From b27a3ea1191b3a422050abc77f9ef4239b6c3db3 Mon Sep 17 00:00:00 2001 From: Santiaago Date: Sat, 9 Mar 2013 23:41:58 +0100 Subject: [PATCH] hw from 4 to 8 need a lot of refactor --- features.test | 2007 +++++++++++++ features.train | 7291 ++++++++++++++++++++++++++++++++++++++++++++++++ hw1.py | 2 +- hw2.py | 47 +- hw2.py~ | 0 hw4.py | 241 +- hw5.py | 165 ++ hw6.py | 132 + hw7.py | 262 ++ hw8.py | 291 ++ in.dta | 35 + out.dta | 250 ++ tools.py | 42 +- tools.py~ | 52 - 14 files changed, 10577 insertions(+), 240 deletions(-) create mode 100644 features.test create mode 100644 features.train delete mode 100644 hw2.py~ create mode 100644 hw5.py create mode 100644 hw6.py create mode 100644 hw7.py create mode 100644 hw8.py create mode 100644 in.dta create mode 100644 out.dta delete mode 100644 tools.py~ diff --git a/features.test b/features.test new file mode 100644 index 0000000..824bcc9 --- /dev/null +++ b/features.test @@ -0,0 +1,2007 @@ + 9.0000000e+00 2.7217773e-01 -4.8479375e+00 + 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9.0000000e+00 2.6123828e-01 -4.1660625e+00 + 3.0000000e+00 3.7133594e-01 -5.0890625e+00 + 3.0000000e+00 4.3002930e-01 -5.5360625e+00 + 3.0000000e+00 3.8016016e-01 -4.8167500e+00 + 0.0000000e+00 3.1038086e-01 -3.6683125e+00 + 3.0000000e+00 5.4072852e-01 -4.2932500e+00 + 3.0000000e+00 4.0919141e-01 -6.5406875e+00 + 3.0000000e+00 4.4399023e-01 -4.7496250e+00 + 3.0000000e+00 4.8939844e-01 -4.6446250e+00 + 1.0000000e+00 1.9510352e-01 -1.2179375e+00 + 1.0000000e+00 1.6884570e-01 -5.8225000e-01 + 3.0000000e+00 2.9617773e-01 -2.5582500e+00 + 3.0000000e+00 2.5279492e-01 -3.1105000e+00 + 3.0000000e+00 3.9370508e-01 -2.9211875e+00 + 0.0000000e+00 5.9758984e-01 -2.2580625e+00 + 1.0000000e+00 2.7622070e-01 -9.1625000e-01 diff --git a/hw1.py b/hw1.py index 55fd996..8b1e404 100644 --- a/hw1.py +++ b/hw1.py @@ -90,7 +90,7 @@ def PLA(N_points,w,f,t_set): def evaluate_diff_f_g(f,w): 'Returns the average of difference between f and g (g is equivalent as vector w )' count = 0 - limit = 100 + limit = 10000 diff = 0 # generate random point as out of sample data # check result and count if there is a difference diff --git a/hw2.py b/hw2.py index 1b2b299..e3644c4 100644 --- a/hw2.py +++ b/hw2.py @@ -1,8 +1,4 @@ -''' -Heads = 0 -Tails = 1 -''' N_COINS = 1000 N_TOSS = 10 N_EXPERIMENT = 100000 @@ -96,6 +92,10 @@ def flip_coin(n = N_TOSS): from tools import build_training_set_fmultipleparams from tools import sign from tools import print_avg +from tools import linear_regression +from tools import target_vector +from tools import input_data_matrix +from tools import pseudo_inverse from hw1 import PLA @@ -108,17 +108,6 @@ def flip_coin(n = N_TOSS): verbose_lr = False -def linear_regression(N_points,t_set): - '''Linear regresion algorithm - from Y and X compute the dagger or pseudo matrix - return the Xdagger.Y as the w vector - ''' - - y_vector = target_vector(t_set) - X_matrix = input_data_matrix(t_set) - X_pseudo_inverse = pseudo_inverse(X_matrix) - - return dot(X_pseudo_inverse,y_vector),X_matrix,y_vector def run_linear_regression(N_samples,N_points): '''runs on N_samples and with N_points a linear regression @@ -195,6 +184,13 @@ def compute_Eout(wlin,f,N_points): def compute_Ein(wlin, X, y): 'fraction of in sample points which got classified incorrectly' N = len(y) + print X + print '--' + print 'wlin' + print wlin + print 'dot' + print dot(X,wlin) + raw_input() g_vector = sign(dot(X,wlin)) vEin = g_vector - y @@ -204,20 +200,6 @@ def compute_Ein(wlin, X, y): return nEin / (len(vEin) *1.0) -def target_vector(t_set): - 'creates a numpy array (eg a Y matrix) from the training set' - y = array([t[1] for t in t_set]) - return y - -def input_data_matrix(t_set): - 'creates a numpy array (eg a X matrix) from the training set' - X = array([t[0] for t in t_set]) - return X - -def pseudo_inverse(X): - 'dagger of pseudo matrix used for linear regression' - return pinv(X) - #-------------------------------------------------------------------------- #Nonlinear Transformation @@ -370,24 +352,19 @@ def compute_g_vector(t_set,g_f): # G functions to compare to f. def gA(x1,x2): - #g(x1; x2) = sign(-1 -0.05x1 + 0.08x2 + 0.13x1x2 + 1.5x1^2 + 1.5x2^2) return sign(-1 - 0.05*x1 + 0.08*x2 + 0.13*x1*x2 + 1.5*x1**2 + 1.5*x2**2) def gB(x1,x2): - #g(x1; x2) = sign(-1 -0.05x1 + 0.08x2 + 0.13x1x2 + 1.5x1^2 + 15x2^2) return sign(-1 -0.05*x1 + 0.08*x2 + 0.13*x1*x2 + 1.5*x1**2 + 15*x2**2) def gC(x1,x2): - #g(x1; x2) = sign(-1 -0.05x1 + 0.08x2 + 0.13x1x2 + 15x1^2 + 1.5x2^2) return sign(-1 -0.05*x1 + 0.08*x2 + 0.13*x1*x2 + 15*x1**2 + 1.5*x2**2) def gD(x1,x2): - #g(x1; x2) = sign(-1 -1.5x1 + 0.08x2 + 0.13x1x2 + 0.05x1^2 + 0.05x2^2) return sign(-1 -1.5*x1 + 0.08*x2 + 0.13*x1*x2 + 0.05*x1**2 + 0.05*x2**2) def gE(x1,x2): - #g(x1; x2) = sign(-1 -0.05x1 + 0.08x2 + 1.5x1x2 + 0.15x1^2 + 0.15x2^2) return sign(-1 -0.05*x1 + 0.08*x2 + 1.5*x1*x2 + 0.15*x1**2 + 0.15*x2**2) def tests(): #-1-2 - hoeffding_inequality() + #hoeffding_inequality() #3 #4 #5-6 diff --git a/hw2.py~ b/hw2.py~ deleted file mode 100644 index e69de29..0000000 diff --git a/hw4.py b/hw4.py index f33b3ec..4dc614c 100644 --- a/hw4.py +++ b/hw4.py @@ -28,67 +28,86 @@ def Devroye(N,dvc,confidence): #use 2**N instead of dvc as it is a bound e = ((sqrt((N*log((4*((2**N)))/confidence)+(1/(N-2)*1.0)*(N-2))) +1)/((N-2)*1.0)) return e +def pick_point(f): + 'returns x coords randomly from interval -1 to 1 and y from function f' + x = uniform(-1,1) + y = f(x) + return