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models.py
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models.py
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from __future__ import division
import numpy as np
import itertools, collections, operator, random, abc
from matplotlib import pyplot as plt
from matplotlib import cm
from basic.abstractions import ModelGibbsSampling, ModelEM
import basic.distributions
from internals import states, initial_state, transitions
# TODO think about factoring out base classes for HMMs and HSMMs
# TODO maybe states classes should handle log_likelihood...
class HMM(ModelGibbsSampling, ModelEM):
'''
The HMM class is a convenient wrapper that provides useful constructors and
packages all the components.
'''
_states_class = states.HMMStatesPython
def __init__(self,
obs_distns,
trans_distn=None,
alpha=None,gamma=None,
alpha_a_0=None,alpha_b_0=None,gamma_a_0=None,gamma_b_0=None,
init_state_distn=None,
init_state_concentration=None):
self.state_dim = len(obs_distns)
self.obs_distns = obs_distns
self.states_list = []
assert (trans_distn is not None) ^ \
(alpha is not None and gamma is not None) ^ \
(alpha_a_0 is not None and alpha_b_0 is not None
and gamma_a_0 is not None and gamma_b_0 is not None)
if trans_distn is not None:
self.trans_distn = trans_distn
elif alpha is not None:
self.trans_distn = transitions.HDPHMMTransitions(
state_dim=self.state_dim,
alpha=alpha,gamma=gamma)
else:
self.trans_distn = transitions.HDPHMMTransitionsConcResampling(
state_dim=self.state_dim,
alpha_a_0=alpha_a_0,alpha_b_0=alpha_b_0,
gamma_a_0=gamma_a_0,gamma_b_0=gamma_b_0)
assert (init_state_distn is not None) ^ \
(init_state_concentration is not None)
if init_state_distn is not None:
self.init_state_distn = init_state_distn
else:
self.init_state_distn = initial_state.InitialState(
state_dim=self.state_dim,
rho=init_state_concentration)
def add_data(self,data,stateseq=None,**kwargs):
self.states_list.append(self._states_class(model=self,data=np.asarray(data,dtype=np.float64),
stateseq=stateseq,**kwargs))
def log_likelihood(self,data):
s = self._states_class(model=self,data=np.asarray(data,dtype=np.float64),
stateseq=np.zeros(len(data))) # placeholder
betal = s.messages_backwards()
return np.logaddexp.reduce(np.log(self.init_state_distn.pi_0) + betal[0] + s.aBl[0])
### generation
def generate(self,T,keep=True):
'''
Generates a forward sample using the current values of all parameters.
Returns an observation sequence and a state sequence of length T.
If keep is True, the states object created is appended to the
states_list. This is mostly useful for generating synthetic data and
keeping it around in an HSMM object as the latent truth.
To construct a posterior sample, one must call both the add_data and
resample methods first. Then, calling generate() will produce a sample
from the posterior (as long as the Gibbs sampling has converged). In
these cases, the keep argument should be False.
