning space $M$ is defined:
\n\n$I(L) := \\sum_{m \\in M} p(m) \\sum_{i \\in L} p(i|m) \\sum_{\\hat{m} \\in i} p(\\hat{m}|i) \\cdot u(m, \\hat{m})$
\n\nBounds :\n A perfectly informative (=1.0) language can be constructed with a exactly one expression for each meaning.
\n\nFor u() = indicator(), every language has nonzero informativity because a language must contain at least one expression, and an expression must contain at least one meaning.\n(\tlanguage : ultk . language . language . Language , \tprior : numpy . ndarray , \tutility : Callable [[ ultk . language . semantics . Referent , ultk . language . semantics . Referent ], float ] = < function indicator_utility > , \tagent_type : str = 'literal' ) -> float : ", "funcdef": "def"}, "ultk.effcomm.informativity.communicative_success": {"fullname": "ultk.effcomm.informativity.communicative_success", "modulename": "ultk.effcomm.informativity", "qualname": "communicative_success", "kind": "function", "doc": "Helper function to compute the literal informativity of a language.
\n\n$I(L) = \\sum_{m, \\hat{m}} P(m, \\hat{m}) \\cdot u(m, \\hat{m})$
\n\n$ = \\sum_{m \\in M} p(m) \\sum_{i \\in L} p(i|m) \\sum_{\\hat{m} \\in i} p(\\hat{m} |i) \\cdot u(m, m')$
\n\n$ = \\sum \\text{diag}(p)SR \\odot U $
\n\nFor more details, see docs/vectorized_informativity .
\n\nArguments: \n\n\nspeaker: a literal or pragmatic speaker, containing a matrix S for P(e | m)listener: a literal or pragmatic listener, containing a matrix R for P(m | e)prior: p(m), distribution over meanings representing communicative needutility: a function u(m, m') representing similarity of meanings, or pair-wise usefulness of listener guesses about speaker meanings. \n", "signature": "(\tspeaker : ultk . effcomm . agent . Speaker , \tlistener : ultk . effcomm . agent . Listener , \tprior : numpy . ndarray , \tutility : Callable [[ ultk . language . semantics . Referent , ultk . language . semantics . Referent ], float ] ) -> float : ", "funcdef": "def"}, "ultk.effcomm.optimization": {"fullname": "ultk.effcomm.optimization", "modulename": "ultk.effcomm.optimization", "kind": "module", "doc": "Classes and functions for generating languages that optimize the simplicity/informativeness trade-off, e.g. via an iterative evolutionary algorithm.
\n"}, "ultk.effcomm.optimization.Mutation": {"fullname": "ultk.effcomm.optimization.Mutation", "modulename": "ultk.effcomm.optimization", "qualname": "Mutation", "kind": "class", "doc": "
\n"}, "ultk.effcomm.optimization.Mutation.precondition": {"fullname": "ultk.effcomm.optimization.Mutation.precondition", "modulename": "ultk.effcomm.optimization", "qualname": "Mutation.precondition", "kind": "function", "doc": "Whether a mutation is allowed to apply to a language.
\n", "signature": "(language : ultk . language . language . Language , ** kwargs ) -> bool : ", "funcdef": "def"}, "ultk.effcomm.optimization.Mutation.mutate": {"fullname": "ultk.effcomm.optimization.Mutation.mutate", "modulename": "ultk.effcomm.optimization", "qualname": "Mutation.mutate", "kind": "function", "doc": "Mutate the language, possibly using a list of expressions.
\n", "signature": "(\tlanguage : ultk . language . language . Language , \texpressions : list [ ultk . language . language . Expression ] , \t** kwargs ) -> ultk . language . language . Language : ", "funcdef": "def"}, "ultk.effcomm.optimization.RemoveExpression": {"fullname": "ultk.effcomm.optimization.RemoveExpression", "modulename": "ultk.effcomm.optimization", "qualname": "RemoveExpression", "kind": "class", "doc": "
\n", "bases": "Mutation"}, "ultk.effcomm.optimization.RemoveExpression.precondition": {"fullname": "ultk.effcomm.optimization.RemoveExpression.precondition", "modulename": "ultk.effcomm.optimization", "qualname": "RemoveExpression.precondition", "kind": "function", "doc": "Whether a mutation is allowed to apply to a language.
\n", "signature": "(language : ultk . language . language . Language , ** kwargs ) -> bool : ", "funcdef": "def"}, "ultk.effcomm.optimization.RemoveExpression.mutate": {"fullname": "ultk.effcomm.optimization.RemoveExpression.mutate", "modulename": "ultk.effcomm.optimization", "qualname": "RemoveExpression.mutate", "kind": "function", "doc": "Mutate the language, possibly using a list of expressions.
\n", "signature": "(\tlanguage : ultk . language . language . Language , \texpressions : list [ ultk . language . language . Expression ] , \t** kwargs ) -> ultk . language . language . Language : ", "funcdef": "def"}, "ultk.effcomm.optimization.AddExpression": {"fullname": "ultk.effcomm.optimization.AddExpression", "modulename": "ultk.effcomm.optimization", "qualname": "AddExpression", "kind": "class", "doc": "
\n", "bases": "Mutation"}, "ultk.effcomm.optimization.AddExpression.precondition": {"fullname": "ultk.effcomm.optimization.AddExpression.precondition", "modulename": "ultk.effcomm.optimization", "qualname": "AddExpression.precondition", "kind": "function", "doc": "Whether a mutation is allowed to apply to a language.
\n", "signature": "(language : ultk . language . language . Language , ** kwargs ) -> bool : ", "funcdef": "def"}, "ultk.effcomm.optimization.AddExpression.mutate": {"fullname": "ultk.effcomm.optimization.AddExpression.mutate", "modulename": "ultk.effcomm.optimization", "qualname": "AddExpression.mutate", "kind": "function", "doc": "Mutate the language, possibly using a list of expressions.
\n", "signature": "(\tlanguage : ultk . language . language . Language , \texpressions : list [ ultk . language . language . Expression ] , \t** kwargs ) -> ultk . language . language . Language : ", "funcdef": "def"}, "ultk.effcomm.optimization.EvolutionaryOptimizer": {"fullname": "ultk.effcomm.optimization.EvolutionaryOptimizer", "modulename": "ultk.effcomm.optimization", "qualname": "EvolutionaryOptimizer", "kind": "class", "doc": "Class for approximating the Pareto frontier of languages optimizing the simplicity/informativity trade-off.
\n"}, "ultk.effcomm.optimization.EvolutionaryOptimizer.__init__": {"fullname": "ultk.effcomm.optimization.EvolutionaryOptimizer.__init__", "modulename": "ultk.effcomm.optimization", "qualname": "EvolutionaryOptimizer.__init__", "kind": "function", "doc": "Initialize the evolutionary algorithm configurations.
\n\nThe measures of complexity and informativity, the expressions, and the mutations are all specific to the particular semantic domain.
\n\nArguments: \n\n\nobjectives: a dict of the two objectives to optimize for, e.g. simplicity and informativeness, of the form, e.g.\n{\n \"complexity\": comp_measure,\n \"comm_cost\": lambda l: 1 - inf_measure(l)\n}expressions: a list of expressions from which to apply mutations to languages.sample_size: the size of the population at every generation.max_muatations: between 1 and this number of mutations will be applied to a subset of the population at the end of each generation.generations: how many iterations to run the evolutionary algorithm for.lang_size: between 1 and this number of expressions comprise a language.mutations: (optional) a list of Mutation objects, defaults to add/remove expression \n", "signature": "(\tobjectives : list [ typing . Callable [[ ultk . language . language . Language ], typing . Any ]] , \texpressions : list [ ultk . language . language . Expression ] , \tsample_size : int , \tmax_mutations : int , \tgenerations : int , \tlang_size : int = None , \tmutations: list[ultk.effcomm.optimization.Mutation] = [<class 'ultk.effcomm.optimization.AddExpression'>, <class 'ultk.effcomm.optimization.RemoveExpression'>] ) "}, "ultk.effcomm.optimization.EvolutionaryOptimizer.objectives": {"fullname": "ultk.effcomm.optimization.EvolutionaryOptimizer.objectives", "modulename": "ultk.effcomm.optimization", "qualname": "EvolutionaryOptimizer.objectives", "kind": "variable", "doc": "
\n"}, "ultk.effcomm.optimization.EvolutionaryOptimizer.expressions": {"fullname": "ultk.effcomm.optimization.EvolutionaryOptimizer.expressions", "modulename": "ultk.effcomm.optimization", "qualname": "EvolutionaryOptimizer.expressions", "kind": "variable", "doc": "
\n"}, "ultk.effcomm.optimization.EvolutionaryOptimizer.mutations": {"fullname": "ultk.effcomm.optimization.EvolutionaryOptimizer.mutations", "modulename": "ultk.effcomm.optimization", "qualname": "EvolutionaryOptimizer.mutations", "kind": "variable", "doc": "
\n"}, "ultk.effcomm.optimization.EvolutionaryOptimizer.sample_size": {"fullname": "ultk.effcomm.optimization.EvolutionaryOptimizer.sample_size", "modulename": "ultk.effcomm.optimization", "qualname": "EvolutionaryOptimizer.sample_size", "kind": "variable", "doc": "
\n"}, "ultk.effcomm.optimization.EvolutionaryOptimizer.max_mutations": {"fullname": "ultk.effcomm.optimization.EvolutionaryOptimizer.max_mutations", "modulename": "ultk.effcomm.optimization", "qualname": "EvolutionaryOptimizer.max_mutations", "kind": "variable", "doc": "
\n"}, "ultk.effcomm.optimization.EvolutionaryOptimizer.generations": {"fullname": "ultk.effcomm.optimization.EvolutionaryOptimizer.generations", "modulename": "ultk.effcomm.optimization", "qualname": "EvolutionaryOptimizer.generations", "kind": "variable", "doc": "
\n"}, "ultk.effcomm.optimization.EvolutionaryOptimizer.lang_size": {"fullname": "ultk.effcomm.optimization.EvolutionaryOptimizer.lang_size", "modulename": "ultk.effcomm.optimization", "qualname": "EvolutionaryOptimizer.lang_size", "kind": "variable", "doc": "
\n"}, "ultk.effcomm.optimization.EvolutionaryOptimizer.dominating_languages": {"fullname": "ultk.effcomm.optimization.EvolutionaryOptimizer.dominating_languages", "modulename": "ultk.effcomm.optimization", "qualname": "EvolutionaryOptimizer.dominating_languages", "kind": "variable", "doc": "
\n"}, "ultk.effcomm.optimization.EvolutionaryOptimizer.explored_languages": {"fullname": "ultk.effcomm.optimization.EvolutionaryOptimizer.explored_languages", "modulename": "ultk.effcomm.optimization", "qualname": "EvolutionaryOptimizer.explored_languages", "kind": "variable", "doc": "
\n"}, "ultk.effcomm.optimization.EvolutionaryOptimizer.fit": {"fullname": "ultk.effcomm.optimization.EvolutionaryOptimizer.fit", "modulename": "ultk.effcomm.optimization", "qualname": "EvolutionaryOptimizer.fit", "kind": "function", "doc": "Computes the Pareto frontier, a set languages which cannot be both more simple and more informative.
\n\nUses pygmo's nondominated_front method for computing a population's best solutions to a multi-objective optimization problem.
\n\nArguments: \n\n\nseed_population: a list of languages representing the population at generation 0 of the algorithm.explore: a float in [0,1] representing how much to optimize for fitness\n(optimality wrt pareto front of complexity and comm_cost), and how much to randomly explore. \n\nReturns: \n\n\n a dict of the estimated optimization solutions, as well as points explored along the way; of the form
\n\n{\n\"dominating_languages\": list of languages as estimated solutions,\n\"explored_languages\": list of all the languages explored during the evolutionary algorithm,\n}\n \n", "signature": "(\tself , \tseed_population : list [ ultk . language . language . Language ] , \texplore : float = 0.0 ) -> dict [ str , list [ ultk . language . language . Language ]] : ", "funcdef": "def"}, "ultk.effcomm.optimization.EvolutionaryOptimizer.sample_mutated": {"fullname": "ultk.effcomm.optimization.EvolutionaryOptimizer.sample_mutated", "modulename": "ultk.effcomm.optimization", "qualname": "EvolutionaryOptimizer.sample_mutated", "kind": "function", "doc": "Arguments: \n\n\nlanguages: dominating languages of a generationamount: sample_size.expressions: the list of expressions \n\nReturns: \n\n\n list of updated languages
\n \n", "signature": "(\tself , \tlanguages : list [ ultk . language . language . Language ] ) -> list [ ultk . language . language . Language ] : ", "funcdef": "def"}, "ultk.effcomm.optimization.EvolutionaryOptimizer.mutate": {"fullname": "ultk.effcomm.optimization.EvolutionaryOptimizer.mutate", "modulename": "ultk.effcomm.optimization", "qualname": "EvolutionaryOptimizer.mutate", "kind": "function", "doc": "Randomly selects a mutation that is allowed to apply and applies it to a language.
\n\nArguments: \n\n\nlanguage: the Language to mutateexpressions: the list of all possible expressions.\nSome mutations need access to this list, so it is part of the mutation api. \n\nReturns: \n\n\n the mutated Language
\n \n", "signature": "(\tself , \tlanguage : ultk . language . language . Language ) -> ultk . language . language . Language : ", "funcdef": "def"}, "ultk.effcomm.optimization.sample_parents": {"fullname": "ultk.effcomm.optimization.sample_parents", "modulename": "ultk.effcomm.optimization", "qualname": "sample_parents", "kind": "function", "doc": "Use the explore parameter to explore possibly suboptimal areas of the language space.
\n\nArguments: \n\n\ndominating_languages: a list of the languages with current best fitness with respect to the objectives.explored_languages: a list of all languages encountered during the evolutionary algorithm.explore: a float in [0,1] specifying how much to explore possibly suboptimal languages.\nIf set to 0, parent_languages is just dominating_languages. \n\nReturns: \n\n\n the languages to serve as the next generation (after possible mutations)
\n \n", "signature": "(\tdominating_languages : set [ ultk . language . language . Language ] , \texplored_languages : set [ ultk . language . language . Language ] , \texplore : float ) -> list [ ultk . language . language . Language ] : ", "funcdef": "def"}, "ultk.effcomm.sampling": {"fullname": "ultk.effcomm.sampling", "modulename": "ultk.effcomm.sampling", "kind": "module", "doc": "Functions for sampling expressions into languages.
\n"}, "ultk.effcomm.sampling.get_hypothetical_variants": {"fullname": "ultk.effcomm.sampling.get_hypothetical_variants", "modulename": "ultk.effcomm.sampling", "qualname": "get_hypothetical_variants", "kind": "function", "doc": "For each system (parameterized by a language or else a speaker), generate num hypothetical variants by permuting the signals that the system assigns to states.