x,y +def mean_sqrt_error(x1,y1,x2,y2): + return abs(x2-x1)/2.,abs(y2-y1)/2. -def bias_and_variance(): - f = lambda x:sin(x*pi) - #d = data_interval(-1,1,1000) - #df = [f(i) for i in d] - table_g = [] - table_a = [] - for i in range(100): - # pick 2 point - x1 = uniform(-1,1) - y1 = f(x1) - x2 = uniform(-1,1) - y2 = f(x2) - # calculate the mean squared errors from the examples - y = abs(y2-y1)/2. - x = abs(x2-x1)/2. - #slope - a = y/x#x/y - #compute g - g1 = lambda x:a*x - table_g.append(g1) - table_a.append(a) - slope = sum(table_a)/(len(table_a)*1.0) - #bias +def print_info_bias_variance(slope,constant,bias,var): + if slope is not None: print 'a: %s'%slope + if constant is not None: print 'b: %s'%constant + print 'bias: %s'%bias + print 'var: %s'%var + print 'Eout: %s'%(bias+var) + +def compute_bias(bias_fn,f): table_bias = [] for i in range(100): x = uniform(-1,1) - gx = slope*x + gx = bias_fn(x) fx = f(x) table_bias.append((gx-fx)**2) bias = sum(table_bias)/(len(table_bias)*1.0) - #variance + return bias + +def compute_var(var_fn, table_g): table_var = [] for i in range(100): x = uniform(-1,1) - gbarx = slope*x + gbarx = var_fn(x) table_one_g = [] for g in table_g: gx = g(x) table_one_g.append((gx - gbarx)**2) table_var.append(sum(table_one_g)/(len(table_one_g)*1.0)) var = sum(table_var)/(len(table_var)*1.0) - print 'a: %s'%slope - print 'bias: %s'%bias - print 'var: %s'%var - print 'Eout: %s'%(bias+var) + return var +def compute_var_ex(var_fn,table_a,table_b): + table_var = [] + for i in range(100): + x = uniform(-1,1) + gbarx = var_fn(x) + table_one_g = [] + for i in range(len(table_a)): + gx = table_a[i]*x**2 + table_b[i] + table_one_g.append((gx - gbarx)**2) + table_var.append(sum(table_one_g)/(len(table_one_g)*1.0)) + var = sum(table_var)/(len(table_var)*1.0) + return var +def bias_and_variance(): + f = lambda x:sin(x*pi) + table_g = [] + table_a = [] + for i in range(100): + x1,y1 = pick_point(f) + x2,y2 = pick_point(f) + x,y = mean_sqrt_error(x1,y1,x2,y2) + a = y/x #slope + #compute g + g1 = lambda x:a*x + table_g.append(g1) + table_a.append(a) + slope = sum(table_a)/(len(table_a)*1.0) + #bias + bias_fn = lambda x: slope*x + bias = compute_bias(bias_fn,f) + #variance + var_fn = lambda x: slope*x + var = compute_var(var_fn,table_g) + #print info + print_info_bias_variance(slope,None,bias,var) def bias_and_variance_constant(): f = lambda x:sin(x*pi) table_g = [] table_b = [] for i in range(100): - # pick 2 point - x1 = uniform(-1,1) - y1 = f(x1) - x2 = uniform(-1,1) - y2 = f(x2) - # calculate the mean squared errors from the examples - y = abs(y2-y1)/2. - x = abs(x2-x1)/2. - #b + x1,y1 = pick_point(f) + x2,y2 = pick_point(f) + x,y = mean_sqrt_error(x1,y1,x2,y2) b = y #compute g g1 = lambda x:b @@ -96,42 +115,22 @@ def bias_and_variance_constant(): table_b.append(b) constant = sum(table_b)/(len(table_b)*1.0) #bias - table_bias = [] - for i in range(100): - x = uniform(-1,1) - gx = constant - fx = f(x) - table_bias.append((gx-fx)**2) - bias = sum(table_bias)/(len(table_bias)*1.0) + bias_fn = lambda x: constant + bias = compute_bias(bias_fn,f) #variance - table_var = [] - for i in range(100): - x = uniform(-1,1) - gbarx = constant - table_one_g = [] - for g in table_g: - gx = g(x) - table_one_g.append((gx - gbarx)**2) - table_var.append(sum(table_one_g)/(len(table_one_g)*1.0)) - var = sum(table_var)/(len(table_var)*1.0) - print 'b: %s'%constant - print 'bias: %s'%bias - print 'var: %s'%var - print 'Eout: %s'%(bias+var) + var_fn = lambda x: constant + var = compute_var(var_fn,table_g) + #print info + print_info_bias_variance(None,constant,bias,var) def bias_and_variance_function(): f = lambda x:sin(x*pi) - #d = data_interval(-1,1,1000) - #df = [f(i) for i in d] table_g = [] table_a = [] table_b = [] for i in range(100): - # pick 2 point - x1 = uniform(-1,1) - y1 = f(x1) - x2 = uniform(-1,1) - y2 = f(x2) + x1,y1 = pick_point(f) + x2,y2 = pick_point(f) #slope a = (y1-y2)/(x1-x2) b = y1 - a*x1 @@ -141,88 +140,45 @@ def bias_and_variance_function(): slope = sum(table_a)/(len(table_a)*1.0) constant = sum(table_b)/(len(table_b)*1.0) #bias - table_bias = [] - for i in range(100): - x = uniform(-1,1) - gx = slope*x + constant - fx = f(x) - table_bias.append((gx-fx)**2) - bias = sum(table_bias)/(len(table_bias)*1.0) + bias_fn = lambda x: slope*x+constant + bias = compute_bias(bias_fn,f) #variance - table_var = [] - for i in range(100): - x = uniform(-1,1) - gbarx = slope*x - table_one_g = [] - for i in range(len(table_a)): - gx = table_a[i]*x + table_b[i] - table_one_g.append((gx - gbarx)**2) - table_var.append(sum(table_one_g)/(len(table_one_g)*1.0)) - var = sum(table_var)/(len(table_var)*1.0) - - print 'b: %s'%constant - print 'bias: %s'%bias - print 'var: %s'%var - print 'Eout: %s'%(bias+var) - + var_fn = lambda x: slope*x + var = compute_var_ex(var_fn,table_a,table_b) + #print info + print_info_bias_variance(None,constant,bias,var) def bias_and_variance_square(): f = lambda x:sin(x*pi) table_g = [] table_a = [] for i in range(100): - # pick 2 point - x1 = uniform(-1,1) - y1 = f(x1) - x2 = uniform(-1,1) - y2 = f(x2) - # calculate the mean squared errors from the examples - y = abs(y2-y1)/2. - x = abs(x2-x1)/2. - #slope - a = y/x#x/y + x1,y1 = pick_point(f) + x2,y2 = pick_point(f) + x,y = mean_sqrt_error(x1,y1,x2,y2) + a = y/x #slope #compute g g1 = lambda x:a*x**2 table_g.append(g1) table_a.append(a) slope = sum(table_a)/(len(table_a)*1.0) #bias - table_bias = [] - for i in