'''
tempstates = self._states_class(self,T=T,initialize_from_prior=True)
return self._generate(tempstates,keep)
def _generate(self,tempstates,keep):
obs,labels = tempstates.generate_obs(), tempstates.stateseq
if keep:
tempstates.added_with_generate = True
tempstates.data = obs
self.states_list.append(tempstates)
return obs, labels
### caching
def _clear_caches(self):
for s in self.states_list:
s.clear_caches()
### Gibbs sampling
def resample_model(self):
self.resample_obs_distns()
self.resample_trans_distn()
self.resample_init_state_distn()
self.resample_states()
def resample_obs_distns(self):
for state, distn in enumerate(self.obs_distns):
distn.resample([s.data[s.stateseq == state] for s in self.states_list])
self._clear_caches()
def resample_trans_distn(self):
self.trans_distn.resample([s.stateseq for s in self.states_list])
self._clear_caches()
def resample_init_state_distn(self):
self.init_state_distn.resample([s.stateseq[:1] for s in self.states_list])
self._clear_caches()
def resample_states(self):
for s in self.states_list:
s.resample()
### parallel
def add_data_parallel(self,data_id,**kwargs):
from pyhsmm import parallel
self.add_data(parallel.alldata[data_id],**kwargs)
self.states_list[-1].data_id = data_id
def resample_model_parallel2(self,numtoresample='all'):
from pyhsmm import parallel
if numtoresample == 'all':
numtoresample = len(self.states_list)
elif numtoresample == 'engines':
numtoresample = len(parallel.dv)
# push model and data to engines
parallel.dv.push({'global_model': self},block=True)
### resample parameters locally
self.obs_distns = parallel.resample_obs_distns.map(xrange(len(self.obs_distns)) )
self.resample_trans_distn()
self.resample_init_state_distn()
### choose which sequences to resample
states_to_resample = random.sample(self.states_list,numtoresample)
### resample states in parallel
self.states_list = parallel.resample_states.map([s for s in self.states_list])
parallel.c.purge_results('all')
def resample_model_parallel(self,numtoresample='all'):
from pyhsmm import parallel
if numtoresample == 'all':
numtoresample = len(self.states_list)
elif numtoresample == 'engines':
numtoresample = len(parallel.dv)
### resample parameters locally
self.resample_obs_distns()
self.resample_trans_distn()
self.resample_init_state_distn()
### choose which sequences to resample
states_to_resample = random.sample(self.states_list,numtoresample)
### resample states in parallel
self._push_self_parallel(states_to_resample)
self._build_states_parallel(states_to_resample)
### purge to prevent memory buildup
parallel.c.purge_results('all')
def _push_self_parallel(self,states_to_resample):
from pyhsmm import parallel
states_to_restore = [s for s in self.states_list if s not in states_to_resample]
self.states_list = []
parallel.dv.push({'global_model':self},block=True)
self.states_list = states_to_restore
def _build_states_parallel(self,states_to_resample):
from pyhsmm import parallel
raw_stateseq_tuples = parallel.build_states.map([s.data_id for s in states_to_resample])
for data_id, stateseq in raw_stateseq_tuples:
self.add_data(data=parallel.alldata[data_id],stateseq=stateseq)
self.states_list[-1].data_id = data_id
### EM
def EM_step(self):
assert len(self.states_list) > 0, 'Must have data to run EM'
self._clear_caches()
## E step
for s in self.states_list:
s.E_step()
## M step
# observation distribution parameters
for state, distn in enumerate(self.obs_distns):
distn.max_likelihood([s.data for s in self.states_list],
[s.expectations[:,state] for s in self.states_list])
# initial distribution parameters
self.init_state_distn.max_likelihood(
None, # placeholder, "should" be np.arange(self.state_dim)
[s.expectations[0] for s in self.states_list])
# transition parameters (requiring more than just the marginal expectations)
self.trans_distn.max_likelihood(None,[(s.alphal,s.betal,s.aBl) for s in self.states_list])
def num_parameters(self):
return sum(o.num_parameters() for o in self.obs_distns) + self.state_dim**2
def BIC(self):