\n\nArguments: \n\n\nlanguages: a list of languages to permute, by constructing LiteralSpeakers and permuting their weights.speakers: a list of speakers of a language, whose weights can be directly permuted. Should be used instead of languages if possible, because it can be more finegrained (every language can be associated with multiple speakers).total: the total number of hypothetical variants to obtain \n\nReturns: \n\n\n hypothetical_variants: a list of type either Language or np.ndarray depending on whether languages or speakers was passed, representing hypothetical variants of the systems passed. If speakers was passed, a list of speakers is returned.
\n \n", "signature": "(\tlanguages : list [ ultk . language . language . Language ] = None , \tspeakers : list [ ultk . effcomm . agent . Speaker ] = None , \ttotal : int = 0 ) -> list [ typing . Any ] : ", "funcdef": "def"}, "ultk.effcomm.tradeoff": {"fullname": "ultk.effcomm.tradeoff", "modulename": "ultk.effcomm.tradeoff", "kind": "module", "doc": "Functions for constructing an efficient communication analysis by measuring the simplicity/informativeness trade-off languages and formatting results as a dataframe or a plot.
\n"}, "ultk.effcomm.tradeoff.dominates": {"fullname": "ultk.effcomm.tradeoff.dominates", "modulename": "ultk.effcomm.tradeoff", "qualname": "dominates", "kind": "function", "doc": "Determine whether p1 dominates p2,\ni.e. whether for every i p1[i] <= p2[i]\nand for some i p1[i] < p2[i].
\n\nArguments: \n\n\np1: a pointp2: another point \n\nReturns: \n\n\n whether or not p1 dominates p2
\n \n", "signature": "(p1 : list [ float ] , p2 : list [ float ] ) -> bool : ", "funcdef": "def"}, "ultk.effcomm.tradeoff.non_dominated_2d": {"fullname": "ultk.effcomm.tradeoff.non_dominated_2d", "modulename": "ultk.effcomm.tradeoff", "qualname": "non_dominated_2d", "kind": "function", "doc": "Return the non-dominated (Pareto) front of a list of 2-D points, using Kung's algorithm.
\n\nArguments: \n\n\npoints: A list of 2-D points \n\nReturns: \n\n\n a list, the indices of points for which no other point is as good on all dimensions\n and better on at least one
\n \n", "signature": "(points : list [ tuple [ float , float ]] ) -> list [ int ] : ", "funcdef": "def"}, "ultk.effcomm.tradeoff.pareto_optimal_languages": {"fullname": "ultk.effcomm.tradeoff.pareto_optimal_languages", "modulename": "ultk.effcomm.tradeoff", "qualname": "pareto_optimal_languages", "kind": "function", "doc": "Use non_dominated_2d to compute the Pareto languages.
\n", "signature": "(\tlanguages : list [ ultk . language . language . Language ] , \tobjectives : list [ typing . Callable [[ ultk . language . language . Language ], typing . Any ]] , \tunique : bool = False ) -> list [ ultk . language . language . Language ] : ", "funcdef": "def"}, "ultk.effcomm.tradeoff.pareto_min_distances": {"fullname": "ultk.effcomm.tradeoff.pareto_min_distances", "modulename": "ultk.effcomm.tradeoff", "qualname": "pareto_min_distances", "kind": "function", "doc": "Measure the Pareto optimality of each language by measuring its Euclidean closeness to the frontier. The frontier is a line (list of points) interpolated from the pareto points.
\n\nArguments: \n\n\npoints: the list of all language (x, y) pairs, where x and y are usually communicative cost and complexity.pareto_points: the list of all dominant language (x, y) pairs to constitute the Pareto frontier. The points should have been measured by pygmo's non_dominated_front_2d function. \n\nReturns: \n\n\n min_distances: an array of shape len(points) Euclidean distances for each language to the closest point on the Pareto frontier.
\n \n", "signature": "(points : list [ tuple ] , pareto_points : list [ tuple ] ) -> numpy . ndarray : ", "funcdef": "def"}, "ultk.effcomm.tradeoff.interpolate_data": {"fullname": "ultk.effcomm.tradeoff.interpolate_data", "modulename": "ultk.effcomm.tradeoff", "qualname": "interpolate_data", "kind": "function", "doc": "Interpolate the points yielded by the pareto optimal languages into a continuous (though not necessarily smooth) curve.
\n\nArguments: \n\n\npoints: an list of (comm_cost, complexity) pairs of size [dominating_languages], a possibly non-smooth set of solutions to the trade-off.min_cost: the minimum communicative cost value possible to interpolate from.max_cost: the maximum communicative cost value possible to interpolate from. A natural assumption is to let complexity=0.0 if max_cost=1.0, which will result in a Pareto curve that spans the entire 2d space, and consequently the plot with x and y limits both ranging [0.0, 1.0].num: the number of x-axis points (cost) to interpolate. Controls smoothness of curve. \n\nReturns: \n\n\n interpolated_points: an array of size (num, num)
\n \n", "signature": "(\tpoints : list [ tuple [ float ]] , \tmin_cost : float = 0.0 , \tmax_cost : float = 1.0 , \tnum = 5000 ) -> numpy . ndarray : ", "funcdef": "def"}, "ultk.effcomm.tradeoff.tradeoff": {"fullname": "ultk.effcomm.tradeoff.tradeoff", "modulename": "ultk.effcomm.tradeoff", "qualname": "tradeoff", "kind": "function", "doc": "Builds a final efficient communication analysis by measuring a list of languages, updating their internal data, and returning the results.
\n\nThis function measures possibly many graded or categorical properties of each language, but minimally the properties of commmunicative cost and complexity. These two measures fully define the results of an efficiency analysis, in the sense they define the optimal solutions.
\n\nArguments: \n\n\nlanguages: A list representing the pool of all languages to be measured for an efficient communication analysis.x: the first pressure to measure, e.g. communicative cost.y: the second pressure to measure, e.g. cognitive complexity.frontier: a list of (comm_cost, complexity) points representing a Pareto frontier to measure optimality w.r.t. \n\nReturns: \n\n\n a dictionary of the population and the pareto front, of the form
\n\n{\n \"languages\": the list of languages, with their internal efficient communication data updated,\n\n \"dominating_languages\": the list of the languages dominating the population w.r.t. comm_cost and complexity. If no `frontier` is none, this can be considered the Pareto frontier.\n}\n \n", "signature": "(\tlanguages : list [ ultk . language . language . Language ] , \tproperties : dict [ str , typing . Callable [[ ultk . language . language . Language ], typing . Any ]] , \tx : str = 'comm_cost' , \ty : str = 'complexity' , \tfrontier : list [ tuple ] = None ) -> dict [ str , list [ ultk . language . language . Language ]] : ", "funcdef": "def"}, "ultk.effcomm.util": {"fullname": "ultk.effcomm.util", "modulename": "ultk.effcomm.util", "kind": "module", "doc": "Various helper functions for computing complexity and informativity.
\n"}, "ultk.effcomm.util.rows_zero_to_uniform": {"fullname": "ultk.effcomm.util.rows_zero_to_uniform", "modulename": "ultk.effcomm.util", "qualname": "rows_zero_to_uniform", "kind": "function", "doc": "Ensure that mat encodes a probability distribution, i.e. each row (indexed by a meaning) is a distribution over expressions: sums to exactly 1.0.
\n\nThis is necessary when exploring mathematically possible languages (including natural languages, like Hausa in the case of modals) which sometimes have that a row of the matrix p(word|meaning) is a vector of 0s.
\n\nArguments: \n\n\nmat: a 2D numpy array that should be normalized so that each row is a probability distribution. \n", "signature": "(mat : numpy . ndarray ) -> numpy . ndarray : ", "funcdef": "def"}, "ultk.effcomm.util.build_utility_matrix": {"fullname": "ultk.effcomm.util.build_utility_matrix", "modulename": "ultk.effcomm.util", "qualname": "build_utility_matrix", "kind": "function", "doc": "Construct the square matrix specifying the utility function defined for pairs of meanings, used for computing communicative success.
\n", "signature": "(\tuniverse : ultk . language . semantics . Universe , \tutility : Callable [[ ultk . language . semantics . Referent , ultk . language . semantics . Referent ], float ] ) -> numpy . ndarray : ", "funcdef": "def"}, "ultk.effcomm.util.PRECISION": {"fullname": "ultk.effcomm.util.PRECISION", "modulename": "ultk.effcomm.util", "qualname": "PRECISION", "kind": "variable", "doc": "
\n", "default_value": "1e-16"}, "ultk.effcomm.util.marginal": {"fullname": "ultk.effcomm.util.marginal", "modulename": "ultk.effcomm.util", "qualname": "marginal", "kind": "function", "doc": "Compute $p(x) = \\sum_x p(x,y)$
\n\nArguments: \n\n\npXY: a numpy array of shape (|X|, |Y|) \n\nReturns: \n\n\n pY: (axis = 0) or pX (default, axis = 1)
\n \n", "signature": "(pXY , axis = 1 ): ", "funcdef": "def"}, "ultk.effcomm.util.conditional": {"fullname": "ultk.effcomm.util.conditional", "modulename": "ultk.effcomm.util", "qualname": "conditional", "kind": "function", "doc": "Compute $p(y|x) = \\frac{p(x,y)}{p(x)}$
\n\nArguments: \n\n\npXY: a numpy array of shape (|X|, |Y|) \n\nReturns: \n\n\n pY_X: a numpy array of shape (|X|, |Y|)
\n \n", "signature": "(pXY ): ", "funcdef": "def"}, "ultk.effcomm.util.joint": {"fullname": "ultk.effcomm.util.joint", "modulename": "ultk.effcomm.util", "qualname": "joint", "kind": "function", "doc": "Compute $p(x,y) = p(y|x) \\cdot p(x) $
\n\nArguments: \n\n\npY_X: a numpy array of shape (|X|, |Y|)pX: a numpy array |X| \n\nReturns: \n\n\n pXY: a numpy array of the shape (|X|, |Y|)
\n \n", "signature": "(pY_X , pX ): ", "funcdef": "def"}, "ultk.effcomm.util.marginalize": {"fullname": "ultk.effcomm.util.marginalize", "modulename": "ultk.effcomm.util", "qualname": "marginalize", "kind": "function", "doc": "Compute $p(y) = \\sum_x p(y|x) \\cdot p(x)$
\n\nArguments: \n\n\npY_X: a numpy array of shape (|X|, |Y|)pX: a numpy array of shape |X| \n\nReturns: \n\n\n pY: a numpy array of shape |Y|
\n \n", "signature": "(pY_X , pX ): ", "funcdef": "def"}, "ultk.effcomm.util.bayes": {"fullname": "ultk.effcomm.util.bayes", "modulename": "ultk.effcomm.util", "qualname": "bayes", "kind": "function", "doc": "Compute $p(x|y) = \\frac{p(y|x) \\cdot p(x)}{p(y)}$
\n\nArguments: \n\n\npY_X: a numpy array of shape (|X|, |Y|) \n", "signature": "(pY_X , pX ): ", "funcdef": "def"}, "ultk.effcomm.util.xlogx": {"fullname": "ultk.effcomm.util.xlogx", "modulename": "ultk.effcomm.util", "qualname": "xlogx", "kind": "function", "doc": "Compute $x \\log p(x)$
\n", "signature": "(p ): ", "funcdef": "def"}, "ultk.effcomm.util.H": {"fullname": "ultk.effcomm.util.H", "modulename": "ultk.effcomm.util", "qualname": "H", "kind": "function", "doc": "Compute the entropy of p, $H(X) = - \\sum_x x \\log p(x)$
\n", "signature": "(p , axis = None ): ", "funcdef": "def"}, "ultk.effcomm.util.MI": {"fullname": "ultk.effcomm.util.MI", "modulename": "ultk.effcomm.util", "qualname": "MI", "kind": "function", "doc": "Compute mutual information, $I[X:Y]$
\n", "signature": "(pXY ): ", "funcdef": "def"}, "ultk.effcomm.util.DKL": {"fullname": "ultk.effcomm.util.DKL", "modulename": "ultk.effcomm.util", "qualname": "DKL", "kind": "function", "doc": "Compute KL divergences, $D_{KL}[p~||~q]$
\n", "signature": "(p , q , axis = None ): ", "funcdef": "def"}, "ultk.effcomm.util.gNID": {"fullname": "ultk.effcomm.util.gNID", "modulename": "ultk.effcomm.util", "qualname": "gNID", "kind": "function", "doc": "Compute Generalized Normalized Informational Distance between two encoders.
\n\nArguments: \n\n\npW_X: first encoder of shape (|meanings|, |words|)pV_X: second encoder of shape (|meanings|, |words|)pX: prior over source variables of shape (|meanings|,) \n", "signature": "(pW_X , pV_X , pX ): ", "funcdef": "def"}, "ultk.language": {"fullname": "ultk.language", "modulename": "ultk.language", "kind": "module", "doc": "Classes for modeling (natural or hypothetical) languagese.
\n\nAt the current stage of development, ULTK focuses on supporting abstractions to model the mapping between expressions and meanings of a language. So far, we leave almost everything besides this basic mapping (morphosyntax, phonology, phonetic inventories, among other features of human languages) to future work.
\n\nThe ultk.language.language submodule contains classes for constructing a language, which can contain one or more expressions.
\n\nThe ultk.language.semantics submodule contains classes for defining a universe (meaning space) of referents (denotations) and meanings (categories).
\n"}, "ultk.language.grammar": {"fullname": "ultk.language.grammar", "modulename": "ultk.language.grammar", "kind": "module", "doc": "
\n"}, "ultk.language.grammar.Rule": {"fullname": "ultk.language.grammar.Rule", "modulename": "ultk.language.grammar", "qualname": "Rule", "kind": "class", "doc": "Basic class for a grammar rule. Grammar rules in ULTK correspond\nto functions. One can think of a grammar as generating complex functions from\nmore basic ones.
\n\nAttributes: \n\n\nlhs: left-hand side of the rule (can be anything)\nconceptually, the output type of a functionrhs: right-hand side; assumed to be an iterable\nconceptually, a list of types of inputsfunc: a callable, the function to be computed when a node with this rule is executedname: name of the functionweight: a relative weight to assign to this rule\nwhen added to a grammar, all rules with the same LHS will be weighted together \n"}, "ultk.language.grammar.Rule.__init__": {"fullname": "ultk.language.grammar.Rule.__init__", "modulename": "ultk.language.grammar", "qualname": "Rule.__init__", "kind": "function", "doc": "
\n", "signature": "(\tname : str , \tlhs : Any , \trhs : collections . abc . Sequence | None , \tfunction : Callable = < function Rule .< lambda >> , \tweight : float = 1.0 ) "}, "ultk.language.grammar.Rule.lhs": {"fullname": "ultk.language.grammar.Rule.lhs", "modulename": "ultk.language.grammar", "qualname": "Rule.lhs", "kind": "variable", "doc": "
\n"}, "ultk.language.grammar.Rule.rhs": {"fullname": "ultk.language.grammar.Rule.rhs", "modulename": "ultk.language.grammar", "qualname": "Rule.rhs", "kind": "variable", "doc": "
\n"}, "ultk.language.grammar.Rule.func": {"fullname": "ultk.language.grammar.Rule.func", "modulename": "ultk.language.grammar", "qualname": "Rule.func", "kind": "variable", "doc": "
\n"}, "ultk.language.grammar.Rule.name": {"fullname": "ultk.language.grammar.Rule.name", "modulename": "ultk.language.grammar", "qualname": "Rule.name", "kind": "variable", "doc": "
\n"}, "ultk.language.grammar.Rule.weight": {"fullname": "ultk.language.grammar.Rule.weight", "modulename": "ultk.language.grammar", "qualname": "Rule.weight", "kind": "variable", "doc": "
\n"}, "ultk.language.grammar.Rule.is_terminal": {"fullname": "ultk.language.grammar.Rule.is_terminal", "modulename": "ultk.language.grammar", "qualname": "Rule.is_terminal", "kind": "function", "doc": "Whether this is a terminal rule. In our framework, this means that RHS is empty,\ni.e. there are no arguments to the function.