range(100): - x = uniform(-1,1) - gx = slope*x**2 - fx = f(x) - table_bias.append((gx-fx)**2) - bias = sum(table_bias)/(len(table_bias)*1.0) + bias_fn = lambda x: slope*x**2 + bias = compute_bias(bias_fn,f) #variance - table_var = [] - for i in range(100): - x = uniform(-1,1) - gbarx = slope*x**2 - table_one_g = [] - for g in table_g: - gx = g(x) - table_one_g.append((gx - gbarx)**2) - table_var.append(sum(table_one_g)/(len(table_one_g)*1.0)) - var = sum(table_var)/(len(table_var)*1.0) - print 'a: %s'%slope - print 'bias: %s'%bias - print 'var: %s'%var - print 'Eout: %s'%(bias+var) + var_fn = lambda x: slope*x**2 + var = compute_var(var_fn,table_g) + #print info + print_info_bias_variance(slope,None,bias,var) def bias_and_variance_square_constant(): f = lambda x:sin(x*pi) - #d = data_interval(-1,1,1000) - #df = [f(i) for i in d] table_g = [] table_a = [] table_b = [] for i in range(100): - # pick 2 point - x1 = uniform(-1,1) - y1 = f(x1) - x2 = uniform(-1,1) - y2 = f(x2) + x1,y1 = pick_point(f) + x2,y2 = pick_point(f) #slope a = (y1-y2)/(x1-x2) b = y1 - a*x1**2 @@ -232,31 +188,14 @@ def bias_and_variance_square_constant(): slope = sum(table_a)/(len(table_a)*1.0) constant = sum(table_b)/(len(table_b)*1.0) #bias - table_bias = [] - for i in range(100): - x = uniform(-1,1) - gx = slope*x**2 + constant - fx = f(x) - table_bias.append((gx-fx)**2) - bias = sum(table_bias)/(len(table_bias)*1.0) + bias_fn = lambda x: slope*x**2 + constant + bias = compute_bias(bias_fn,f) #variance - table_var = [] - for i in range(100): - x = uniform(-1,1) - gbarx = slope*x**2 - table_one_g = [] - for i in range(len(table_a)): - gx = table_a[i]*x**2 + table_b[i] - table_one_g.append((gx - gbarx)**2) - table_var.append(sum(table_one_g)/(len(table_one_g)*1.0)) - var = sum(table_var)/(len(table_var)*1.0) - - print 'b: %s'%constant - print 'bias: %s'%bias - print 'var: %s'%var - print 'Eout: %s'%(bias+var) + var_fn = lambda x: slope*x**2 + var = compute_var_ex(var_fn,table_a,table_b) + #print info + print_info_bias_variance(None,constant,bias,var) - def tests(): print 'Tests begin' print '--------------------' diff --git a/hw5.py b/hw5.py new file mode 100644 index 0000000..547e912 --- /dev/null +++ b/hw5.py @@ -0,0 +1,165 @@ + +from copy import copy + +from math import exp +from math import sqrt +from math import log + +from numpy import array +from numpy import dot +from numpy import array +from numpy.linalg import norm + +from random import shuffle + +from tools import target_random_function +from tools import randomline +from tools import data +from tools import build_training_set_fmultipleparams + + +def err(u,v): + u = float(u) + v = float(v) + return (u*exp(v)-2*v*exp(-u))**2 #non linear error surface + +def linear_reg_err(sigma,d,N): + return (sigma**2)*(1-((d+1)/(N*1.0))) + +def deriv_u(u, v): + u = float(u) + v = float(v) + return 2*u*exp(2*v) + 4*u*v*exp(v-u) - 4*v*exp(v-u) - 8*v**2*exp(-2*u) + +def deriv_v(u, v): + u = float(u) + v = float(v) + return 2*u**2*exp(2*v) - 4*u*v*exp(v-u) - 4*u*exp(v-u) + 8*v*exp(-2*u) + +def gradient_descent(): + u = 1 + v = 1 + learn_rate = 0.1 + error = 10e-14 + iteration = 0 + + while(err(u, v) > error): + delta_u = u - learn_rate*deriv_u(u,v) + delta_v = v - learn_rate*deriv_v(u,v) + u,v = delta_u,delta_v + iteration = iteration + 1 + print "Iteration:%s, u: %s, v: %s E:%s" % (iteration,u,v,err(u,v)) + +def coordinate_descent(): + u = 1 + v = 1 + learn_rate = 0.1 + error = 10e-14 + iteration = 0 + + while(err(u, v) > error and iteration < 15): + u = u - learn_rate*deriv_u(u,v) + delta_v = v - learn_rate*deriv_v(u,v) + u,v = u,delta_v + iteration = iteration + 1 + print "Iteration:%s, u: %s, v: %s E:%s" % (iteration,u,v,err(u,v)) + +def gradient(sample, y,w): + vector = [y*1.0] + [y*x*1.0 for x in sample] + A = array([1]+sample) + B = array(w) + div = (1.0 + exp(y*1.0*dot(A,B))) + vector = [-1.0 * x / div for x in vector] + return vector + +def log_regression_sgd(t_set,eps,lr): + w = [0]*len(t_set[0][0]) + + converged = False + nb_epochs = 0 + old_w = [] + index_order = range(len(t_set)) + while not converged: + old_w = copy(w) + shuffle(index_order) + for i in index_order: + s = t_set[i][0][1:]# get all params expect w0 + y = t_set[i][1] + grad = gradient(s,y,w) + + for j in range(len(w)): + w[j] = w[j] - lr * grad[j] + nb_epochs += 1 + W_old = array(old_w) + W = array(w) + converged = norm(W_old - W) < eps + return nb_epochs,w + +def log_regression_compute_Eout(t_set,w): + cee = 0 + for t in t_set: + x = t[0][1] + y = t[0][2] + target = t[1] + cee += cross_entropy_error([x,y],target,w) + return cee*1.0/len(t_set) + +def cross_entropy_error(sample,y,w): + A = array([1]+sample) + B = array(w) + return log(1.0 + exp(-y*1.0*dot(A,B))) + +def run_log_regression(): + + nb_in_sample = 100 + nb_out_of_sample = 100000 + nb_runs = 100 + nb_epochs = 0 + nb_Eout = 0 + lr = 0.01 + eps = 0.01 + + for i in range(nb_runs): + + l = randomline() + f = target_random_function(l) + + data_in_sample = data(nb_in_sample) + data_out_of_sample = data(nb_out_of_sample) + + t_set_in = build_training_set_fmultipleparams(data_in_sample,f) + t_set_out = build_training_set_fmultipleparams(data_out_of_sample,f) + + epochs,w = log_regression_sgd(t_set_in,eps,lr) + e_out = log_regression_compute_Eout(t_set_out,w) + + print "Run: %s - epochs: %s"%(i, epochs) + print "Eout: %s"%(e_out) + + nb_Eout += e_out + nb_epochs += epochs + + print 'Number of runs:%s'%(nb_runs) + print "Avg epochs: %s"%(nb_epochs / nb_runs*1.0) + print "Avg Eout: %s"%(nb_Eout / nb_runs*1.0) + +def tests(): + print 'Tests begin' + print '--------------------' + print '-1-' + #sigma = 0.1 + #d = 8 + #print 'sigma:%s d:%s '%(sigma,d) + #lN = [10,25,100,500,1000] + #for N in lN: + # print 'For N:%s\t Ein:%s '%(N,linear_reg_err(sigma,d,N)) + print '-5-' + print '-Gradient descent-' + #gradient_descent() + print '-7' + print '-Coordinate descent-' + #coordinate_descent() + print '-Logistic regression-' + print '-8-' + print '-9-' + run_log_regression() diff --git a/hw6.py b/hw6.py new file mode 100644 index 0000000..b78d96d --- /dev/null +++ b/hw6.py @@ -0,0 +1,132 @@ + +from numpy import array +from numpy import transpose +from numpy import dot +from numpy import sign +from numpy.linalg import pinv as pinv # pseudo inverse aka dagger +from numpy.linalg import inv +from numpy.linalg import norm +from numpy import identity + +from tools import target_vector +from tools import input_data_matrix +from tools import pseudo_inverse + +KA = -3 +LAMBDA = 10**KA + +def compute_Ein(wlin, X, y): + 'fraction of in sample points which got classified incorrectly' + N = len(y) + g_vector = sign(dot(X,wlin)) + + vEin = g_vector - y + nEin = 0 + for i in range(len(vEin)): + if vEin[i]!= 0: nEin = nEin + 1 + + return nEin / (len(vEin) *1.0) + +def compute_Eout_nonlineartrans(wlin,outdata): + N_points = len(outdata) + + t_set_trans = transform_t_set(outdata) + X_matrix = input_data_matrix(t_set_trans) + y_vector = target_vector(t_set_trans) + + g_vector = dot(X_matrix,wlin) + for i in range(len(g_vector)): + g_vector[i] = sign(g_vector[i]) + vEout = g_vector - y_vector + nEout = 0 + for i in range(len(vEout)): + if vEout[i] != 0: + nEout = nEout+1 + Eout = nEout / (len(vEout)*1.0) + return Eout + + +def transform_t_set(data): + trans_data=[] + + for i in range(len(data)): + x1 = data[i][0][0] + x2 = data[i][0][1] + y = data[i][1] + tX = [1,x1,x2,x1**2,x2**2,x1*x2,abs(x1-x2),abs(x1+x2)] + trans_data.append([ tX,y ]) + return trans_data + +def compute_weight_decay(wlin,t_set,X,y,k): + sumsq = 0 + for wi in wlin: + sumsq = sumsq + wi**2 + wdc = ((10**k)/(len(t_set)*1.0))*sumsq + t1 = dot(transpose(X),X) + t2 = t1 + wdc*identity(len(t1)) + t3 = inv(t2) + t4 = dot(t3,transpose(X)) + w_decay = dot(t4,y) + return w_decay + +def run_nonlineartransformation(indata,outdata): + N_points = len(indata) + + t_set_trans = transform_t_set(indata) + wtrans,Xtrans,ytrans = linear_regression(N_points,t_set_trans) + print '-2-' + Eintrans = compute_Ein(wtrans,Xtrans,ytrans) + Eouttrans = compute_Eout_nonlineartrans(wtrans,outdata) + print Eintrans + print Eouttrans + print '-3-' + w_decay = compute_weight_decay(wtrans,t_set_trans,Xtrans,ytrans,-3) + Eintrans_decay = compute_Ein(w_decay,Xtrans,ytrans) + Eouttrans_decay=compute_Eout_nonlineartrans(w_decay,outdata) + print Eintrans_decay + print Eouttrans_decay + print '-4-' + w_decay = compute_weight_decay(wtrans,t_set_trans,Xtrans,ytrans,3) + Eintrans_decay = compute_Ein(w_decay,Xtrans,ytrans) + Eouttrans_decay=compute_Eout_nonlineartrans(w_decay,outdata) + print Eintrans_decay + print Eouttrans_decay + print '-5-' + for k in [2,1,0,-1,-2]: + w_decay = compute_weight_decay(wtrans,t_set_trans,Xtrans,ytrans,k) + Eintrans_decay = compute_Ein(w_decay,Xtrans,ytrans) + Eouttrans_decay=compute_Eout_nonlineartrans(w_decay,outdata) + print Eintrans_decay + print Eouttrans_decay + print '-6-' + mink = 999 + minEout = 999 + for k in range(-100,100): + w_decay = compute_weight_decay(wtrans,t_set_trans,Xtrans,ytrans,k) + Eintrans_decay = compute_Ein(w_decay,Xtrans,ytrans) + Eout_decay=compute_Eout_nonlineartrans(w_decay,outdata) + if Eout_decay < minEout: + minEout = Eout_decay + mink = k + print k + print minEout + +def getData(filename): + datafile = open(filename, 'r') + data = [] + for line in datafile: + split = line.split() + x1 = float(split[0]) + x2 = float(split[1]) + y = float(split[2]) + data.append([ [x1,x2],y ]) + return data + +def tests(): + print '-1-' + print '-2-' + indata = getData('in.dta') + outdata = getData('out.dta') + run_nonlineartransformation(indata,outdata) + print '-8-' + demo() diff --git a/hw7.py b/hw7.py new file mode 100644 index 0000000..6af0eed --- /dev/null +++ b/hw7.py @@ -0,0 +1,262 @@ + +from tools import linear_regression +from tools import target_vector +from tools import input_data_matrix +from tools import sign + +from hw1 import evaluate_diff_f_g + +from math import sqrt + +from numpy import dot +from numpy import sign + +def getData(filename): + datafile = open(filename, 'r') + data = [] + for line in datafile: + split = line.split() + x1 = float(split[0]) + x2 = float(split[1]) + y = float(split[2]) + data.append([ [x1,x2],y ]) + return data + +def compute_Eval(wlin, X, y): + 'fraction of in sample points which got classified incorrectly from Validation data set' + N = len(y) + g_vector = sign(dot(X,wlin)) + + vEin = g_vector - y + nEin = 0 + for i in range(len(vEin)): + if vEin[i]!= 0: nEin = nEin + 1 + + return nEin / (len(vEin) *1.0) + +def compute_Eout_from_data(w,t_set_out,N_points): + 'number of out-of-sample points misclassifed / total number of out-of-sample points from data' + + X_matrix = input_data_matrix(t_set_out) + y_vector = target_vector(t_set_out) + + g_vector = dot(X_matrix,w) + for i in range(len(g_vector)): + g_vector[i] = sign(g_vector[i]) + + vEout = g_vector - y_vector + nEout = 0 + for i in range(len(vEout)): + if vEout[i]!