# NOTE: in principle this method computes the BIC only after finding the
# maximum likelihood parameters (or, of course, an EM fixed-point as an
# approximation!)
assert len(self.states_list) > 0, 'Must have data to get BIC'
return -2*sum(self.log_likelihood(s.data).sum() for s in self.states_list) + \
self.num_parameters() * np.log(sum(s.data.shape[0] for s in self.states_list))
def Viterbi_EM_step(self):
assert len(self.states_list) > 0, 'Must have data to run Viterbi EM'
self._clear_caches()
## Viterbi step
for s in self.states_list:
s.Viterbi()
## M step
for state, distn in enumerate(self.obs_distns):
distn.max_likelihood([s.data[s.stateseq == state] for s in self.states_list])
self.init_state_distn.max_likelihood(
np.array([s.stateseq[0] for s in self.states_list]))
self.trans_distn.max_likelihood([s.stateseq for s in self.states_list])
### plotting
def _get_used_states(self,states_objs=None):
if states_objs is None:
states_objs = self.states_list
canonical_ids = collections.defaultdict(itertools.count().next)
for s in states_objs:
for state in s.stateseq:
canonical_ids[state]
return map(operator.itemgetter(0),sorted(canonical_ids.items(),key=operator.itemgetter(1)))
def _get_colors(self):
states = self._get_used_states()
numstates = len(states)
return dict(zip(states,np.linspace(0,1,numstates,endpoint=True)))
def plot_observations(self,colors=None,states_objs=None):
if colors is None:
colors = self._get_colors()
if states_objs is None:
states_objs = self.states_list
cmap = cm.get_cmap()
used_states = self._get_used_states(states_objs)
for state,o in enumerate(self.obs_distns):
if state in used_states:
o.plot(
color=cmap(colors[state]),
data=[s.data[s.stateseq == state] if s.data is not None else None
for s in states_objs],
label='%d' % state)
plt.title('Observation Distributions')
def plot(self,color=None,legend=True):
plt.gcf() #.set_size_inches((10,10))
colors = self._get_colors()
num_subfig_cols = len(self.states_list)
for subfig_idx,s in enumerate(self.states_list):
plt.subplot(2,num_subfig_cols,1+subfig_idx)
self.plot_observations(colors=colors,states_objs=[s])
plt.subplot(2,num_subfig_cols,1+num_subfig_cols+subfig_idx)
s.plot(colors_dict=colors)
class HMMEigen(HMM):
_states_class = states.HMMStatesEigen
class StickyHMM(HMM, ModelGibbsSampling):
'''
The HMM class is a convenient wrapper that provides useful constructors and
packages all the components.
'''
def __init__(self,
obs_distns,
trans_distn=None,
kappa=None,alpha=None,gamma=None,
rho_a_0=None,rho_b_0=None,alphakappa_a_0=None,alphakappa_b_0=None,gamma_a_0=None,gamma_b_0=None,
**kwargs):
assert (trans_distn is not None) ^ \
(kappa is not None and alpha is not None and gamma is not None) ^ \
(rho_a_0 is not None and rho_b_0 is not None
and alphakappa_a_0 is not None and alphakappa_b_0 is not None
and gamma_a_0 is not None and gamma_b_0 is not None)
if trans_distn is not None:
self.trans_distn = trans_distn
elif kappa is not None:
self.trans_distn = transitions.StickyHDPHMMTransitions(
state_dim=len(obs_distns),
alpha=alpha,gamma=gamma,kappa=kappa)
else:
self.trans_distn = transitions.StickyHDPHMMTransitionsConcResampling(
state_dim=len(obs_distns),
rho_a_0=rho_a_0,rho_b_0=rho_b_0,
alphakappa_a_0=alphakappa_a_0,alphakappa_b_0=alphakappa_b_0,
gamma_a_0=gamma_a_0,gamma_b_0=gamma_b_0)
super(StickyHMM,self).__init__(obs_distns,trans_distn=self.trans_distn,**kwargs)
def EM_step(self):
raise NotImplementedError, "Can't run EM on a StickyHMM"
class StickyHMMEigen(StickyHMM):
_states_class = states.HMMStatesEigen
class HSMM(HMM, ModelGibbsSampling):
'''
The HSMM class is a wrapper to package all the pieces of an HSMM:
* HSMM internals, including distribution objects for
- states
- transitions
- initial state
* the main distributions that define the HSMM:
- observations
- durations
When an HSMM is instantiated, it is a ``prior'' model object. Observation
sequences can be added via the add_data(data_seq) method, making it a
``posterior'' model object and then the latent components (including all
state sequences and parameters) can be resampled by calling the resample()
method.