\n", "signature": "(self ) -> bool : ", "funcdef": "def"}, "ultk.language.grammar.GrammaticalExpression": {"fullname": "ultk.language.grammar.GrammaticalExpression", "modulename": "ultk.language.grammar", "qualname": "GrammaticalExpression", "kind": "class", "doc": "A GrammaticalExpression has been built up from a Grammar by applying a sequence of Rules.\nCrucially, it is _callable_, using the functions corresponding to each rule.
\n\nA GrammaticalExpression, when called, takes in a Referent. Because of this, a Meaning can\nbe generated by specifying a Universe (which contains Referents).
\n\nAttributes: \n\n\nname: name of the top-most functionfunc: the functionchildren: child expressions (possibly empty) \n", "bases": "ultk.language.language.Expression"}, "ultk.language.grammar.GrammaticalExpression.__init__": {"fullname": "ultk.language.grammar.GrammaticalExpression.__init__", "modulename": "ultk.language.grammar", "qualname": "GrammaticalExpression.__init__", "kind": "function", "doc": "
\n", "signature": "(\trule_name : str , \tfunc : Callable , \tchildren : tuple | None , \tmeaning : ultk . language . semantics . Meaning | None = None , \tform : str | None = None ) "}, "ultk.language.grammar.GrammaticalExpression.rule_name": {"fullname": "ultk.language.grammar.GrammaticalExpression.rule_name", "modulename": "ultk.language.grammar", "qualname": "GrammaticalExpression.rule_name", "kind": "variable", "doc": "
\n"}, "ultk.language.grammar.GrammaticalExpression.func": {"fullname": "ultk.language.grammar.GrammaticalExpression.func", "modulename": "ultk.language.grammar", "qualname": "GrammaticalExpression.func", "kind": "variable", "doc": "
\n"}, "ultk.language.grammar.GrammaticalExpression.children": {"fullname": "ultk.language.grammar.GrammaticalExpression.children", "modulename": "ultk.language.grammar", "qualname": "GrammaticalExpression.children", "kind": "variable", "doc": "
\n"}, "ultk.language.grammar.GrammaticalExpression.yield_string": {"fullname": "ultk.language.grammar.GrammaticalExpression.yield_string", "modulename": "ultk.language.grammar", "qualname": "GrammaticalExpression.yield_string", "kind": "function", "doc": "Get the 'yield' string of this term, i.e. the concatenation\nof the leaf nodes.
\n\nThis is useful for thinking of a Grammar as generating derivation trees for\nan underlying CFG. This method will then generate the strings generated by\nthe corresponding CFG.
\n", "signature": "(self ) -> str : ", "funcdef": "def"}, "ultk.language.grammar.GrammaticalExpression.evaluate": {"fullname": "ultk.language.grammar.GrammaticalExpression.evaluate", "modulename": "ultk.language.grammar", "qualname": "GrammaticalExpression.evaluate", "kind": "function", "doc": "
\n", "signature": "(\tself , \tuniverse : ultk . language . semantics . Universe ) -> ultk . language . semantics . Meaning : ", "funcdef": "def"}, "ultk.language.grammar.GrammaticalExpression.add_child": {"fullname": "ultk.language.grammar.GrammaticalExpression.add_child", "modulename": "ultk.language.grammar", "qualname": "GrammaticalExpression.add_child", "kind": "function", "doc": "
\n", "signature": "(self , child ) -> None : ", "funcdef": "def"}, "ultk.language.grammar.GrammaticalExpression.to_dict": {"fullname": "ultk.language.grammar.GrammaticalExpression.to_dict", "modulename": "ultk.language.grammar", "qualname": "GrammaticalExpression.to_dict", "kind": "function", "doc": "
\n", "signature": "(self ) -> dict : ", "funcdef": "def"}, "ultk.language.grammar.UniquenessArgs": {"fullname": "ultk.language.grammar.UniquenessArgs", "modulename": "ultk.language.grammar", "qualname": "UniquenessArgs", "kind": "class", "doc": "Arguments for specifying uniqueness of GrammaticalExpressions in a Grammar.
\n\nAttributes: \n\n\nunique_expressions: a dictionary in which to store unique Expressionskey: a function used to evaluate uniquenesscompare_func: a comparison function, used to decide which Expression to add to the dict\nnew Expressions will be added as values to unique_dict only if they are minimal\namong those sharing the same key (by unique_key) according to this func \n", "bases": "typing.TypedDict"}, "ultk.language.grammar.UniquenessArgs.unique_expressions": {"fullname": "ultk.language.grammar.UniquenessArgs.unique_expressions", "modulename": "ultk.language.grammar", "qualname": "UniquenessArgs.unique_expressions", "kind": "variable", "doc": "
\n", "annotation": ": dict[typing.Any, dict[typing.Any, ultk.language.grammar.GrammaticalExpression]]"}, "ultk.language.grammar.UniquenessArgs.key": {"fullname": "ultk.language.grammar.UniquenessArgs.key", "modulename": "ultk.language.grammar", "qualname": "UniquenessArgs.key", "kind": "variable", "doc": "
\n", "annotation": ": Callable[[ultk.language.grammar.GrammaticalExpression], Any]"}, "ultk.language.grammar.UniquenessArgs.compare_func": {"fullname": "ultk.language.grammar.UniquenessArgs.compare_func", "modulename": "ultk.language.grammar", "qualname": "UniquenessArgs.compare_func", "kind": "variable", "doc": "
\n", "annotation": ": Callable[[ultk.language.grammar.GrammaticalExpression, ultk.language.grammar.GrammaticalExpression], bool]"}, "ultk.language.grammar.Grammar": {"fullname": "ultk.language.grammar.Grammar", "modulename": "ultk.language.grammar", "qualname": "Grammar", "kind": "class", "doc": "At its core, a Grammar is a set of Rules with methods for generating GrammaticalExpressions.
\n"}, "ultk.language.grammar.Grammar.__init__": {"fullname": "ultk.language.grammar.Grammar.__init__", "modulename": "ultk.language.grammar", "qualname": "Grammar.__init__", "kind": "function", "doc": "
\n", "signature": "(start : Any "}, "ultk.language.grammar.Grammar.add_rule": {"fullname": "ultk.language.grammar.Grammar.add_rule", "modulename": "ultk.language.grammar", "qualname": "Grammar.add_rule", "kind": "function", "doc": "
\n", "signature": "(self , rule : ultk . language . grammar . Rule ): ", "funcdef": "def"}, "ultk.language.grammar.Grammar.parse": {"fullname": "ultk.language.grammar.Grammar.parse", "modulename": "ultk.language.grammar", "qualname": "Grammar.parse", "kind": "function", "doc": "Parse a string representation of an expression of a grammar.\nNote that this is not a general-purpose parsing algorithm. We assume that the strings are of the form\n parent_name(child1_name, ..., childn_name)\nwhere parent_name is the name of a rule of this grammar that has a length-n RHS, and that\nchildi_name is the name of a rule for each child i.
\n\nArguments: \n\n\nexpression: string in the above format \n\nReturns: \n\n\n the corresponding GrammaticalExpression
\n \n", "signature": "(\tself , \texpression : str , \topener : str = '(' , \tcloser : str = ')' , \tdelimiter : str = ',' ) -> ultk . language . grammar . GrammaticalExpression : ", "funcdef": "def"}, "ultk.language.grammar.Grammar.generate": {"fullname": "ultk.language.grammar.Grammar.generate", "modulename": "ultk.language.grammar", "qualname": "Grammar.generate", "kind": "function", "doc": "Generate an expression from a given lhs.
\n", "signature": "(self , lhs : Any = None ) -> ultk . language . grammar . GrammaticalExpression : ", "funcdef": "def"}, "ultk.language.grammar.Grammar.enumerate": {"fullname": "ultk.language.grammar.Grammar.enumerate", "modulename": "ultk.language.grammar", "qualname": "Grammar.enumerate", "kind": "function", "doc": "Enumerate all expressions from the grammar up to a given depth from a given LHS.\nThis method also can update a specified dictionary to store only _unique_ expressions, with\na user-specified criterion of uniqueness.
\n\nArguments: \n\n\ndepth: how deep the trees should belhs: left hand side to start from; defaults to the grammar's start symboluniqueness_args: a dictionary specifying the parameters for uniqueness:\nunique_dict: a dictionary in which to store unique Expressions\nkey: a function used to evaluate uniqueness\ncompare_func: a comparison function, used to decide which Expression to add to the dict\n new Expressions will be added as values to unique_dict only if they are _minimal_\n among those sharing the same key (by unique_key) according to this func \n\nYields: \n\n\n all GrammaticalExpressions up to depth
\n \n", "signature": "(\tself , \tdepth : int = 8 , \tlhs : Any = None , \tuniqueness_args : ultk . language . grammar . UniquenessArgs | None = None ) -> Generator [ ultk . language . grammar . GrammaticalExpression , NoneType , NoneType ] : ", "funcdef": "def"}, "ultk.language.grammar.Grammar.enumerate_at_depth": {"fullname": "ultk.language.grammar.Grammar.enumerate_at_depth", "modulename": "ultk.language.grammar", "qualname": "Grammar.enumerate_at_depth", "kind": "function", "doc": "Enumerate GrammaticalExpressions for this Grammar _at_ a fixed depth.
\n", "signature": "(\tself , \tdepth : int , \tlhs : Any , \tuniqueness_args : ultk . language . grammar . UniquenessArgs | None = None , \tcache : dict | None = None ) -> Generator [ ultk . language . grammar . GrammaticalExpression , NoneType , NoneType ] : ", "funcdef": "def"}, "ultk.language.grammar.Grammar.get_unique_expressions": {"fullname": "ultk.language.grammar.Grammar.get_unique_expressions", "modulename": "ultk.language.grammar", "qualname": "Grammar.get_unique_expressions", "kind": "function", "doc": "Get all unique GrammaticalExpressions, up to a certain depth, with a user-specified criterion\nof uniqueness, and a specified comparison function for determining which Expression to save when there's a clash.\nThis can be used, for instance, to measure the minimum description length of some\nMeanings, by using expression.evaluate(), which produces a Meaning for an Expression, as the\nkey for determining uniqueness, and length of the expression as comparison.
\n\nThis is a wrapper around enumerate, but which produces the dictionary of key->Expression entries\nand returns it. (enumerate is a generator with side effects).
\n\nFor Args, see the docstring for enumerate.
\n\nNote: if you additionally want to store _all_ expressions, and not just the unique ones, you should\ndirectly use enumerate.
\n\nReturns: \n\n\n dictionary of {key: GrammaticalExpression}, where the keys are generated by unique_key\n The GrammticalExpression which is the value will be the one that is minimum among\n compare_func amongst all Expressions up to depth which share the same key
\n \n", "signature": "(\tself , \tdepth : int , \tunique_key : Callable [[ ultk . language . grammar . GrammaticalExpression ], Any ] , \tcompare_func : Callable [[ ultk . language . grammar . GrammaticalExpression , ultk . language . grammar . GrammaticalExpression ], bool ] , \tlhs : Any = None , \tmax_size : float = inf ) -> dict [ ultk . language . grammar . GrammaticalExpression , typing . Any ] : ", "funcdef": "def"}, "ultk.language.grammar.Grammar.get_all_rules": {"fullname": "ultk.language.grammar.Grammar.get_all_rules", "modulename": "ultk.language.grammar", "qualname": "Grammar.get_all_rules", "kind": "function", "doc": "Get all rules as a list.
\n", "signature": "(self ) -> list [ ultk . language . grammar . Rule ] : ", "funcdef": "def"}, "ultk.language.grammar.Grammar.from_yaml": {"fullname": "ultk.language.grammar.Grammar.from_yaml", "modulename": "ultk.language.grammar", "qualname": "Grammar.from_yaml", "kind": "function", "doc": "Read a grammar specified in a simple YAML format.
\n\nExpected format:
\n\nstart: bool\nrules:\n- lhs: bool\n rhs:\n - bool\n - bool\n name: \"and\"\n function: \"lambda p1, p2 : p1 and p2\"\n- lhs: bool\n rhs:\n - bool\n - bool\n name: \"or\"\n function: \"lambda p1, p2 : p1 or p2\"\nNote that for each fule, the value for function will be passed to\neval, so be careful!
\n\nArguments: \n\n\nfilename: file containing a grammar in the above format \n", "signature": "(cls , filename : str ): ", "funcdef": "def"}, "ultk.language.language": {"fullname": "ultk.language.language", "modulename": "ultk.language.language", "kind": "module", "doc": "Classes for modeling languages as form-meaning mappings, most important among them the Language and Expression classes.
\n\nExample usage: \n\n\n \n
>>> from ultk.language.language import Expression , Language \n>>> # assuming the meaning `a_few_meaning` has already been constructed \n>>> # define the expression \n>>> a_few = NumeralExpression ( form = "a few" , meaning = a_few_meaning ) \n>>> # define a very small language \n>>> lang_1 = Language ([ a_few ]) \n>>> # or a slightly larger one with synonymy \n>>> lang_2 = Language ([ a_few ] * 3 ) \n\n
\n"}, "ultk.language.language.Expression": {"fullname": "ultk.language.language.Expression", "modulename": "ultk.language.language", "qualname": "Expression", "kind": "class", "doc": "Minimally contains a form and a meaning.
\n"}, "ultk.language.language.Expression.__init__": {"fullname": "ultk.language.language.Expression.__init__", "modulename": "ultk.language.language", "qualname": "Expression.__init__", "kind": "function", "doc": "
\n", "signature": "(\tform : str | None = None , \tmeaning : ultk . language . semantics . Meaning | None = None ) "}, "ultk.language.language.Expression.form": {"fullname": "ultk.language.language.Expression.form", "modulename": "ultk.language.language", "qualname": "Expression.form", "kind": "variable", "doc": "
\n"}, "ultk.language.language.Expression.meaning": {"fullname": "ultk.language.language.Expression.meaning", "modulename": "ultk.language.language", "qualname": "Expression.meaning", "kind": "variable", "doc": "
\n"}, "ultk.language.language.Expression.can_express": {"fullname": "ultk.language.language.Expression.can_express", "modulename": "ultk.language.language", "qualname": "Expression.can_express", "kind": "function", "doc": "Return True if the expression can express the input single meaning point and false otherwise.