=0: + nEout = nEout + 1 + Eout = nEout/(len(vEout)*1.0) + return Eout + +def run_validation(indata_train,indata_val,outdata): + #t_set train + t_set3 = transform_t_set(indata_train,3) + t_set4 = transform_t_set(indata_train,4) + t_set5 = transform_t_set(indata_train,5) + t_set6 = transform_t_set(indata_train,6) + t_set7 = transform_t_set(indata_train,7) + + #lnr + wlin3,X,y = linear_regression(len(t_set3),t_set3) + wlin4,X,y = linear_regression(len(t_set4),t_set4) + wlin5,X,y = linear_regression(len(t_set5),t_set5) + wlin6,X,y = linear_regression(len(t_set6),t_set6) + wlin7,X,y = linear_regression(len(t_set7),t_set7) + + #t_set validation + t_setVal3 = transform_t_set(indata_val,3) + t_setVal4 = transform_t_set(indata_val,4) + t_setVal5 = transform_t_set(indata_val,5) + t_setVal6 = transform_t_set(indata_val,6) + t_setVal7 = transform_t_set(indata_val,7) + + yVal3 = target_vector(t_setVal3) + XVal3 = input_data_matrix(t_setVal3) + + yVal4 = target_vector(t_setVal4) + XVal4 = input_data_matrix(t_setVal4) + + yVal5 = target_vector(t_setVal5) + XVal5 = input_data_matrix(t_setVal5) + + yVal6 = target_vector(t_setVal6) + XVal6 = input_data_matrix(t_setVal6) + + yVal7 = target_vector(t_setVal7) + XVal7 = input_data_matrix(t_setVal7) + #Eval + Eval3 = compute_Eval(wlin3,XVal3,yVal3) + Eval4 = compute_Eval(wlin4,XVal4,yVal4) + Eval5 = compute_Eval(wlin5,XVal5,yVal5) + Eval6 = compute_Eval(wlin6,XVal6,yVal6) + Eval7 = compute_Eval(wlin7,XVal7,yVal7) + + #Eout + outdata3 = transform_t_set(outdata,3) + outdata4 = transform_t_set(outdata,4) + outdata5 = transform_t_set(outdata,5) + outdata6 = transform_t_set(outdata,6) + outdata7 = transform_t_set(outdata,7) + + Eout3 = compute_Eout_from_data(wlin3,outdata3,len(outdata3)) + Eout4 = compute_Eout_from_data(wlin4,outdata4,len(outdata4)) + Eout5 = compute_Eout_from_data(wlin5,outdata5,len(outdata5)) + Eout6 = compute_Eout_from_data(wlin6,outdata6,len(outdata6)) + Eout7 = compute_Eout_from_data(wlin7,outdata7,len(outdata7)) + + print 'Eval for k = 3 is: %s'%Eval3 + print 'Eout for k = 3 is: %s'%Eout3 + print '' + print 'Eval for k = 4 is: %s'%Eval4 + print 'Eout for k = 4 is: %s'%Eout4 + print '' + print 'Eval for k = 5 is: %s'%Eval5 + print 'Eout for k = 5 is: %s'%Eout5 + print '' + print 'Eval for k = 6 is: %s'%Eval6 + print 'Eout for k = 6 is: %s'%Eout6 + print '' + print 'Eval for k = 7 is: %s'%Eval7 + print 'Eout for k = 7 is: %s'%Eout7 + + +def transform_t_set(data,filter_k): + trans_data=[] + + for i in range(len(data)): + x1 = data[i][0][0] + x2 = data[i][0][1] + y = data[i][1] + tX = [1,x1,x2,x1**2,x2**2,x1*x2,abs(x1-x2),abs(x1+x2)] + + tX = tX[:filter_k+1] + + trans_data.append([ tX,y ]) + return trans_data +def cross_validation(p): + p = float(p) + return 4/(1+p)**2 + 4/(p-1)**2 + 1 + +def test_cv(): + ps = [ sqrt(sqrt(3)+4), sqrt(sqrt(3)-1), sqrt(9+4*sqrt(6)), sqrt(9 - sqrt(6)) ] + for p in ps: + print cross_validation(p) + +def computeEout_svm(f,w): + return evaluate_diff_f_g(f,w) + +def run_pla_vs_svm(nbruns = 1, N = 10): + from tools import data + from tools import randomline + from tools import target_function + from tools import build_training_set + from tools import target_vector + + from hw1 import PLA + #cvxopt Python Software for Convex Optimization + #from http://abel.ee.ucla.edu/cvxopt/ + import cvxopt + from cvxopt import solvers + solvers.options['show_progress'] = False + from numpy import dot + from numpy import array + + from math import fabs + + d = [] + l = 0 + f = 0 + t_set = [] + y = [] + svm_vs_pla = [] + for i in range(nbruns): + onBothSides = False + while(not onBothSides): + d = data(N) + l = randomline() + f = target_function(l) + t_set = build_training_set(d,f) + y = target_vector(t_set) + if (1 in y) and (-1 in y): + onBothSides = True + else: + onBothSides = False + w = [0,0,0] + w_pla,iteration = PLA(N,w,f,t_set) + plaEout = evaluate_diff_f_g(f,w_pla) + X_matrix = input_data_matrix(t_set) + dimension = len(X_matrix[0]) + #identity matrix of size dim X dim matrix x,I,J,typecode double + P = cvxopt.spmatrix(1, range(dimension), range(dimension), tc='d') + #vector of zeros of size dim, typecode double + q = cvxopt.matrix([0]*(dimension), tc='d') + + mat = [] + for t in t_set: + y = t[1] + temp = [x * -1.0*y for x in t[0]] + mat.append(temp) + + G = cvxopt.matrix(mat, tc='d') + G = G.trans() + # vectors of -1 of size t_set + h = cvxopt.matrix([-1]*len(t_set), tc='d') + #http://abel.ee.ucla.edu/cvxopt/examples/tutorial/qp.html + qp_sln = cvxopt.solvers.qp(P, q, G, h) + wsvm = list(qp_sln['x']) + # number of support vectors you can get at each run + count_sv = 0 + for t in t_set: + wsvm = array(wsvm) + x = array(t[0]) + y = t[1] + res = fabs(y*dot(wsvm,x)-1) + if res < 0.001: + count_sv = count_sv + 1 + #print count_sv + # Eout of svm + svmEout = computeEout_svm(f,wsvm) + #print 'svmEout: %s'%svmEout + if(svmEout < plaEout): + svm_vs_pla.append([True,count_sv]) + else: + svm_vs_pla.append([False,count_sv]) + + print 'after run: ' + print "svm win pla %f" % (len(filter(lambda a: a[0] is True, svm_vs_pla))*1.0/N) + print "svm win pla %f" % (len(filter(lambda a: a[0] is True, svm_vs_pla))*1.0/len(svm_vs_pla)) + print "svm %f"%(len(filter(lambda a:a[0] is True,svm_vs_pla))) + print "len svm_vs_pla %s"%len(svm_vs_pla) + percent_svm_won = len([r[0] for r in svm_vs_pla if r[0] is True])*1.0/len(svm_vs_pla) + print "question 9: svm beat pla %f percent of the time" % percent_svm_won + + avg_sv = sum([a[1] for a in