'''
_states_class = states.HSMMStatesPython
def __init__(self,
obs_distns,dur_distns,
trunc=None,
trans_distn=None,
alpha=None,gamma=None,
alpha_a_0=None,alpha_b_0=None,gamma_a_0=None,gamma_b_0=None,
**kwargs):
self.state_dim = len(obs_distns)
self.trunc = trunc
self.dur_distns = dur_distns
assert (trans_distn is not None) ^ \
(alpha is not None and gamma is not None) ^ \
(alpha_a_0 is not None and alpha_b_0 is not None
and gamma_a_0 is not None and gamma_b_0 is not None)
if trans_distn is not None:
self.trans_distn = trans_distn
elif alpha is not None:
self.trans_distn = transitions.HDPHSMMTransitions(
state_dim=self.state_dim,
alpha=alpha,gamma=gamma)
else:
self.trans_distn = transitions.HDPHSMMTransitionsConcResampling(
state_dim=self.state_dim,
alpha_a_0=alpha_a_0,alpha_b_0=alpha_b_0,
gamma_a_0=gamma_a_0,gamma_b_0=gamma_b_0)
super(HSMM,self).__init__(obs_distns=obs_distns,trans_distn=self.trans_distn,**kwargs)
def add_data(self,data,stateseq=None,censoring=True,**kwargs):
self.states_list.append(self._states_class(self,
data=np.asarray(data,dtype=np.float64),stateseq=stateseq,censoring=censoring,
trunc=self.trunc,**kwargs))
def log_likelihood(self,data,trunc=None,**kwargs):
s = self._states_class(model=self,data=np.asarray(data,dtype=np.float64),trunc=trunc,
stateseq=np.zeros(len(data)),**kwargs)
betal, _ = s.messages_backwards()
return np.logaddexp.reduce(np.log(self.init_state_distn.pi_0) + betal[0] + s.aBl[0])
### generation
def generate(self,T,keep=True,**kwargs):
tempstates = self._states_class(self,T=T,initialize_from_prior=True,trunc=self.trunc,**kwargs)
return self._generate(tempstates,keep)
### Gibbs sampling
def resample_model(self):
self.resample_dur_distns()
super(HSMM,self).resample_model()
def resample_dur_distns(self):
for state, distn in enumerate(self.dur_distns):
distn.resample([s.durations[s.stateseq_norep == state] for s in self.states_list])
self._clear_caches()
### parallel
def add_data_parallel(self,data_id,**kwargs):
from pyhsmm import parallel
self.add_data(parallel.alldata[data_id],**kwargs)
self.states_list[-1].data_id = data_id
def resample_model_parallel(self,numtoresample='all'):
self.resample_dur_distns()
super(HSMM,self).resample_model_parallel(self,numtoresample)
### EM
def EM_step(self):
super(HSMM,self).EM_step()
# M step for duration distributions
for state, distn in enumerate(self.dur_distns):
distn.max_likelihood(
None, # placeholder, "should" be [np.arange(s.T) for s in self.states_list]
[s.expectations[:,state] for s in self.states_list])
def num_parameters(self):
return sum(o.num_parameters() for o in self.obs_distns) \
+ sum(d.num_parameters() for d in self.dur_distns) \
+ self.state_dim**2 - self.state_dim
### plotting
def plot_durations(self,colors=None,states_objs=None):
if colors is None:
colors = self._get_colors()
if states_objs is None:
states_objs = self.states_list
cmap = cm.get_cmap()
used_states = self._get_used_states(states_objs)
for state,d in enumerate(self.dur_distns):
if state in used_states:
d.plot(color=cmap(colors[state]),
data=[s.durations[s.stateseq_norep == state]
for s in states_objs])
plt.title('Durations')
def plot(self,color=None):
plt.gcf() #.set_size_inches((10,10))
colors = self._get_colors()
num_subfig_cols = len(self.states_list)
for subfig_idx,s in enumerate(self.states_list):
plt.subplot(3,num_subfig_cols,1+subfig_idx)
self.plot_observations(colors=colors,states_objs=[s])
plt.subplot(3,num_subfig_cols,1+num_subfig_cols+subfig_idx)