\n", "signature": "(self , referent : ultk . language . semantics . Referent ) -> bool : ", "funcdef": "def"}, "ultk.language.language.Expression.to_dict": {"fullname": "ultk.language.language.Expression.to_dict", "modulename": "ultk.language.language", "qualname": "Expression.to_dict", "kind": "function", "doc": "
\n", "signature": "(self ) -> dict : ", "funcdef": "def"}, "ultk.language.language.Language": {"fullname": "ultk.language.language.Language", "modulename": "ultk.language.language", "qualname": "Language", "kind": "class", "doc": "Minimally contains Expression objects.
\n"}, "ultk.language.language.Language.__init__": {"fullname": "ultk.language.language.Language.__init__", "modulename": "ultk.language.language", "qualname": "Language.__init__", "kind": "function", "doc": "
\n", "signature": "(expressions : tuple [ ultk . language . language . Expression , ... ] , ** kwargs "}, "ultk.language.language.Language.expressions": {"fullname": "ultk.language.language.Language.expressions", "modulename": "ultk.language.language", "qualname": "Language.expressions", "kind": "variable", "doc": "
\n", "annotation": ": tuple[ultk.language.language.Expression, ...]"}, "ultk.language.language.Language.universe": {"fullname": "ultk.language.language.Language.universe", "modulename": "ultk.language.language", "qualname": "Language.universe", "kind": "variable", "doc": "
\n", "annotation": ": ultk.language.semantics.Universe"}, "ultk.language.language.Language.add_expression": {"fullname": "ultk.language.language.Language.add_expression", "modulename": "ultk.language.language", "qualname": "Language.add_expression", "kind": "function", "doc": "Add an expression to the list of expressions in a language.
\n", "signature": "(self , e : ultk . language . language . Expression ): ", "funcdef": "def"}, "ultk.language.language.Language.pop": {"fullname": "ultk.language.language.Language.pop", "modulename": "ultk.language.language", "qualname": "Language.pop", "kind": "function", "doc": "Removes an expression at the specified index of the list of expressions, and returns it.
\n", "signature": "(self , index : int ) -> ultk . language . language . Expression : ", "funcdef": "def"}, "ultk.language.language.Language.is_natural": {"fullname": "ultk.language.language.Language.is_natural", "modulename": "ultk.language.language", "qualname": "Language.is_natural", "kind": "function", "doc": "Whether a language represents a human natural language.
\n", "signature": "(self ) -> bool : ", "funcdef": "def"}, "ultk.language.language.Language.degree_property": {"fullname": "ultk.language.language.Language.degree_property", "modulename": "ultk.language.language", "qualname": "Language.degree_property", "kind": "function", "doc": "Count what percentage of expressions in a language have a given property.
\n", "signature": "(\tself , \tproperty : Callable [[ ultk . language . language . Expression ], bool ] ) -> float : ", "funcdef": "def"}, "ultk.language.language.Language.binary_matrix": {"fullname": "ultk.language.language.Language.binary_matrix", "modulename": "ultk.language.language", "qualname": "Language.binary_matrix", "kind": "function", "doc": "Get a binary matrix of shape (num_meanings, num_expressions)\nspecifying which expressions can express which meanings.
\n", "signature": "(self ) -> numpy . ndarray : ", "funcdef": "def"}, "ultk.language.language.Language.to_dict": {"fullname": "ultk.language.language.Language.to_dict", "modulename": "ultk.language.language", "qualname": "Language.to_dict", "kind": "function", "doc": "
\n", "signature": "(self , ** kwargs ) -> dict : ", "funcdef": "def"}, "ultk.language.language.aggregate_expression_complexity": {"fullname": "ultk.language.language.aggregate_expression_complexity", "modulename": "ultk.language.language", "qualname": "aggregate_expression_complexity", "kind": "function", "doc": "Aggregate complexities for individual Expressions into a complexity for a Language.
\n\nArguments: \n\n\nlanguage: the Language to measureexpression_complexity_func: the function that returns the complexity of an individual expressionaggregator: (optional, default = sum) the function that aggregates individual complexities \n\nReturns: \n\n\n a float, the complexity of a language
\n \n", "signature": "(\tlanguage : ultk . language . language . Language , \texpression_complexity_func : Callable [[ ultk . language . language . Expression ], float ] , \taggregator : Callable [[ Iterable [ float ]], float ] = < built - in function sum > ) -> float : ", "funcdef": "def"}, "ultk.language.sampling": {"fullname": "ultk.language.sampling", "modulename": "ultk.language.sampling", "kind": "module", "doc": "
\n"}, "ultk.language.sampling.powerset": {"fullname": "ultk.language.sampling.powerset", "modulename": "ultk.language.sampling", "qualname": "powerset", "kind": "function", "doc": "Enumerate all _non-empty_ subsets of an iterable up to a given maximum size, e.g.:\npowerset([1,2,3]) --> (1,) (2,) (3,) (1,2) (1,3) (2,3) (1,2,3)
\n\nlightly adapted from itertools Recipes at\nhttps://docs.python.org/3/library/itertools.html#itertools-recipes
\n\nArguments: \n\n\niterable: elements from which to form subsetsmax_size: largest subsets (inclusive) to return \n\nReturns: \n\n\n iterator over all subsets from size 1 to max_size of elements from iterable
\n \n", "signature": "(iterable : Iterable , max_size : int = None ) -> Iterable : ", "funcdef": "def"}, "ultk.language.sampling.all_meanings": {"fullname": "ultk.language.sampling.all_meanings", "modulename": "ultk.language.sampling", "qualname": "all_meanings", "kind": "function", "doc": "Generate all Meanings (sets of Referents) from a given Universe.
\n", "signature": "(\tuniverse : ultk . language . semantics . Universe ) -> Generator [ ultk . language . semantics . Meaning , NoneType , NoneType ] : ", "funcdef": "def"}, "ultk.language.sampling.all_expressions": {"fullname": "ultk.language.sampling.all_expressions", "modulename": "ultk.language.sampling", "qualname": "all_expressions", "kind": "function", "doc": "Generate Expressions from an iterable of Meanings.
\n", "signature": "(\tmeanings : Iterable [ ultk . language . semantics . Meaning ] ) -> Generator [ ultk . language . language . Expression , NoneType , NoneType ] : ", "funcdef": "def"}, "ultk.language.sampling.all_languages": {"fullname": "ultk.language.sampling.all_languages", "modulename": "ultk.language.sampling", "qualname": "all_languages", "kind": "function", "doc": "Generate all Languages (sets of Expressions) from a given set of Expressions.
\n\nArguments: \n\n\nexpressions: iterable of all possible expressionslanguage_class: the type of language to generatemax_size: largest size for a language; if None, all subsets of expressions will be used \n\nYields: \n\n\n Languages with subsets of Expressions from expressions
\n \n", "signature": "(\texpressions : Iterable [ ultk . language . language . Expression ] , \tlanguage_class: Type[ultk.language.language.Language] = <class 'ultk.language.language.Language'>, \tmax_size : int = None ) -> Generator [ ultk . language . language . Language , NoneType , NoneType ] : ", "funcdef": "def"}, "ultk.language.sampling.upto_comb": {"fullname": "ultk.language.sampling.upto_comb", "modulename": "ultk.language.sampling", "qualname": "upto_comb", "kind": "function", "doc": "Return the number of ways of choosing _up to max_k_ items from\nn items without repetition. Just an iterator of math.comb for n from\n1 to max_k.
\n", "signature": "(num : int , max_k : int ) -> int : ", "funcdef": "def"}, "ultk.language.sampling.random_languages": {"fullname": "ultk.language.sampling.random_languages", "modulename": "ultk.language.sampling", "qualname": "random_languages", "kind": "function", "doc": "Generate unique Languages by randomly sampling subsets of Expressions, either in a uniform or stratified way.\nIf there are fewer than sample_size possible Languages up to size max_size,\nthis method will just return all languages up to that size (and so the sample may\nbe smaller than sample_size).
\n\nSome use cases:
\n\nWith sample_size=None, get all languages.
\n\n\n
>>> random_languages ( expressions ) \n\n
With sample_size and uniform sampling, get random languages:
\n\n\n
>>> random_languages ( expressions , sample_size = 1000 ) \n\n
Stratified sampling, with and without a max_size:
\n\n\n
>>> random_languages ( expressions , sample_size = 1000 , sampling_strategy = "stratified" ) \n>>> random_languages ( expressions , sample_size = 1000 , sampling_strategy = "stratified" , max_size = 10 ) \n\n
Arguments: \n\n\nexpressions: all possible expressionssampling_strategy: how to sample subsets of expressions\nuniform: for every expression, choose whether or not to include it in a given language\nstratified: first sample a size for a Language, then choose that many random Expressions\n (i) this has the effect of \"upsampling\" from smaller Language sizes\n (ii) this can be used with max_size to only generate Languages up to a given number of expressionssample_size: how many languages to return\nif None, will return all languages up to max_sizelanguage_class: type of Languagemax_size: largest possible Language to generate\nif None, will be the length of expressions\nNB: this argument has no effect when sampling_strategy is \"uniform\" \n\nReturns: \n\n\n a list of randomly sampled Languages
\n \n", "signature": "(\texpressions : Iterable [ ultk . language . language . Expression ] , \tsampling_strategy : str = 'uniform' , \tsample_size : int = None , \tlanguage_class: Type[ultk.language.language.Language] = <class 'ultk.language.language.Language'>, \tmax_size : int = None ) -> list [ ultk . language . language . Language ] : ", "funcdef": "def"}, "ultk.language.sampling.generate_languages": {"fullname": "ultk.language.sampling.generate_languages", "modulename": "ultk.language.sampling", "qualname": "generate_languages", "kind": "function", "doc": "Generate languages by randomly sampling vocabularies as bags of expressions.
\n\nA predicate (binary-valued property) of expressions may be supplied, which can be used to adjust the composition of vocabularies (e.g., by the percent of expressions satisfying the predicate).
\n\nIf sample size <= nCr, then take a random sample_size set of combinations. Otherwise, to prevent repeat languages, treat nCr as the sample size.
\n\nArguments: \n\n\nexpressions: a list of the possible expressions to sample from.lang_size: the maximum (or exact) number of expressions in each language.sample_size: the number of languages to generate.criterion: the predicate, (e.g. semantic universal) by which to split the expressions into those satisfying and those not, and then sample languages with degrees of naturalness based on the percentage from those satisfying. Must apply at the expression level. By default is a trivial criterion, so that all expressions are 'quasi-natural'.fixed_wordcount: whether to vary the language size from 1 to lang_size.verbose: How detailed the progress of sampling should be, printed to stdout.dummy_name: the default name to give to each sampled language, e.g. sampled_lang_42. These should not collide with any actual natural language names if the efficient communication experiment does use natural language data.id_start: an integer representing the number of languages already generated in an experiment. Languages sampled will be named according to this number. For example, if id_start is 0, the first language sampled will be named sampled_lang_0. Note that the largest id does not necessarily track the actual size of languages saved for the experiment, but it does track how many languages have been generated.exact_sample: a boolean representing whether to sample until the exact sample size is filled. If True, the resulting pool of languages may not be unique.verbose: a boolean representing how verbose output should be during sampling. \n\nReturns: \n\n\n a dict representing the generated pool of languages and the updated id_start, of the form
\n\n{\n \"languages\": (list of updated languages)\n \"id_start\": (updated length of languages)\n}\n \n\nExamples: \n\n\n \n
>>> # Turn the knob on a universal property for modals \n>>> expressions = load_expressions ( expressions_file ) \n>>> universal_property = iff \n>>> result = generate_languages ( \n... ModalLanguage , \n... expressions , \n... lang_size , \n... sample_size , \n... universal_property , \n...) \n>>> languages = result [ "languages" ] \n>>> id_start = result [ "id_start" ] \n\n
\n", "signature": "(\tlanguage_class : Type [ ultk . language . language . Language ] , \texpressions : list [ ultk . language . language . Expression ] , \tlang_size : int , \tsample_size : int , \tcriterion : Callable [[ ultk . language . language . Expression ], bool ] = < function < lambda >> , \tfixed_wordcount = False , \tdummy_name = 'sampled_lang_' , \tid_start : int = 0 , \texact_sample = False , \tverbose = False ) -> dict [ str , typing . Any ] : ", "funcdef": "def"}, "ultk.language.sampling.sample_lang_size": {"fullname": "ultk.language.sampling.sample_lang_size", "modulename": "ultk.language.sampling", "qualname": "sample_lang_size", "kind": "function", "doc": "Get a sample of languages each of exactly lang_size.
\n\nArguments: \n\n\nlanguage_class: a subclass of ultk.Languageexpressions: a list of Expressions to sample fromlang_size: int representing the maximum language size to samplesample_size: int representing the number of total languages to returnid_start: an int representing the number of languages already generated in an experiment. \n\nReturns: \n\n\n a dict containing the randomly sampled languages and the updated id_start, of the form
\n\n{\n \"languages\": (list of updated languages)\n \"id_start\": (updated length of languages)\n}\n \n", "signature": "(\tlanguage_class : Type [ ultk . language . language . Language ] , \texpressions : list [ ultk . language . language . Expression ] , \tlang_size : int , \tsample_size : int , \tid_start : int = 0 , \tverbose = False , \tdummy_name = 'sampled_lang_id' ) -> list [ ultk . language . language . Language ] : ", "funcdef": "def"}, "ultk.language.sampling.sample_quasi_natural": {"fullname": "ultk.language.sampling.sample_quasi_natural", "modulename": "ultk.language.sampling", "qualname": "sample_quasi_natural", "kind": "function", "doc": "Turn the knob on degree quasi-naturalness for a sample of languages, either by enumerating or randomly sampling unique subsets of all possible combinations.
\n\nArguments: \n\n\nnatural_terms: expressions satisfying some criteria of quasi-naturalness, e.g, a semantic universal.unnatural_terms: expressions not satisfying the criteria.lang_size: the exact number of expressions a language must have.sample_size: how many languages to sample. \n\nReturns: \n\n\n a dict containing the randomly sampled quasi-natural languages and the updated id_start, of the form
\n\n{\n \"languages\": (list of updated languages)\n \"id_start\": (updated length of languages)\n}\n \n", "signature": "(\tlanguage_class : Type [ ultk . language . language . Language ] , \tnatural_terms : list [ ultk . language . language . Expression ] , \tunnatural_terms : list [ ultk . language . language . Expression ] , \tlang_size : int , \tsample_size : int , \tid_start : int , \tdummy_name = 'sampled_lang_id' , \tverbose = False ) -> dict [ str , typing . Any ] : ", "funcdef": "def"}, "ultk.language.sampling.rename_id": {"fullname": "ultk.language.sampling.rename_id", "modulename": "ultk.language.sampling", "qualname": "rename_id", "kind": "function", "doc": "Updates a string of form sampled_lang_X with a new id for X.