svm_vs_pla])*1.0/len(svm_vs_pla) + print "avg sv:", avg_sv +def tests(): + print '-1-' + print '-2-' + indata = getData('in.dta') + #split in.dta into training(25) and validation(10) + indata_train = indata[:25] + indata_val = indata[25:] + outdata = getData('out.dta') + # train on 25 examples + # validate on 10 examples + run_validation(indata_train,indata_val,outdata) + print '-3-' + print '-4-' + print '-5-' + run_validation(indata_val,indata_train,outdata) + print '-6-' + print '-7-' + test_cv() + print '-8-' + #run_pla_vs_svm(1000,10) + print '-9-' + print '-10-' + run_pla_vs_svm(1000,100) + diff --git a/hw8.py b/hw8.py new file mode 100644 index 0000000..d27fb33 --- /dev/null +++ b/hw8.py @@ -0,0 +1,291 @@ +from svmutil import svm_train +from svmutil import svm_predict + +def getDataFeatures(filename): + 'from file return list of items in the form of [digit, symmerty, intensity]' + datafile = open(filename, 'r') + data = [] + for line in datafile: + split = line.split() + digit = float(split[0]) + symmetry = float(split[1]) + intensity = float(split[2]) + data.append([ float(digit),float(symmetry),float(intensity) ]) + return data + +def getDataOneVsOne(dataset,d1,d2): + 'binary classifier: d1 will be class 1, d2 will be class -1, other digits are discarded' + new_d = [] + for d in dataset: + digit, symmerty, intensity = d + if digit in (d1,d2): + if digit == d1: + digit = 1.0 + else: + digit = -1.0 + new_d.append([float(digit),float(symmerty),float(intensity)]) + return new_d + +def getDataOneVsAll(dataset,d1): + 'binary classifier: d1 will be class 1, other digits will be class -1' + new_d = [] + for d in dataset: + digit,symmerty,intensity = d + if digit == d1: + digit = 1.0 + else: + digit = -1.0 + new_d.append([float(digit),float(symmerty),float(intensity)]) + return new_d + +def get_svm_vector_format(data): + '''This method formats data in lib svm format: + Y is a 1 dimention vector, + X is a dictionary of key 1: symmerty, key 2: intensity''' + + Y=[] + X=[] + for i in range(len(data)): + Y.append(data[i][0]) + X.append({1 : data[i][1], 2:data[i][2]}) + return X,Y + +def run_poly_kernel(dTrain,dTest): + 'Work on polynomial kernel and compare different classifiers' + + print '--run poly kernel--' + dTrain_all = [] + dTest_all = [] + X_train_all = [] + Y_train_all = [] + # get data for all One vs All and format X and Y + for i in range(10): + dTrain_current = getDataOneVsAll(dTrain,i) + dTrain_all.append(getDataOneVsAll(dTrain,i)) + dTest_all.append(getDataOneVsAll(dTest,i)) + X_train,Y_train = get_svm_vector_format(dTrain_current) + X_train_all.append(X_train) + Y_train_all.append(Y_train) + + # train all models + print '--starting training--' + model_all =[] + # Type = Polynomial. Degree = 2. Gamma 1. Coef = 1. C = 0.01. be quiet. + options = '-t 1 -d 2 -g 1 -r 1 -c 0.01 -q' + for i in range(10): + model = svm_train(Y_train_all[i],X_train_all[i],options) + model_all.append(model) + # test even models + print '--testing model --' + max_Ein_q2 = 0 + max_Ein_q2_index = -1 + for i in [0,2,4,6,8]: + plabel, paccuracy,pvals = svm_predict(Y_train_all[i],X_train_all[i],model_all[i]) + ein = 100 - paccuracy[0] + if ein > max_Ein_q2: + max_Ein_q2 = ein + max_Ein_q2_index = i + # test odd models + min_Ein_q3 = 100 + min_Ein_q3_index = -1 + for i in [1,3,5,7,9]: + plabel, paccuracy,pvals = svm_predict(Y_train_all[i],X_train_all[i],model_all[i]) + ein = 100 - paccuracy[0] + if ein < min_Ein_q3: + min_Ein_q3 = ein + min_Ein_q3_index = i + # display + print + print 'The classifier ''%s versus all'' has the highest Ein: %s = from the following group %s'%(max_Ein_q2_index,max_Ein_q2,[0,2,4,6,8]) + print + print 'The classifier ''%s versus all'' has the lowest Ein: %s from the following group: %s'%(min_Ein_q3_index,min_Ein_q3,[1,3,5,7,9]) + # Comparing Models + print + print 'Comparing previous classifiers' + print + m0 = model_all[max_Ein_q2_index] + m1 = model_all[min_Ein_q3_index] + print '--m0--' + print 'Number of Support Vectors from model: %s versus all is: %s'%(str(max_Ein_q2_index),str(m0.get_nr_sv())) + print + print '--m1--' + print 'Number of Support Vectors from model: %s versus all is: %s'%(str(min_Ein_q3_index),str(m1.get_nr_sv())) + print + print 'Difference: %s'%(abs(m0.get_nr_sv()-m1.get_nr_sv())) + +def run_1vs5_q2_q5(dTrain,dTest): + 'Work on 1 vs 5 classifiers with Polynomial kernel by comparing degree Q' + + print '-- 1 Vs 5 with Q = 2 and Q = 5 --' + Cs = [0.0001,0.001,0.01,0.1,1] + # vars for polynomial of degree 5 + model_q5 = [] + Eins_q5 = [] + Eouts_q5 = [] + nb_svs_q5 = [] + # vars for polynomial of degree 2 + model_q2 = [] + Eins_q2 = [] + Eouts_q2 = [] + nb_svs_q2 = [] + + # Get data and format it + dTrain_1vs5 = getDataOneVsOne(dTrain,1,5) + dTest_1vs5 = getDataOneVsOne(dTest,1,5) + + X_train_1vs5,Y_train_1vs5 = get_svm_vector_format(dTrain_1vs5) + X_test_1vs5,Y_test_1vs5 = get_svm_vector_format(dTest_1vs5) + + # run Train and Test on all Cs + for c in Cs: + # Type = Polynomial. Degree = 5. Gamma 1. Coef = 1. C = Cs[i]. be quiet. + options = '-t 1 -d 5 -g 1 -r 1 -c '+str(c) + ' -q' + # Train + m = svm_train(Y_train_1vs5,X_train_1vs5,options) + # Test in sample + plabel, paccuracy,pvals = svm_predict(Y_train_1vs5,X_train_1vs5,m) + # Test out of sample + plabel, paccuracy_test,pvals = svm_predict(Y_test_1vs5,X_test_1vs5,m) + + nb_svs_q5.append(m.get_nr_sv()) + Eins_q5.append(100 - paccuracy[0]) + Eouts_q5.append(100 - paccuracy_test[0]) + model_q5.append(m) + + # Type = Polynomial. Degree = 2. Gamma 1. Coef = 1. C = Cs[i]. be quiet. + options = '-t 1 -d 2 -g 1 -r 1 -c '+str(c) +' -q' + # Train + m = svm_train(Y_train_1vs5,X_train_1vs5,options) + # Test in sample + plabel, paccuracy,pvals = svm_predict(Y_train_1vs5,X_train_1vs5,m) + # Test out of sample + plabel, paccuracy_test,pvals = svm_predict(Y_test_1vs5,X_test_1vs5,m) + + nb_svs_q2.append(m.get_nr_sv()) + Eins_q2.append(100 - paccuracy[0]) + Eouts_q2.append(100 - paccuracy_test[0]) + model_q2.append(m) + # Display + print + print '-- analysis --' + print + print '-- analysis Q = 2 --' + for i in range(len(Cs)): + print 'C = %s \tnumber of SV = %s'%(Cs[i],nb_svs_q2[i]) + print + for i in range(len(Cs)): + print 'C = %s \tEin = %s'%(Cs[i],Eins_q2[i]) + print + for i in range(len(Cs)): + print 'C = %s \tEout = %s'%(Cs[i],Eouts_q2[i]) + print + print '-- analysis Q = 2 vs Q = 5 --' + print 'Ein for C = %s and Q = 2 is %s'%(Cs[0],Eins_q2[0]) + print 'Ein for C = %s and Q = 5 is %s'%(Cs[0],Eins_q5[0]) + print + print 'Number of support vectors for C = %s and Q = 2 is %s'%(Cs[1],nb_svs_q2[1]) + print 'Number of support vectors for C = %s and Q = 5 is %s'%(Cs[1],nb_svs_q5[1]) + print + print 'Ein for C = %s and Q = 2 is %s'%(Cs[2],Eins_q2[2]) + print 'Ein for C = %s and Q = 5 is %s'%(Cs[2],Eins_q5[2]) + print + print 'Eout for C = %s and Q = 2 is %s'%(Cs[4],Eouts_q2[4]) + print 'Eout for C = %s and Q = 5 is %s'%(Cs[4],Eouts_q5[4]) + +def run_cross_validation(dTrain,dTest): + 'Work with Polynomal kernel with cross validation' + from svmutil import svm_train + from svmutil import svm_predict + from random import shuffle + print '--run_cross_validation--' + + print '-- 1 versus 5 with Q = 2 and Cross Validation--' + + Cs = [0.0001,0.001,0.01,0.1,1] + Ecvs = [[],[],[],[],[]] + + print '-- Train and Test --' + + dTrain_shuffle = dTrain + # Try 100 runs with different partitions + for j in range(100): + # roll those dices + shuffle(dTrain_shuffle) + # Get data and formated vectors + dTrain_1vs5 = getDataOneVsOne(dTrain_shuffle,1,5) + X_train_1vs5,Y_train_1vs5 = get_svm_vector_format(dTrain_1vs5) + # Try all Cs with cross validation + for i in range(len(Cs)): + # Type = Polynomial. Degree = 2. Gamma 1. + # Coef = 1. C = Cs[i].Cross Validation at 10. be quiet + options = '-t 1 -d 2 -g 1 -r 1 -c '+str(Cs[i])+ ' -v 10 -q' + m = svm_train(Y_train_1vs5,X_train_1vs5,options) + Ecvs[i].append(100 - m) + # display + print + for i in range(len(Ecvs)): + print 'Ecv = %s \tfor C = %s'%(sum(Ecvs[i])/100.,Cs[i]) + + print + + +def run_rbf_kernel(dTrain,dTest): + 'Work on Radial Basis function' + from svmutil import svm_train + from svmutil import svm_predict + print '--run_rbf_kernel--' + + # Get data for 1 vs 5 + dTrain_1vs5 = getDataOneVsOne(dTrain,1,5) + dTest_1vs5 = getDataOneVsOne(dTest,1,5) + # Get formated vectors Train and Test + X_train_1vs5,Y_train_1vs5 = get_svm_vector_format(dTrain_1vs5) + X_test_1vs5,Y_test_1vs5 = get_svm_vector_format(dTest_1vs5) + + Eins = [] + Eouts = [] + Cs = [0.01,1.0,100.0,1.0*10**4,1.0*10**6] + + for i in range(len(Cs)): + print 'Current C: %s'%(Cs[i]) + + # Gamma = 1. Type = RBF : exp(-gamma*|u-v|^2). shrinking: off. Be quiet. + options = '-c '+str(Cs[i])+ ' -g 1 -t 2 -h 0 -q' + # Train + print 'train' + m = svm_train(Y_train_1vs5,X_train_1vs5,options) + # Test + print 'test In sample' + plabel, paccuracy,pvals = svm_predict(Y_train_1vs5,X_train_1vs5,m) + print 'test Out of sample' + plabel, paccuracy_test,pvals = svm_predict(Y_test_1vs5,X_test_1vs5,m) + # append Errors + Eins.append(100 - paccuracy[0]) + Eouts.append(100 - paccuracy_test[0]) + #display + print + for i in range(len(Eins)): + print 'For C = %s \tEin = %s'%(Cs[i],Eins[i]) + print 'Min value for Ein is : %s'%(min(Eins)) + print + for i in range(len(Eouts)): + print 'For C = %s \tEout = %s'%(Cs[i],Eouts[i]) + print 'Min value for Eout is : %s'%(min(Eouts)) + +def tests(): + dFeaturesTrain = getDataFeatures('features.train') + dFeaturesTest = getDataFeatures('features.test') + print '-1-' + print '-2-' + print '-3-' + print '-4-' + #run_poly_kernel(dFeaturesTrain,dFeaturesTest) + print '-5-' + print '-6-' + #run_1vs5_q2_q5(dFeaturesTrain,dFeaturesTest) + print '-7-' + print '-8-' + run_cross_validation(dFeaturesTrain,dFeaturesTest) + print '-9-' + print '-10-' + #run_rbf_kernel(dFeaturesTrain,dFeaturesTest) diff --git a/in.dta b/in.dta new file mode 100644 index 0000000..c610f60 --- /dev/null +++ b/in.dta @@ -0,0 +1,35 @@ + -7.7947021e-01 8.3822138e-01 1.0000000e+00 + 1.5563491e-01 8.9537743e-01 1.0000000e+00 + -5.9907703e-02 -7.1777995e-01 1.0000000e+00 + 2.0759636e-01 7.5893338e-01 1.0000000e+00 + -1.9598312e-01 -3.7548716e-01 -1.0000000e+00 + 5.8848947e-01 -8.4255381e-01 1.0000000e+00 + 7.1985874e-03 -5.4831650e-01 -1.0000000e+00 + 7.3883852e-01 -6.0339369e-01 1.0000000e+00 + 7.0464808e-01 -2.0420052e-02 1.0000000e+00 + 9.6992666e-01 6.4137120e-01 -1.0000000e+00 + 4.3543099e-01 7.4477254e-01 -1.0000000e+00 + -8.4425822e-01 7.4235423e-01 1.0000000e+00 + 5.9142471e-01 -5.4602118e-01 1.0000000e+00 + -6.9093124e-02 3.7659995e-02 -1.0000000e+00 + -9.5154865e-01 -7.3305502e-01 -1.0000000e+00 + -1.2988138e-01 7.5676096e-01 1.0000000e+00 + -4.9534647e-01 -5.6627908e-01 -1.0000000e+00 + -9.0399413e-01 5.0922150e-01 1.0000000e+00 + 2.9235128e-01 1.6089015e-01 -1.0000000e+00 + 6.4798552e-01 -7.7933769e-01 1.0000000e+00 + 3.7595574e-01 7.8203087e-02 -1.0000000e+00 + 2.4588993e-01 4.5146739e-03 -1.0000000e+00 + -4.5719155e-01 