s.plot(colors_dict=colors)
plt.subplot(3,num_subfig_cols,1+2*num_subfig_cols+subfig_idx)
self.plot_durations(colors=colors,states_objs=[s])
def plot_summary(self,color=None):
# if there are too many state sequences in states_list, make an
# alternative plot that isn't so big
raise NotImplementedError # TODO
class HSMMEigen(HSMM):
_states_class = states.HSMMStatesEigen
class HSMMPossibleChangepoints(HSMM, ModelGibbsSampling):
_states_class = states.HSMMStatesPossibleChangepoints
def add_data(self,data,changepoints,**kwargs):
self.states_list.append(
self._states_class(self,changepoints,data=np.asarray(data,dtype=np.float64),
trunc=self.trunc,**kwargs))
def add_data_parallel(self,data_id,**kwargs):
from pyhsmm import parallel
self.add_data(parallel.alldata[data_id],parallel.allchangepoints[data_id],**kwargs)
self.states_list[-1].data_id = data_id
def _build_states_parallel(self,states_to_resample):
from pyhsmm import parallel
raw_stateseq_tuples = parallel.build_states_changepoints.map([s.data_id for s in states_to_resample])
for data_id, stateseq in raw_stateseq_tuples:
self.add_data(
data=parallel.alldata[data_id],
changepoints=parallel.allchangepoints[data_id],
stateseq=stateseq)
self.states_list[-1].data_id = data_id
def generate(self,T,changepoints,keep=True):
raise NotImplementedError
def log_likelihood(self,data,trunc=None):
raise NotImplementedError
class HSMMGeoApproximation(HSMM):
_states_class = states.HSMMStatesGeoApproximation
class _HSMMIntNegBinBase(HSMM, HMMEigen):
__metaclass__ = abc.ABCMeta
def EM_step(self):
# needs to use HMM messages that the states objects give us (only betal)
# on top of that, need to hand things duration distributions... UGH
# probably need betastarl too plus some indicator variable magic
raise NotImplementedError # TODO
def Viterbi_EM_step(self):
self._clear_caches()
## Viterbi step
for s in self.states_list:
s.Viterbi()
## M step
for state, distn in enumerate(self.obs_distns):
distn.max_likelihood([s.data[s.stateseq == state] for s in self.states_list])
self.init_state_distn.max_likelihood(
np.array([s.stateseq[0] for s in self.states_list]))
# this is the only difference from parent's Viterbi_EM_step: use
# stateseq_norep
self.trans_distn.max_likelihood([s.stateseq_norep for s in self.states_list])
for state, distn in enumerate(self.dur_distns):
distn.max_likelihood([s.durations[:-1][s.stateseq_norep[:-1] == state] for s in self.states_list])
def log_likelihood(self,data):
s = self._states_class(model=self,data=np.asarray(data,dtype=np.float64),
stateseq=np.zeros(len(data))) # placeholder
betal,_ = s.messages_backwards()
return np.logaddexp.reduce(np.log(s.pi_0) + betal[0] + s.aBl[0])
class HSMMIntNegBinVariant(_HSMMIntNegBinBase):
_states_class = states.HSMMStatesIntegerNegativeBinomialVariant
def __init__(self,obs_distns,dur_distns,*args,**kwargs):
assert all(isinstance(d,basic.distributions.NegativeBinomialIntegerRVariantDuration) or
isinstance(d,basic.distributions.NegativeBinomialFixedRVariantDuration)
for d in dur_distns)
super(HSMMIntNegBinVariant,self).__init__(obs_distns,dur_distns,*args,**kwargs)
class HSMMIntNegBin(_HSMMIntNegBinBase):
_states_class = states.HSMMStatesIntegerNegativeBinomial
def __init__(self,obs_distns,dur_distns,*args,**kwargs):
assert all(isinstance(d,basic.distributions.NegativeBinomialIntegerRDuration) or
isinstance(d,basic.distributions.NegativeBinomialFixedRDuration)
for d in dur_distns)
super(HSMMIntNegBin,self).__init__(obs_distns,dur_distns,*args,**kwargs)