\n", "signature": "(name : str , id : int ) -> str : ", "funcdef": "def"}, "ultk.language.sampling.enumerate_all_languages": {"fullname": "ultk.language.sampling.enumerate_all_languages", "modulename": "ultk.language.sampling", "qualname": "enumerate_all_languages", "kind": "function", "doc": "When the sample size requested is greater than the size of all possible languages, just enumerate all the possible languages.
\n\nArguments: \n\n\nlanguage_class: the kind of Language to constructid_start: a number to start counting from for assigning names with numerical ids to languages.natural_indices: the indices of quasi-natural languages already seennum_natural: the number of quasi-natural languages to samplenatural_terms: the list of quasi-natural terms to sample fromunnatural_indices: the indices of non-quasi-natural languages already seennum_unnatural: the number of non-quasi-natural languages to sample; 0 by defaultunnatural_terms: the list of non-quasi-natural terms to sample from; empty by default.dummy_name: the format of the string to name each language constructed. \n\nReturns: \n\n\n a dict containing a set of languages and the updated id_start, of the form
\n\n{\n \"languages\": (list of updated languages)\n \"id_start\": (updated length of languages)\n}\n \n", "signature": "(\tlanguage_class : Type [ ultk . language . language . Language ] , \tid_start : int , \tnatural_terms : list [ ultk . language . language . Expression ] , \tnatural_indices : list [ int ] , \tnum_natural : int = 0 , \tunnatural_terms : list [ ultk . language . language . Expression ] = [] , \tunnatural_indices : list [ int ] = [] , \tnum_unnatural : int = 0 , \tdummy_name = 'sampled_lang_id' , \tverbose = False ) -> dict [ str , typing . Any ] : ", "funcdef": "def"}, "ultk.language.sampling.random_combination_vocabulary": {"fullname": "ultk.language.sampling.random_combination_vocabulary", "modulename": "ultk.language.sampling", "qualname": "random_combination_vocabulary", "kind": "function", "doc": "Get a single vocabulary for a specific language size by choosing a random combination of natural and unnatural terms.
\n\nArguments: \n\n\nseen: the list of language indices already seennum_natural: intnatural_terms: list[Expression]num_unnatural: int=0unnatural_terms: list[Expression]=[] \n\nReturns: \n\n\n languages: the extended list of input languages.
\n \n", "signature": "(\tseen : set , \tnum_natural : int , \tnatural_terms : list [ ultk . language . language . Expression ] , \tnum_unnatural : int = 0 , \tunnatural_terms : list [ ultk . language . language . Expression ] = [] ) -> list [ ultk . language . language . Language ] : ", "funcdef": "def"}, "ultk.language.semantics": {"fullname": "ultk.language.semantics", "modulename": "ultk.language.semantics", "kind": "module", "doc": "Classes for modeling the meanings of a language.
\n\nMeanings are modeled as things which map linguistic forms to objects of reference. The linguistic forms and objects of reference can in principle be very detailed, and future work may elaborate the meaning classes and implement a Form class.
\n\nIn efficient communication analyses, simplicity and informativeness can be measured as properties of semantic aspects of a language. E.g., a meaning is simple if it is easy to represent, or to compress into some code; a meaning is informative if it is easy for a listener to recover a speaker's intended literal meaning.
\n\nExamples: \n\n\n \n
>>> from ultk.language.semantics import Referent , Meaning , Universe \n>>> from ultk.language.language import Expression \n>>> # construct the meaning space for numerals \n>>> numerals_universe = NumeralUniverse ( referents = [ NumeralReferent ( str ( i )) for i in range ( 1 , 100 )]) \n>>> # construct a list of referents for the expression 'a few' \n>>> a_few_refs = [ NumeralReferent ( name = str ( i )) for i in range ( 2 , 6 )] \n>>> a_few_meaning = NumeralMeaning ( referents = a_few_refs , universe = numerals_universe ) \n>>> # define the expression \n>>> a_few = NumeralExpression ( form = "a few" , meaning = a_few_meaning ) \n\n
\n"}, "ultk.language.semantics.Referent": {"fullname": "ultk.language.semantics.Referent", "modulename": "ultk.language.semantics", "qualname": "Referent", "kind": "class", "doc": "A referent is some object in the universe for a language.
\n"}, "ultk.language.semantics.Referent.__init__": {"fullname": "ultk.language.semantics.Referent.__init__", "modulename": "ultk.language.semantics", "qualname": "Referent.__init__", "kind": "function", "doc": "Initialize a referent.
\n\nArguments: \n\n\nname: a string representing the name of the referent \n", "signature": "(name : str , properties : dict = {} , ** kwargs "}, "ultk.language.semantics.Referent.name": {"fullname": "ultk.language.semantics.Referent.name", "modulename": "ultk.language.semantics", "qualname": "Referent.name", "kind": "variable", "doc": "
\n"}, "ultk.language.semantics.Referent.to_dict": {"fullname": "ultk.language.semantics.Referent.to_dict", "modulename": "ultk.language.semantics", "qualname": "Referent.to_dict", "kind": "function", "doc": "
\n", "signature": "(self ) -> dict : ", "funcdef": "def"}, "ultk.language.semantics.Universe": {"fullname": "ultk.language.semantics.Universe", "modulename": "ultk.language.semantics", "qualname": "Universe", "kind": "class", "doc": "The universe is the set of possible referent objects for a meaning.
\n"}, "ultk.language.semantics.Universe.__init__": {"fullname": "ultk.language.semantics.Universe.__init__", "modulename": "ultk.language.semantics", "qualname": "Universe.__init__", "kind": "function", "doc": "
\n", "signature": "(\treferents : Iterable [ ultk . language . semantics . Referent ] , \tprior : dict [ str , float ] = None ) "}, "ultk.language.semantics.Universe.referents": {"fullname": "ultk.language.semantics.Universe.referents", "modulename": "ultk.language.semantics", "qualname": "Universe.referents", "kind": "variable", "doc": "
\n"}, "ultk.language.semantics.Universe.set_prior": {"fullname": "ultk.language.semantics.Universe.set_prior", "modulename": "ultk.language.semantics", "qualname": "Universe.set_prior", "kind": "function", "doc": "
\n", "signature": "(self , prior : dict [ str , float ] ): ", "funcdef": "def"}, "ultk.language.semantics.Universe.prior_numpy": {"fullname": "ultk.language.semantics.Universe.prior_numpy", "modulename": "ultk.language.semantics", "qualname": "Universe.prior_numpy", "kind": "function", "doc": "
\n", "signature": "(self ) -> numpy . ndarray : ", "funcdef": "def"}, "ultk.language.semantics.Universe.from_dataframe": {"fullname": "ultk.language.semantics.Universe.from_dataframe", "modulename": "ultk.language.semantics", "qualname": "Universe.from_dataframe", "kind": "function", "doc": "Build a Universe from a DataFrame.\nIt's assumed that each row specifies one Referent, and each column will be a property\nof that Referent. We assume that name is one of the columns of the DataFrame.
\n\nArguments: \n\n\na DataFrame representing the meaning space of interest, assumed to have a column name \n \n", "signature": "(cls , df : pandas . core . frame . DataFrame ): ", "funcdef": "def"}, "ultk.language.semantics.Universe.from_csv": {"fullname": "ultk.language.semantics.Universe.from_csv", "modulename": "ultk.language.semantics", "qualname": "Universe.from_csv", "kind": "function", "doc": "Build a Universe from a CSV file. This is a small wrapper around\nUniverse.from_dataframe, so see that documentation for more information.
\n", "signature": "(cls , filename : str ): ", "funcdef": "def"}, "ultk.language.semantics.Meaning": {"fullname": "ultk.language.semantics.Meaning", "modulename": "ultk.language.semantics", "qualname": "Meaning", "kind": "class", "doc": "A meaning picks out a set of objects from the universe.
\n\nOn one tradition (from formal semantics), we might model an underspecified meaning as a subset of the universe.\nSometimes these different referents are not equally likely,\nin which it can be helpful to define a meaning explicitly as a distribution over the universe.
\n"}, "ultk.language.semantics.Meaning.__init__": {"fullname": "ultk.language.semantics.Meaning.__init__", "modulename": "ultk.language.semantics", "qualname": "Meaning.__init__", "kind": "function", "doc": "A meaning is the set of things it refers to.
\n\nThe objects of reference are a subset of the universe of discourse. Sometimes it is natural to construe the meaning as as a probability distribution over the universe, instead of just a binary predicate.
\n\nArguments: \n\n\nreferents: a list of Referent objects, which must be a subset of the referents in universe.universe: a Universe object that defines the probability space for a meaning.dist: a dict of with Referent names as keys and weights or probabilities as values, representing the distribution over referents to associate with the meaning. By default is None, and the distribution will be uniform over the passed referents, and any remaining referents are assigned 0 probability. \n", "signature": "(\treferents : Iterable [ ultk . language . semantics . Referent ] , \tuniverse : ultk . language . semantics . Universe , \tdist : dict [ str , float ] = None ) "}, "ultk.language.semantics.Meaning.referents": {"fullname": "ultk.language.semantics.Meaning.referents", "modulename": "ultk.language.semantics", "qualname": "Meaning.referents", "kind": "variable", "doc": "
\n"}, "ultk.language.semantics.Meaning.universe": {"fullname": "ultk.language.semantics.Meaning.universe", "modulename": "ultk.language.semantics", "qualname": "Meaning.universe", "kind": "variable", "doc": "
\n"}, "ultk.language.semantics.Meaning.to_dict": {"fullname": "ultk.language.semantics.Meaning.to_dict", "modulename": "ultk.language.semantics", "qualname": "Meaning.to_dict", "kind": "function", "doc": "
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altk API documentation
+ ultk API documentation
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+ Helper functions for Rate-Distortion based (including Information Bottleneck) efficient communication analyses.
+
View Source 1 """Helper functions for Rate-Distortion based (including Information Bottleneck) efficient communication analyses."""
+ 2 3 import numpy as np
+ 4 from ultk.language.language import Language
+ 5 from ultk.language.semantics import Universe , Referent
+ 6 from ultk.effcomm.agent import LiteralSpeaker , BayesianListener
+ 7 from ultk.effcomm import util
+ 8 from embo import InformationBottleneck
+ 9 from typing import Callable
+ 10 11 12 def information_rate ( source : np . ndarray , encoder : np . ndarray ) -> float :
+ 13 """Compute the information rate / complexity of the encoder q(w|m) as $I[W:M]$."""
+ 14 pXY = util . joint ( pY_X = encoder , pX = source )
+ 15 return util . MI ( pXY = pXY )
+ 16 17 18 ##############################################################################
+ 19 # Rate-Distortion Theory
+ 20 ##############################################################################
+ 21 22 23 def get_rd_curve (
+ 24 prior : np . ndarray ,
+ 25 dist_mat : np . ndarray ,
+ 26 betas : np . ndarray = None ,
+ 27 ) -> list [ tuple [ float ]]:
+ 28 """Use the Blahut Arimoto algorithm to obtain a list of (rate, distortion) points."""
+ 29 if betas is None :
+ 30 # B-A gets a bit sparse in low-rate regions for just one np.linspace
+ 31 # betas = np.linspace(start=0, stop=2**7, num=50)
+ 32 betas = np . concatenate (
+ 33 [
+ 34 np . linspace ( start = 0 , stop = 0.29 , num = 333 ),
+ 35 np . linspace ( start = 0.3 , stop = 0.9 , num = 333 ),
+ 36 np . linspace ( start = 1.0 , stop = 2 ** 7 , num = 334 ),
+ 37 ]
+ 38 )
+ 39 # TODO: unify or something
+ 40 prior = np . array ( prior )
+ 41 dist_mat = np . array ( dist_mat )
+ 42 43 rd = lambda beta : blahut_arimoto ( dist_mat , p_x = prior , beta = beta )[ "final" ]
+ 44 pareto_points = [ rd ( beta ) for beta in betas ]
+ 45 return pareto_points
+ 46 47 48 def expected_distortion (
+ 49 p_x : np . ndarray , p_xhat_x : np . ndarray , dist_mat : np . ndarray
+ 50 ) -> float :
+ 51 """$D[X, \hat{X}] = \sum_x p(x) \sum_{\hat{x}} p(\hat{x}|x) \cdot d(x, \hat{x})$"""
+ 52 # BUG to fix: you need to diagonalize the prior.
+ 53 return np . sum ( np . diag ( p_x ) @ ( p_xhat_x * dist_mat ))
+ 54 55 56 def compute_rate_distortion (
+ 57 p_x ,
+ 58 p_xhat_x ,
+ 59 dist_mat ,
+ 60 ) -> tuple [ np . ndarray ]:
+ 61 """Compute the information rate $I(X;\hat{X})$ and total distortion $D[X, \hat{X}]$ of a joint distribution defind by $P(X)$ and $P(\hat{X}|X)$.
+ 62 63 Args:
+ 64 p_x: array of shape `|X|` the prior probability of an input symbol (i.e., the source)
+ 65 66 p_xhat_x: array of shape `(|X|, |X_hat|)` the probability of an output symbol given the input
+ 67 68 dist_mat: array of shape `(|X|, |X_hat|)` representing the distoriton matrix between the input alphabet and the reconstruction alphabet.
+ 69 70 Returns:
+ 71 a (rate, distortion) tuple containing the information rate (in bits) of compressing X into X_hat and the expected distortion between X, X_hat
+ 72 """
+ 73 return (
+ 74 information_rate ( p_x , p_xhat_x ),
+ 75 expected_distortion ( p_x , p_xhat_x , dist_mat ),
+ 76 )
+ 77 78 79 def blahut_arimoto (
+ 80 dist_mat : np . ndarray ,
+ 81 p_x : np . ndarray ,
+ 82 beta : float ,
+ 83 max_it : int = 200 ,
+ 84 eps : float = 1e-5 ,
+ 85 ignore_converge : bool = False ,
+ 86 ) -> tuple [ float ]:
+ 87 """Compute the rate-distortion function of an i.i.d distribution
+ 88 89 Args:
+ 90 dist_mat: array of shape `(|X|, |X_hat|)` representing the distortion matrix between the input alphabet and the reconstruction alphabet. dist_mat[i,j] = dist(x[i],x_hat[j]). In this context, X is a random variable representing the a speaker's meaning (target referent), and X_hat is a random variable representing a listener's meaning (guessed referent).
+ 91 92 p_x: (1D array of shape `|X|`) representing the probability mass function of the source. In this context, the prior over states of nature.
+ 93 94 beta: (scalar) the slope of the rate-distoriton function at the point where evaluation is required
+ 95 96 max_it: max number of iterations
+ 97 98 eps: accuracy required by the algorithm: the algorithm stops if there is no change in distoriton value of more than 'eps' between consequtive iterations
+ 99 100 ignore_converge: whether to run the optimization until `max_it`, ignoring the stopping criterion specified by `eps`.
+101 102 Returns:
+103 a dict of the form
+104 105 {
+106 'final': a tuple of (rate, distortion) values. This is the rate (in bits) of compressing X into X_hat, and distortion between X, X_hat
+107 108 'trajectory': a list of the (rate, distortion) points discovered during optimization
+109 }
+110 """
+111 # start with iid conditional distribution, as p(x) may not be uniform
+112 p_xhat_x = np . tile ( p_x , ( dist_mat . shape [ 1 ], 1 )) . T
+113 114 # normalize
+115 p_x /= np . sum ( p_x )
+116 p_xhat_x /= np . sum ( p_xhat_x , 1 , keepdims = True )
+117 118 it = 0
+119 traj = []
+120 distortion = 2 * eps
+121 converged = False
+122 while not converged :
+123 it += 1
+124 distortion_prev = distortion
+125 126 # p(x_hat) = sum p(x) p(x_hat | x)
+127 p_xhat = p_x @ p_xhat_x
+128 129 # p(x_hat | x) = p(x_hat) exp(- beta * d(x_hat, x)) / Z
+130 p_xhat_x = np . exp ( - beta * dist_mat ) * p_xhat
+131 p_xhat_x /= np . expand_dims ( np . sum ( p_xhat_x , 1 ), 1 )
+132 133 # update for convergence check
+134 rate , distortion = compute_rate_distortion ( p_x , p_xhat_x , dist_mat )
+135 136 # collect point
+137 traj . append (( rate , distortion ))
+138 139 # convergence check
+140 if ignore_converge :
+141 converged = it == max_it
+142 else :
+143 converged = it == max_it or np . abs ( distortion - distortion_prev ) < eps
+144 145 return {
+146 "final" : ( rate , distortion ),
+147 "trajectory" : traj ,
+148 }
+149 150 151 ##############################################################################
+152 # Information Bottleneck
+153 ##############################################################################
+154 155 # === Main IB methods ===
+156 157 158 def get_ib_curve (
+159 prior : np . ndarray ,
+160 meaning_dists : np . ndarray ,
+161 maxbeta : float ,
+162 minbeta : float ,
+163 numbeta : float ,
+164 processes : int = 1 ,
+165 curve_type : str = "informativity" ,
+166 ) -> tuple [ float ]:
+167 """Get a list of (complexity, accuracy) or (complexity, distortion) points. A minimal wrapper of `get_bottleneck.`
+168 169 Args:
+170 prior: array of shape `|meanings|`
+171 172 meaning_dists: array of shape `(|meanings|, |meanings|)` representing the distribution over world states given meanings.
+173 174 curve_type: {'informativity', 'comm_cost'} specifies whether to return the (classic) IB axes of informativity vs. complexity, or the more Rate-Distortion Theory aligned axes of comm_cost vs. complexity. The latter can be obtained easily from the former by subtracting each informativity value from I[M:U], which is a constant for all languages in the same domain.
+175 176 maxbeta: the maximum value of beta to use to compute the curve.
+177 178 minbeta: the minimum value of beta to use.
+179 180 numbeta: the number of (equally-spaced) beta values to consider to compute the curve.
+181 182 processes: number of cpu threads to run in parallel (default = 1)
+183 184 Returns:
+185 an array of shape `(num_points, 2)` representing the list of (accuracy/comm_cost, complexity) points on the information plane.
+186 """
+187 188 complexity , accuracy , distortion = get_bottleneck (
+189 prior , meaning_dists , maxbeta , minbeta , numbeta , processes
+190 )
+191 if curve_type == "comm_cost" :
+192 return np . array (
+193 list (
+194 zip (
+195 distortion ,
+196 complexity ,
+197 )
+198 )
+199 ) # expected kl divergence, complexity
+200 201 else :
+202 points = np . array (
+203 list (
+204 zip (
+205 accuracy ,
+206 complexity ,
+207 )
+208 )
+209 ) # informativity, complexity
+210 return points
+211 212 213 def get_bottleneck (
+214 prior : np . ndarray ,
+215 meaning_dists : np . ndarray ,
+216 maxbeta : float ,
+217 minbeta : float ,
+218 numbeta : float ,
+219 processes : int = 1 ,
+220 ) -> np . ndarray :
+221 """Compute the IB curve bound (I[M:W] vs. I[W:U]). We use the embo package, which has support for smoothing any non-monotonicity in the bound resulting from BA optimization getting stuck in local minima.
+222 223 Args:
+224 prior: array of shape `|meanings|`
+225 226 meaning_dists: array of shape `(|meanings|, |meanings|)` representing the distribution over world states given meanings.
+227 228 curve_type: {'informativity', 'comm_cost'} specifies whether to return the (classic) IB axes of informativity vs. complexity, or the more Rate-Distortion Theory aligned axes of comm_cost vs. complexity. The comm_cost can be obtained easily from informativity by subtracting each informativity value from I[M:U], which is a constant for all languages in the same domain.
+229 230 maxbeta: the maximum value of beta to use to compute the curve.
+231 232 minbeta: the minimum value of beta to use.
+233 234 numbeta: the number of (equally-spaced) beta values to consider to compute the curve.
+235 236 processes: number of cpu threads to run in parallel (default = 1)
+237 238 Returns:
+239 a dict containing the coordinates and encoders corresponding to IB optima, of the form
+240 241 {
+242 "encoders": an array of shape `(num_meanings, num_words)`,\n
+243 "coordinates": a tuple of arrays `(complexity, accuracy, comm_cost)` each of shape (`numbeta`,)
+244 "beta": an array of shape (`numbeta`,) corresponding to the actually used betas after non-monotonicity corrections.
+245 }
+246 """
+247 # N.B.: embo only uses numpy and scipy
+248 prior = np . array ( prior )
+249 meaning_dists = np . array ( meaning_dists )
+250 251 joint_pmu = util . joint ( meaning_dists , prior ) # P(u) = P(m)
+252 I_mu = util . MI ( joint_pmu )
+253 254 # I[M:W], I[W:U], H[W], beta, encoders
+255 I_mw , I_wu , _ , beta , encoders = InformationBottleneck (
+256 pxy = joint_pmu ,
+257 maxbeta = maxbeta ,
+258 minbeta = minbeta ,
+259 numbeta = numbeta ,
+260 processes = processes ,
+261 ) . get_bottleneck ()
+262 263 def normalize_rows ( mat : np . ndarray ):
+264 return mat / mat . sum ( 1 , keepdims = True )
+265 266 # compute by hand for debug
+267 # NOTE: I don't remember why I was doing this, maybe there's a bug
+268 # Oh i remember, it's because the encoders computed by embo don't always sum to 1.
+269 # encoders = np.array([normalize_rows(encoder) for encoder in encoders])
+270 # points = [ib_encoder_to_point(meaning_dists, prior, encoder)[:-1] for encoder in encoders]
+271 # I_mw, I_wu = tuple(zip(*points))
+272 273 coordinates = list ( zip ( * ( I_mw , I_wu , I_mu - I_wu )))
+274 275 return {
+276 "encoders" : encoders ,
+277 "coordinates" : coordinates ,
+278 "betas" : beta ,
+279 }
+280 281 282 ##############################################################################
+283 # Using ultk.Language
+284 ##############################################################################
+285 286 287 def ib_complexity (
+288 language : Language ,
+289 prior : np . ndarray ,
+290 ) -> float :
+291 """Compute the IB encoder complexity of a language $I[M:W]$."""
+292 return float (
+293 information_rate (
+294 source = prior ,
+295 encoder = language_to_ib_encoder_decoder (
+296 language ,
+297 prior ,
+298 )[ "encoder" ],
+299 )
+300 )
+301 302 303 def ib_informativity (
+304 language : Language ,
+305 prior : np . ndarray ,
+306 meaning_dists : np . ndarray ,
+307 ) -> float :
+308 """Compute the expected informativity (accuracy) $I[W:U]$ of a lexicon.
+309 310 Args:
+311 language: the Language to measure for informativity
+312 313 prior: communicative need distribution
+314 315 meaning_dists: array of shape `(|meanings|, |meanings|)` representing the distribution over world states given meanings.
+316 317 Returns:
+318 the informativity of the language I[W:U] in bits.
+319 """
+320 return float (
+321 ib_accuracy (
+322 language_to_ib_encoder_decoder ( language , prior )[ "encoder" ],
+323 prior ,
+324 meaning_dists ,
+325 )
+326 )
+327 328 329 def ib_comm_cost (
+330 language : Language ,
+331 prior : np . ndarray ,
+332 meaning_dists : np . ndarray ,
+333 ) -> float :
+334 """Compute the IB communicative cost, i.e. expected KL-divergence betweeen speaker and listener meanings, for a language.
+335 336 Args:
+337 language: the Language to measure for communicative cost
+338 339 prior: communicative need distribution
+340 341 meaning_dists: array of shape `(|meanings|, |meanings|)` representing the distribution over world states given meanings.
+342 343 Returns:
+344 the communicative cost, $\mathbb{E}[D_{KL}[M || \hat{M}]] = I[M:U] - I[W:U]$ in bits.
+345 """
+346 return ib_distortion (
+347 language_to_ib_encoder_decoder ( language , prior )[ "encoder" ],
+348 prior ,
+349 meaning_dists ,
+350 )
+351 352 353 def language_to_ib_encoder_decoder (
+354 language : Language ,
+355 prior : np . ndarray ,
+356 ) -> dict [ str , np . ndarray ]:
+357 """Convert a Language, a mapping of words to meanings, to IB encoder, q(w|m) and IB decoder q(m|w).
+358 359 Args:
+360 language: the lexicon from which to infer a speaker (encoder).
+361 362 prior: communicative need distribution
+363 364 Returns:
+365 a dict of the form
+366 {
+367 "encoder": np.ndarray of shape `(|meanings|, |words|)`,
+368 "decoder": np.ndarray of shape `(|words|, |meanings|)`,
+369 }
+370 """
+371 # In the IB framework, the encoder _can_ be a literal speaker and the decoder is a bayes optimal listener.
+372 speaker = LiteralSpeaker ( language )
+373 speaker . weights = util . rows_zero_to_uniform ( speaker . normalized_weights ())
+374 listener = BayesianListener ( speaker , prior )
+375 return {
+376 "encoder" : speaker . normalized_weights (),
+377 "decoder" : listener . normalized_weights (),
+378 }
+379 380 381 ##############################################################################
+382 # Without using ultk.Language
+383 ##############################################################################
+384 385 386 def ib_accuracy (
+387 encoder : np . ndarray , prior : np . ndarray , meaning_dists : np . ndarray
+388 ) -> float :
+389 """Return the accuracy of the lexicon I[W:U]
+390 391 Args:
+392 encoder: array of shape `(|M|, |W|)` representing P(W | M)
+393 394 decoder: array of shape `(|W|, |M|)` representing P(M | W)
+395 396 meaning_dists: array of shape `(|M|, |U|)` representing P(U | M)
+397 398 prior: array of shape `|M|` representing P(M)
+399 400 Returns:
+401 the accuracy of the lexicon I[W:U]
+402 """
+403 pMW = util . joint ( encoder , prior )
+404 pWU = pMW . T @ meaning_dists
+405 return util . MI ( pWU )
+406 407 408 def ib_distortion (
+409 encoder : np . ndarray , prior : np . ndarray , meaning_dists : np . ndarray
+410 ) -> float :
+411 """Return the IB distortion measure E[DKL[ M || M_hat ]]
+412 413 Args:
+414 encoder: array of shape `(|M|, |W|)` representing P(W | M)
+415 416 decoder: array of shape `(|W|, |M|)` representing P(M | W)
+417 418 meaning_dists: array of shape `(|M|, |U|)` representing P(U | M)
+419 420 prior: array of shape `|M|` representing P(M)
+421 422 Returns:
+423 the distortion E[DKL[ M || M_hat ]] = I[M:U] - I[W:U]
+424 """
+425 pMU = util . joint ( meaning_dists , prior )
+426 I_mu = util . MI ( pMU )
+427 accuracy = ib_accuracy ( encoder , prior , meaning_dists )
+428 return I_mu - accuracy
+429 430 431 def ib_encoder_to_point (
+432 meaning_dists : np . ndarray ,
+433 prior : np . ndarray ,
+434 encoder : np . ndarray ,
+435 decoder : np . ndarray = None ,
+436 ) -> tuple [ float ]:
+437 """Return (complexity, accuracy, comm_cost) IB coordinates.
+438 439 Args:
+440 meaning_dists: array of shape `(|meanings|, |meanings|)` representing the distribution over world states given meanings.
+441 442 prior: array of shape `|M|` representing the cognitive source
+443 444 encoder: array of shape `(|M|, |W|)` representing P(W | M)
+445 446 decoder: array of shape `(|W|, |M|)` representing P(M | W). By default is None, and the Bayesian optimal decoder will be inferred.
+447 """
+448 # TODO: be consistent about tensors vs arrays
+449 encoder = np . array ( encoder )
+450 meaning_dists = np . array ( meaning_dists )
+451 prior = np . array ( prior )
+452 if decoder is not None :
+453 decoder = np . array ( decoder )
+454 else :
+455 decoder = ib_optimal_decoder ( encoder , prior , meaning_dists )
+456 457 encoder = util . rows_zero_to_uniform ( encoder )
+458 decoder = util . rows_zero_to_uniform ( decoder )
+459 460 complexity = information_rate ( prior , encoder )
+461 accuracy = ib_accuracy ( encoder , prior , meaning_dists )
+462 distortion = ib_distortion ( encoder , prior , meaning_dists )
+463 464 return ( complexity , accuracy , distortion )
+465 466 467 def ib_optimal_decoder (
+468 encoder : np . ndarray ,
+469 prior : np . ndarray ,
+470 meaning_dists : np . ndarray ,
+471 ) -> np . ndarray :
+472 """Compute the bayesian optimal decoder. See https://github.com/nogazs/ib-color-naming/blob/master/src/ib_naming_model.py#L40
+473 474 Args:
+475 encoder: array of shape `(|words|, |meanings|)`
+476 477 prior: array of shape `(|meanings|,)`
+478 479 meaning_dists: array of shape `(|meanings|, |meanings|)`
+480 481 Returns:
+482 array of shape `(|words|, |meanings|)` representing the 'optimal' deterministic decoder
+483 """
+484 pMW = util . joint ( encoder , prior )
+485 pW_M = pMW . T / pMW . sum ( axis = 0 )[:, None ]
+486 return pW_M @ meaning_dists
+
+
+
+
+
+ def
+ get_rd_curve ( prior : numpy . ndarray , dist_mat : numpy . ndarray , betas : numpy . ndarray = None ) -> list [ tuple [ float ]] :
+
+ View Source
+
+ 24 def get_rd_curve (
+25 prior : np . ndarray ,
+26 dist_mat : np . ndarray ,
+27 betas : np . ndarray = None ,
+28 ) -> list [ tuple [ float ]]:
+29 """Use the Blahut Arimoto algorithm to obtain a list of (rate, distortion) points."""
+30 if betas is None :
+31 # B-A gets a bit sparse in low-rate regions for just one np.linspace
+32 # betas = np.linspace(start=0, stop=2**7, num=50)
+33 betas = np . concatenate (
+34 [
+35 np . linspace ( start = 0 , stop = 0.29 , num = 333 ),
+36 np . linspace ( start = 0.3 , stop = 0.9 , num = 333 ),
+37 np . linspace ( start = 1.0 , stop = 2 ** 7 , num = 334 ),
+38 ]
+39 )
+40 # TODO: unify or something
+41 prior = np . array ( prior )
+42 dist_mat = np . array ( dist_mat )
+43 44 rd = lambda beta : blahut_arimoto ( dist_mat , p_x = prior , beta = beta )[ "final" ]
+45 pareto_points = [ rd ( beta ) for beta in betas ]
+46 return pareto_points
+Use the Blahut Arimoto algorithm to obtain a list of (rate, distortion) points.
+
+
+
+
+ def
+ expected_distortion ( p_x : numpy . ndarray , p_xhat_x : numpy . ndarray , dist_mat : numpy . ndarray ) -> float :
+
+ View Source
+
+ 49 def expected_distortion (
+50 p_x : np . ndarray , p_xhat_x : np . ndarray , dist_mat : np . ndarray
+51 ) -> float :
+52 """$D[X, \hat{X}] = \sum_x p(x) \sum_{\hat{x}} p(\hat{x}|x) \cdot d(x, \hat{x})$"""
+53 # BUG to fix: you need to diagonalize the prior.
+54 return np . sum ( np . diag ( p_x ) @ ( p_xhat_x * dist_mat ))
+$D[X, \hat{X}] = \sum_x p(x) \sum_{\hat{x}} p(\hat{x}|x) \cdot d(x, \hat{x})$
+
+
+
+
+ def
+ compute_rate_distortion (p_x , p_xhat_x , dist_mat ) -> tuple [ numpy . ndarray ] :
+
+ View Source
+
+ 57 def compute_rate_distortion (
+58 p_x ,
+59 p_xhat_x ,
+60 dist_mat ,
+61 ) -> tuple [ np . ndarray ]:
+62 """Compute the information rate $I(X;\hat{X})$ and total distortion $D[X, \hat{X}]$ of a joint distribution defind by $P(X)$ and $P(\hat{X}|X)$.
+63 64 Args:
+65 p_x: array of shape `|X|` the prior probability of an input symbol (i.e., the source)
+66 67 p_xhat_x: array of shape `(|X|, |X_hat|)` the probability of an output symbol given the input
+68 69 dist_mat: array of shape `(|X|, |X_hat|)` representing the distoriton matrix between the input alphabet and the reconstruction alphabet.
+70 71 Returns:
+72 a (rate, distortion) tuple containing the information rate (in bits) of compressing X into X_hat and the expected distortion between X, X_hat
+73 """
+74 return (
+75 information_rate ( p_x , p_xhat_x ),
+76 expected_distortion ( p_x , p_xhat_x , dist_mat ),
+77 )
+Compute the information rate $I(X;\hat{X})$ and total distortion $D[X, \hat{X}]$ of a joint distribution defind by $P(X)$ and $P(\hat{X}|X)$.
+
+
Arguments:
+
+
+p_x: array of shape |X| the prior probability of an input symbol (i.e., the source)p_xhat_x: array of shape (|X|, |X_hat|) the probability of an output symbol given the inputdist_mat: array of shape (|X|, |X_hat|) representing the distoriton matrix between the input alphabet and the reconstruction alphabet.
+
+
Returns:
+
+
+ a (rate, distortion) tuple containing the information rate (in bits) of compressing X into X_hat and the expected distortion between X, X_hat
+
+
+
+
+
+ def
+ blahut_arimoto ( dist_mat : numpy . ndarray , p_x : numpy . ndarray , beta : float , max_it : int = 200 , eps : float = 1e-05 , ignore_converge : bool = False ) -> tuple [ float ] :
+
+ View Source
+
+ 80 def blahut_arimoto (
+ 81 dist_mat : np . ndarray ,
+ 82 p_x : np . ndarray ,
+ 83 beta : float ,
+ 84 max_it : int = 200 ,
+ 85 eps : float = 1e-5 ,
+ 86 ignore_converge : bool = False ,
+ 87 ) -> tuple [ float ]:
+ 88 """Compute the rate-distortion function of an i.i.d distribution
+ 89 90 Args:
+ 91 dist_mat: array of shape `(|X|, |X_hat|)` representing the distortion matrix between the input alphabet and the reconstruction alphabet. dist_mat[i,j] = dist(x[i],x_hat[j]). In this context, X is a random variable representing the a speaker's meaning (target referent), and X_hat is a random variable representing a listener's meaning (guessed referent).
+ 92 93 p_x: (1D array of shape `|X|`) representing the probability mass function of the source. In this context, the prior over states of nature.
+ 94 95 beta: (scalar) the slope of the rate-distoriton function at the point where evaluation is required
+ 96 97 max_it: max number of iterations
+ 98 99 eps: accuracy required by the algorithm: the algorithm stops if there is no change in distoriton value of more than 'eps' between consequtive iterations
+100 101 ignore_converge: whether to run the optimization until `max_it`, ignoring the stopping criterion specified by `eps`.
+102 103 Returns:
+104 a dict of the form
+105 106 {
+107 'final': a tuple of (rate, distortion) values. This is the rate (in bits) of compressing X into X_hat, and distortion between X, X_hat
+108 109 'trajectory': a list of the (rate, distortion) points discovered during optimization
+110 }
+111 """
+112 # start with iid conditional distribution, as p(x) may not be uniform
+113 p_xhat_x = np . tile ( p_x , ( dist_mat . shape [ 1 ], 1 )) . T
+114 115 # normalize
+116 p_x /= np . sum ( p_x )
+117 p_xhat_x /= np . sum ( p_xhat_x , 1 , keepdims = True )
+118 119 it = 0
+120 traj = []
+121 distortion = 2 * eps
+122 converged = False
+123 while not converged :
+124 it += 1
+125 distortion_prev = distortion
+126 127 # p(x_hat) = sum p(x) p(x_hat | x)
+128 p_xhat = p_x @ p_xhat_x
+129 130 # p(x_hat | x) = p(x_hat) exp(- beta * d(x_hat, x)) / Z
+131 p_xhat_x = np . exp ( - beta * dist_mat ) * p_xhat
+132 p_xhat_x /= np . expand_dims ( np . sum ( p_xhat_x , 1 ), 1 )
+133 134 # update for convergence check
+135 rate , distortion = compute_rate_distortion ( p_x , p_xhat_x , dist_mat )
+136 137 # collect point
+138 traj . append (( rate , distortion ))
+139 140 # convergence check
+141 if ignore_converge :
+142 converged = it == max_it
+143 else :
+144 converged = it == max_it or np . abs ( distortion - distortion_prev ) < eps
+145 146 return {
+147 "final" : ( rate , distortion ),
+148 "trajectory" : traj ,
+149 }
+Compute the rate-distortion function of an i.i.d distribution
+
+
Arguments:
+
+
+dist_mat: array of shape (|X|, |X_hat|) representing the distortion matrix between the input alphabet and the reconstruction alphabet. dist_mat[i,j] = dist(x[i],x_hat[j]). In this context, X is a random variable representing the a speaker's meaning (target referent), and X_hat is a random variable representing a listener's meaning (guessed referent).p_x: (1D array of shape |X|) representing the probability mass function of the source. In this context, the prior over states of nature.beta: (scalar) the slope of the rate-distoriton function at the point where evaluation is requiredmax_it: max number of iterationseps: accuracy required by the algorithm: the algorithm stops if there is no change in distoriton value of more than 'eps' between consequtive iterationsignore_converge: whether to run the optimization until max_it, ignoring the stopping criterion specified by eps.
+
+
Returns:
+
+
+ a dict of the form
+
+{
+ 'final': a tuple of (rate, distortion) values. This is the rate (in bits) of compressing X into X_hat, and distortion between X, X_hat
+
+ 'trajectory': a list of the (rate, distortion) points discovered during optimization
+}
+
+
+
+
+
+ def
+ get_ib_curve ( prior : numpy . ndarray , meaning_dists : numpy . ndarray , maxbeta : float , minbeta : float , numbeta : float , processes : int = 1 , curve_type : str = 'informativity' ) -> tuple [ float ] :
+
+ View Source
+
+ 159 def get_ib_curve (
+160 prior : np . ndarray ,
+161 meaning_dists : np . ndarray ,
+162 maxbeta : float ,
+163 minbeta : float ,
+164 numbeta : float ,
+165 processes : int = 1 ,
+166 curve_type : str = "informativity" ,
+167 ) -> tuple [ float ]:
+168 """Get a list of (complexity, accuracy) or (complexity, distortion) points. A minimal wrapper of `get_bottleneck.`
+169 170 Args:
+171 prior: array of shape `|meanings|`
+172 173 meaning_dists: array of shape `(|meanings|, |meanings|)` representing the distribution over world states given meanings.
+174 175 curve_type: {'informativity', 'comm_cost'} specifies whether to return the (classic) IB axes of informativity vs. complexity, or the more Rate-Distortion Theory aligned axes of comm_cost vs. complexity. The latter can be obtained easily from the former by subtracting each informativity value from I[M:U], which is a constant for all languages in the same domain.
+176 177 maxbeta: the maximum value of beta to use to compute the curve.
+178 179 minbeta: the minimum value of beta to use.
+180 181 numbeta: the number of (equally-spaced) beta values to consider to compute the curve.
+182 183 processes: number of cpu threads to run in parallel (default = 1)
+184 185 Returns:
+186 an array of shape `(num_points, 2)` representing the list of (accuracy/comm_cost, complexity) points on the information plane.
+187 """
+188 189 complexity , accuracy , distortion = get_bottleneck (
+190 prior , meaning_dists , maxbeta , minbeta , numbeta , processes
+191 )
+192 if curve_type == "comm_cost" :
+193 return np . array (
+194 list (
+195 zip (
+196 distortion ,
+197 complexity ,
+198 )
+199 )
+200 ) # expected kl divergence, complexity
+201 202 else :
+203 points = np . array (
+204 list (
+205 zip (
+206 accuracy ,
+207 complexity ,
+208 )
+209 )
+210 ) # informativity, complexity
+211 return points
+Get a list of (complexity, accuracy) or (complexity, distortion) points. A minimal wrapper of get_bottleneck.
+
+
Arguments:
+
+
+prior: array of shape |meanings|meaning_dists: array of shape (|meanings|, |meanings|) representing the distribution over world states given meanings.curve_type: {'informativity', 'comm_cost'} specifies whether to return the (classic) IB axes of informativity vs. complexity, or the more Rate-Distortion Theory aligned axes of comm_cost vs. complexity. The latter can be obtained easily from the former by subtracting each informativity value from I[M:U], which is a constant for all languages in the same domain.maxbeta: the maximum value of beta to use to compute the curve.minbeta: the minimum value of beta to use.numbeta: the number of (equally-spaced) beta values to consider to compute the curve.processes: number of cpu threads to run in parallel (default = 1)
+
+
Returns:
+
+
+ an array of shape (num_points, 2) representing the list of (accuracy/comm_cost, complexity) points on the information plane.
+
+
+
+
+
+ def
+ get_bottleneck ( prior : numpy . ndarray , meaning_dists : numpy . ndarray , maxbeta : float , minbeta : float , numbeta : float , processes : int = 1 ) -> numpy . ndarray :
+
+ View Source
+
+ 214 def get_bottleneck (
+215 prior : np . ndarray ,
+216 meaning_dists : np . ndarray ,
+217 maxbeta : float ,
+218 minbeta : float ,
+219 numbeta : float ,
+220 processes : int = 1 ,
+221 ) -> np . ndarray :
+222 """Compute the IB curve bound (I[M:W] vs. I[W:U]). We use the embo package, which has support for smoothing any non-monotonicity in the bound resulting from BA optimization getting stuck in local minima.
+223 224 Args:
+225 prior: array of shape `|meanings|`
+226 227 meaning_dists: array of shape `(|meanings|, |meanings|)` representing the distribution over world states given meanings.
+228 229 curve_type: {'informativity', 'comm_cost'} specifies whether to return the (classic) IB axes of informativity vs. complexity, or the more Rate-Distortion Theory aligned axes of comm_cost vs. complexity. The comm_cost can be obtained easily from informativity by subtracting each informativity value from I[M:U], which is a constant for all languages in the same domain.
+230 231 maxbeta: the maximum value of beta to use to compute the curve.
+232 233 minbeta: the minimum value of beta to use.
+234 235 numbeta: the number of (equally-spaced) beta values to consider to compute the curve.
+236 237 processes: number of cpu threads to run in parallel (default = 1)
+238 239 Returns:
+240 a dict containing the coordinates and encoders corresponding to IB optima, of the form
+241 242 {
+243 "encoders": an array of shape `(num_meanings, num_words)`,\n
+244 "coordinates": a tuple of arrays `(complexity, accuracy, comm_cost)` each of shape (`numbeta`,)
+245 "beta": an array of shape (`numbeta`,) corresponding to the actually used betas after non-monotonicity corrections.
+246 }
+247 """
+248 # N.B.: embo only uses numpy and scipy
+249 prior = np . array ( prior )
+250 meaning_dists = np . array ( meaning_dists )
+251 252 joint_pmu = util . joint ( meaning_dists , prior ) # P(u) = P(m)
+253 I_mu = util . MI ( joint_pmu )
+254 255 # I[M:W], I[W:U], H[W], beta, encoders
+256 I_mw , I_wu , _ , beta , encoders = InformationBottleneck (
+257 pxy = joint_pmu ,
+258 maxbeta = maxbeta ,
+259 minbeta = minbeta ,
+260 numbeta = numbeta ,
+261 processes = processes ,
+262 ) . get_bottleneck ()
+263 264 def normalize_rows ( mat : np . ndarray ):
+265 return mat / mat . sum ( 1 , keepdims = True )
+266 267 # compute by hand for debug
+268 # NOTE: I don't remember why I was doing this, maybe there's a bug
+269 # Oh i remember, it's because the encoders computed by embo don't always sum to 1.
+270 # encoders = np.array([normalize_rows(encoder) for encoder in encoders])
+271 # points = [ib_encoder_to_point(meaning_dists, prior, encoder)[:-1] for encoder in encoders]
+272 # I_mw, I_wu = tuple(zip(*points))
+273 274 coordinates = list ( zip ( * ( I_mw , I_wu , I_mu - I_wu )))
+275 276 return {
+277 "encoders" : encoders ,
+278 "coordinates" : coordinates ,
+279 "betas" : beta ,
+280 }
+Compute the IB curve bound (I[M:W] vs. I[W:U]). We use the embo package, which has support for smoothing any non-monotonicity in the bound resulting from BA optimization getting stuck in local minima.
+
+
Arguments:
+
+
+prior: array of shape |meanings|meaning_dists: array of shape (|meanings|, |meanings|) representing the distribution over world states given meanings.curve_type: {'informativity', 'comm_cost'} specifies whether to return the (classic) IB axes of informativity vs. complexity, or the more Rate-Distortion Theory aligned axes of comm_cost vs. complexity. The comm_cost can be obtained easily from informativity by subtracting each informativity value from I[M:U], which is a constant for all languages in the same domain.maxbeta: the maximum value of beta to use to compute the curve.minbeta: the minimum value of beta to use.numbeta: the number of (equally-spaced) beta values to consider to compute the curve.processes: number of cpu threads to run in parallel (default = 1)
+
+
Returns:
+
+
+ a dict containing the coordinates and encoders corresponding to IB optima, of the form
+
+{
+"encoders": an array of shape `(num_meanings, num_words)`,
+
+"coordinates": a tuple of arrays `(complexity, accuracy, comm_cost)` each of shape (`numbeta`,)
+"beta": an array of shape (`numbeta`,) corresponding to the actually used betas after non-monotonicity corrections.
+}
+
+
+
+
+
+ 330 def ib_comm_cost (
+331 language : Language ,
+332 prior : np . ndarray ,
+333 meaning_dists : np . ndarray ,
+334 ) -> float :
+335 """Compute the IB communicative cost, i.e. expected KL-divergence betweeen speaker and listener meanings, for a language.
+336 337 Args:
+338 language: the Language to measure for communicative cost
+339 340 prior: communicative need distribution
+341 342 meaning_dists: array of shape `(|meanings|, |meanings|)` representing the distribution over world states given meanings.
+343 344 Returns:
+345 the communicative cost, $\mathbb{E}[D_{KL}[M || \hat{M}]] = I[M:U] - I[W:U]$ in bits.
+346 """
+347 return ib_distortion (
+348 language_to_ib_encoder_decoder ( language , prior )[ "encoder" ],
+349 prior ,
+350 meaning_dists ,
+351 )
+Compute the IB communicative cost, i.e. expected KL-divergence betweeen speaker and listener meanings, for a language.
+
+
Arguments:
+
+
+language: the Language to measure for communicative costprior: communicative need distributionmeaning_dists: array of shape (|meanings|, |meanings|) representing the distribution over world states given meanings.
+
+
Returns:
+
+
+ the communicative cost, $\mathbb{E}[D_{KL}[M || \hat{M}]] = I[M:U] - I[W:U]$ in bits.
+
+
+
+
+
+
def
+
language_to_ib_encoder_decoder ( language : ultk.language.language.Language prior : numpy . ndarray ) -> dict [ str , numpy . ndarray ] :
+
+
View Source
+
+
354 def language_to_ib_encoder_decoder (
+355 language : Language ,
+356 prior : np . ndarray ,
+357 ) -> dict [ str , np . ndarray ]:
+358 """Convert a Language, a mapping of words to meanings, to IB encoder, q(w|m) and IB decoder q(m|w).
+359 360 Args:
+361 language: the lexicon from which to infer a speaker (encoder).
+362 363 prior: communicative need distribution
+364 365 Returns:
+366 a dict of the form
+367 {
+368 "encoder": np.ndarray of shape `(|meanings|, |words|)`,
+369 "decoder": np.ndarray of shape `(|words|, |meanings|)`,
+370 }
+371 """
+372 # In the IB framework, the encoder _can_ be a literal speaker and the decoder is a bayes optimal listener.
+373 speaker = LiteralSpeaker ( language )
+374 speaker . weights = util . rows_zero_to_uniform ( speaker . normalized_weights ())
+375 listener = BayesianListener ( speaker , prior )
+376 return {
+377 "encoder" : speaker . normalized_weights (),
+378 "decoder" : listener . normalized_weights (),
+379 }
+Convert a Language, a mapping of words to meanings, to IB encoder, q(w|m) and IB decoder q(m|w).
+
+
Arguments:
+
+
+language: the lexicon from which to infer a speaker (encoder).prior: communicative need distribution
+
+
Returns:
+
+
+ a dict of the form
+ {
+ "encoder": np.ndarray of shape (|meanings|, |words|),
+ "decoder": np.ndarray of shape (|words|, |meanings|),
+ }
+
+
+
+
+
+ def
+ ib_accuracy ( encoder : numpy . ndarray , prior : numpy . ndarray , meaning_dists : numpy . ndarray ) -> float :
+
+ View Source
+
+ 387 def ib_accuracy (
+388 encoder : np . ndarray , prior : np . ndarray , meaning_dists : np . ndarray
+389 ) -> float :
+390 """Return the accuracy of the lexicon I[W:U]
+391 392 Args:
+393 encoder: array of shape `(|M|, |W|)` representing P(W | M)
+394 395 decoder: array of shape `(|W|, |M|)` representing P(M | W)
+396 397 meaning_dists: array of shape `(|M|, |U|)` representing P(U | M)
+398 399 prior: array of shape `|M|` representing P(M)
+400 401 Returns:
+402 the accuracy of the lexicon I[W:U]
+403 """
+404 pMW = util . joint ( encoder , prior )
+405 pWU = pMW . T @ meaning_dists
+406 return util . MI ( pWU )
+Return the accuracy of the lexicon I[W:U]
+
+
Arguments:
+
+
+encoder: array of shape (|M|, |W|) representing P(W | M)decoder: array of shape (|W|, |M|) representing P(M | W)meaning_dists: array of shape (|M|, |U|) representing P(U | M)prior: array of shape |M| representing P(M)
+
+
Returns:
+
+
+ the accuracy of the lexicon I[W:U]
+
+
+
+
+
+ def
+ ib_distortion ( encoder : numpy . ndarray , prior : numpy . ndarray , meaning_dists : numpy . ndarray ) -> float :
+
+ View Source
+
+ 409 def ib_distortion (
+410 encoder : np . ndarray , prior : np . ndarray , meaning_dists : np . ndarray
+411 ) -> float :
+412 """Return the IB distortion measure E[DKL[ M || M_hat ]]
+413 414 Args:
+415 encoder: array of shape `(|M|, |W|)` representing P(W | M)
+416 417 decoder: array of shape `(|W|, |M|)` representing P(M | W)
+418 419 meaning_dists: array of shape `(|M|, |U|)` representing P(U | M)
+420 421 prior: array of shape `|M|` representing P(M)
+422 423 Returns:
+424 the distortion E[DKL[ M || M_hat ]] = I[M:U] - I[W:U]
+425 """
+426 pMU = util . joint ( meaning_dists , prior )
+427 I_mu = util . MI ( pMU )
+428 accuracy = ib_accuracy ( encoder , prior , meaning_dists )
+429 return I_mu - accuracy
+Return the IB distortion measure E[DKL[ M || M_hat ]]
+
+
Arguments:
+
+
+encoder: array of shape (|M|, |W|) representing P(W | M)decoder: array of shape (|W|, |M|) representing P(M | W)meaning_dists: array of shape (|M|, |U|) representing P(U | M)prior: array of shape |M| representing P(M)
+
+
Returns:
+
+
+ the distortion E[DKL[ M || M_hat ]] = I[M:U] - I[W:U]
+
+
+
+
+
+ def
+ ib_encoder_to_point ( meaning_dists : numpy . ndarray , prior : numpy . ndarray , encoder : numpy . ndarray , decoder : numpy . ndarray = None ) -> tuple [ float ] :
+
+ View Source
+
+ 432 def ib_encoder_to_point (
+433 meaning_dists : np . ndarray ,
+434 prior : np . ndarray ,
+435 encoder : np . ndarray ,
+436 decoder : np . ndarray = None ,
+437 ) -> tuple [ float ]:
+438 """Return (complexity, accuracy, comm_cost) IB coordinates.
+439 440 Args:
+441 meaning_dists: array of shape `(|meanings|, |meanings|)` representing the distribution over world states given meanings.
+442 443 prior: array of shape `|M|` representing the cognitive source
+444 445 encoder: array of shape `(|M|, |W|)` representing P(W | M)
+446 447 decoder: array of shape `(|W|, |M|)` representing P(M | W). By default is None, and the Bayesian optimal decoder will be inferred.
+448 """
+449 # TODO: be consistent about tensors vs arrays
+450 encoder = np . array ( encoder )
+451 meaning_dists = np . array ( meaning_dists )
+452 prior = np . array ( prior )
+453 if decoder is not None :
+454 decoder = np . array ( decoder )
+455 else :
+456 decoder = ib_optimal_decoder ( encoder , prior , meaning_dists )
+457 458 encoder = util . rows_zero_to_uniform ( encoder )
+459 decoder = util . rows_zero_to_uniform ( decoder )
+460 461 complexity = information_rate ( prior , encoder )
+462 accuracy = ib_accuracy ( encoder , prior , meaning_dists )
+463 distortion = ib_distortion ( encoder , prior , meaning_dists )
+464 465 return ( complexity , accuracy , distortion )
+Return (complexity, accuracy, comm_cost) IB coordinates.
+
+
Arguments:
+
+
+meaning_dists: array of shape (|meanings|, |meanings|) representing the distribution over world states given meanings.prior: array of shape |M| representing the cognitive sourceencoder: array of shape (|M|, |W|) representing P(W | M)decoder: array of shape (|W|, |M|) representing P(M | W). By default is None, and the Bayesian optimal decoder will be inferred.
+
+
+
+
+ def
+ ib_optimal_decoder ( encoder : numpy . ndarray , prior : numpy . ndarray , meaning_dists : numpy . ndarray ) -> numpy . ndarray :
+
+ View Source
+
+ 468 def ib_optimal_decoder (
+469 encoder : np . ndarray ,
+470 prior : np . ndarray ,
+471 meaning_dists : np . ndarray ,
+472 ) -> np . ndarray :
+473 """Compute the bayesian optimal decoder. See https://github.com/nogazs/ib-color-naming/blob/master/src/ib_naming_model.py#L40
+474 475 Args:
+476 encoder: array of shape `(|words|, |meanings|)`
+477 478 prior: array of shape `(|meanings|,)`
+479 480 meaning_dists: array of shape `(|meanings|, |meanings|)`
+481 482 Returns:
+483 array of shape `(|words|, |meanings|)` representing the 'optimal' deterministic decoder
+484 """
+485 pMW = util . joint ( encoder , prior )
+486 pW_M = pMW . T / pMW . sum ( axis = 0 )[:, None ]
+487 return pW_M @ meaning_dists
+
+
+
+ 
+
## Introduction
-ALTK is a software library that aims to support [efficient communication analyses](https://github.com/CLMBRs/altk/blob/main/images/mit-altk.pdf) of natural language. This is a line of research that aims to explain why natural languages have the structure that they do in terms competing pressures to minimize cognitive complexity and maximize communicative accuracy.
+ULTK is a software library that aims to support [efficient communication analyses](https://github.com/CLMBRs/ultk/blob/main/images/mit-altk.pdf) of natural language. This is a line of research that aims to explain why natural languages have the structure that they do in terms competing pressures to minimize cognitive complexity and maximize communicative accuracy.
Key features:
@@ -13,45 +13,45 @@ Key features:
- Language population sampling and optimization w.r.t Pareto fronts
- Rate-Distortion and Information Bottleneck style analyses
-ALTK is a long term project and it is currently in its early stages. It is intended to help lower the barrier to entry for certain research in computational semantics, and to unify methodologies. If you find something confusing, please open an issue. If you have a phenomena of interest in linguistic semantics that you want to run an efficient communication analysis on, please contact the contributors.
+ULTK is a long term project and it is currently in its early stages. It is intended to help lower the barrier to entry for certain research in computational semantics, and to unify methodologies. If you find something confusing, please open an issue. If you have a phenomena of interest in linguistic semantics that you want to run an efficient communication analysis on, please contact the contributors.
-Read the [documentation](https://clmbr.shane.st/altk).
+Read the [documentation](https://clmbr.shane.st/ultk).
-## Installing ALTK
+## Installing ULTK
-First, set up a virtual environment (e.g. via [miniconda](https://docs.conda.io/en/latest/miniconda.html), `conda create -n altk python=3.11`, and `conda activate altk`).
+First, set up a virtual environment (e.g. via [miniconda](https://docs.conda.io/en/latest/miniconda.html), `conda create -n ultk python=3.11`, and `conda activate ultk`).
1. Download or clone this repository and navigate to the root folder.
-2. Install ALTK (We recommend doing this inside a virtual environment)
+2. Install ULTK (We recommend doing this inside a virtual environment)
`pip install -e .`
## Getting started
-- Check out the [examples](https://github.com/CLMBRs/altk/tree/main/src/examples), starting with a basic signaling game. The examples folder also contains a simiple efficient communication analysis of [indefinites](https://github.com/CLMBRs/altk/tree/main/src/examples/indefinites).
+- Check out the [examples](https://github.com/CLMBRs/ultk/tree/main/src/examples), starting with a basic signaling game. The examples folder also contains a simiple efficient communication analysis of [indefinites](https://github.com/CLMBRs/ultk/tree/main/src/examples/indefinites).
- To see more scaled up usage examples, visit the codebase for an efficient communication analysis of [modals](https://github.com/nathimel/modals-effcomm) or [sim-max games](https://github.com/nathimel/rdsg).
- For an introduction to efficient communication research, here is a [survey paper](https://www.annualreviews.org/doi/abs/10.1146/annurev-linguistics-011817-045406) of the field.
- For an introduction to the RSA framework, see [this online textbook](http://www.problang.org/).
## Modules
-There are two modules. The first is [altk.effcomm](https://clmbr.shane.st/altk/altk/effcomm.html), which includes methods for measuring informativity of languages and/or communicative success of Rational Speech Act agents, and for language population sampling and optimization w.r.t Pareto fronts.
+There are two modules. The first is [ultk.effcomm](https://clmbr.shane.st/ultk/ultk/effcomm.html), which includes methods for measuring informativity of languages and/or communicative success of Rational Speech Act agents, and for language population sampling and optimization w.r.t Pareto fronts.
-The second module is [altk.language](https://clmbr.shane.st/altk/altk/language.html), which contains primitives for constructing semantic spaces, expressions, and languages. It also has a `grammar` module which can be used for building expressions in a Language of Thought and measuring complexity in terms of minimum description length, as well as for natural language syntax.
+The second module is [ultk.language](https://clmbr.shane.st/ultk/ultk/language.html), which contains primitives for constructing semantic spaces, expressions, and languages. It also has a `grammar` module which can be used for building expressions in a Language of Thought and measuring complexity in terms of minimum description length, as well as for natural language syntax.
-The source code is available on github [here](https://github.com/CLMBRs/altk).
+The source code is available on github [here](https://github.com/CLMBRs/ultk).
## Testing
-Unit tests are written in [pytest](https://docs.pytest.org/en/7.3.x/) and executed via running `pytest` in the `src/tests` folder.
+Unit tests are written in [pytest](https://docs.pytest.org/en/7.3.x/) and executed via running `pytest` in the `src/tests` folder.
## References
![\"Four](\"https://github.com/CLMBRs/altk/blob/main/images/plots.jpeg\")
![\"Four](\"https://raw.githubusercontent.com/CLMBRs/ultk/main/images/plots.jpeg\")