4.2390461e-01 1.0000000e+00 + -4.4127876e-01 7.0571892e-01 1.0000000e+00 + 5.0744669e-01 7.5872586e-01 -1.0000000e+00 + -1.3258381e-01 -5.8178837e-01 -1.0000000e+00 + -4.4749067e-01 1.9576364e-01 1.0000000e+00 + 8.1658199e-01 -4.5449182e-01 1.0000000e+00 + -9.4422408e-01 8.8273421e-01 1.0000000e+00 + 4.6265533e-01 3.5583605e-01 -1.0000000e+00 + 8.8311642e-01 -1.9930013e-01 1.0000000e+00 + 1.0016050e+00 5.2575476e-01 -1.0000000e+00 + 6.0370095e-01 -5.4553701e-01 1.0000000e+00 + -1.4858757e-01 -2.1308372e-01 -1.0000000e+00 + 1.1652163e-02 8.8923931e-01 1.0000000e+00 diff --git a/out.dta b/out.dta new file mode 100644 index 0000000..a3f0201 --- /dev/null +++ b/out.dta @@ -0,0 +1,250 @@ + -1.0600562e-01 -8.1467034e-02 -1.0000000e+00 + 1.7792951e-01 -3.4595141e-01 -1.0000000e+00 + 1.0216153e-01 7.1825825e-01 1.0000000e+00 + 6.9407831e-01 6.2339743e-01 -1.0000000e+00 + 2.3541068e-02 7.2743221e-01 1.0000000e+00 + -3.1972776e-01 -8.3411411e-01 -1.0000000e+00 + -1.8674372e-01 5.3887798e-01 1.0000000e+00 + -6.3696719e-01 1.5268485e-01 1.0000000e+00 + -4.7446260e-01 8.5434436e-01 1.0000000e+00 + -3.5627652e-02 -2.7158819e-01 -1.0000000e+00 + -1.4860269e-01 1.6176177e-01 -1.0000000e+00 + -1.8065154e-01 -1.2873906e-01 -1.0000000e+00 + -6.0241113e-01 9.2550746e-01 1.0000000e+00 + 6.9808093e-01 7.9474170e-01 -1.0000000e+00 + 8.8150888e-01 -2.0124822e-01 1.0000000e+00 + -9.2384936e-01 3.8662506e-01 1.0000000e+00 + -7.6571338e-01 -1.1281293e-02 1.0000000e+00 + 1.3559198e-01 3.1705057e-02 -1.0000000e+00 + -1.5515148e-01 -3.3141997e-01 -1.0000000e+00 + 4.8517476e-01 2.9903104e-01 -1.0000000e+00 + -6.0290010e-01 3.3323420e-01 1.0000000e+00 + -5.7285816e-01 8.2835226e-01 1.0000000e+00 + -6.3539998e-01 -4.7456571e-01 -1.0000000e+00 + 9.0931654e-01 -7.8488922e-01 1.0000000e+00 + 2.5210516e-01 -8.9393713e-01 1.0000000e+00 + -5.1763422e-01 9.6044364e-01 1.0000000e+00 + -3.8587212e-01 -3.1786995e-01 -1.0000000e+00 + 8.2316659e-01 -1.2779654e-01 1.0000000e+00 + 8.2248638e-01 -8.7684295e-01 1.0000000e+00 + -5.0366208e-01 9.8027386e-01 1.0000000e+00 + 5.3387369e-01 8.2123374e-01 -1.0000000e+00 + -8.9497008e-01 -2.4011485e-01 1.0000000e+00 + 3.4287096e-01 4.7497683e-01 -1.0000000e+00 + 7.0928861e-01 5.6220681e-01 -1.0000000e+00 + -1.0004317e+00 6.0457567e-02 1.0000000e+00 + 5.2428439e-01 7.3519522e-01 -1.0000000e+00 + -5.6033040e-01 7.5583819e-01 1.0000000e+00 + 6.9752202e-01 -6.7198955e-01 1.0000000e+00 + 4.9042314e-01 7.8508662e-01 -1.0000000e+00 + -3.2677396e-01 3.4337193e-01 1.0000000e+00 + -2.9342093e-03 -4.1518173e-01 -1.0000000e+00 + -6.3123891e-01 3.5263395e-01 1.0000000e+00 + 9.1388134e-01 5.9305320e-01 -1.0000000e+00 + 2.1828280e-01 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-9.9011601e-01 1.0000000e+00 + 2.9083625e-01 -4.4320360e-01 1.0000000e+00 + 3.1974619e-01 -4.0070957e-01 1.0000000e+00 + 2.3353842e-01 6.3672589e-01 1.0000000e+00 + -1.9596922e-01 -9.9010507e-01 1.0000000e+00 + -4.3776733e-01 1.1653144e-02 1.0000000e+00 + -3.5482986e-01 8.1982000e-01 1.0000000e+00 + 3.4704463e-01 -5.4508368e-01 1.0000000e+00 + 8.3637625e-01 3.4383080e-01 -1.0000000e+00 + -7.1385080e-01 -6.4057506e-01 -1.0000000e+00 diff --git a/tools.py b/tools.py index 2feac00..5cb8548 100644 --- a/tools.py +++ b/tools.py @@ -1,6 +1,11 @@ from random import uniform from random import randint +from numpy import array +from numpy.linalg import pinv as pinv # pseudo inverse aka dagger +from numpy import dot + + def data_interval(low_b,high_b,N=100): d = [] for i in range(N): @@ -31,6 +36,17 @@ def target_function(l): f = lambda x: l[0]*x + l[1] return f +def target_random_function(l): + func = target_function(l) + def f(X): + x = X[0] + y = X[1] + if func(x) < y: + return 1.0 + else: + return -1.0 + return f + def sign(x,compare_to = 0): 'returns +1 or -1 by comparing x to compare_to param (by default = 0)' if x > compare_to: @@ -42,7 +58,6 @@ def map_point(point,f): 'maps a point (x1,x2) to a sign -+1 following function f ' x1 = point[0] y1 = point[1] - y = f(x1) compare_to = y1 return sign(y,compare_to) @@ -72,3 +87,28 @@ def build_training_set_fmultipleparams(data,func): def print_avg(name,vector): print 'Average %s: %s'%(name,sum(vector)/(len(vector)*1.0)) + +def target_vector(t_set): + 'creates a numpy array (eg a Y matrix) from the training set' + y = array([t[1] for t in t_set]) + return y + +def input_data_matrix(t_set): + 'creates a numpy array (eg a X matrix) from the training set' + X = array([t[0] for t in t_set]) + return X + +def pseudo_inverse(X): + 'dagger of pseudo matrix used for linear regression' + return pinv(X) + +def linear_regression(N_points,t_set): + '''Linear regresion algorithm + from Y and X compute the dagger or pseudo matrix + return the Xdagger.Y as the w vector + ''' + y_vector = target_vector(t_set) + X_matrix = input_data_matrix(t_set) + X_pseudo_inverse = pseudo_inverse(X_matrix) + return dot(X_pseudo_inverse,y_vector),X_matrix,y_vector + diff --git a/tools.py~ b/tools.py~ deleted file mode 100644 index 613d086..0000000 --- a/tools.py~ +++ /dev/null @@ -1,52 +0,0 @@ -from random import uniform -from random import randint - -def data(N = 10): - 'return N random points (x1,x2)' - d = [] - for i in range(N): - x = uniform(-1,1) - y = uniform(-1,1) - d.append([x,y]) - return d - -def randomline(): - 'computes a random line and returns a and b params: y = ax + b' - x1 = uniform(-1,1) - y1 = uniform(-1,1) - x2 = uniform(-1,1) - y2 = uniform(-1,1) - - a = abs(x1-x2)/abs(y1-y2) - b = y1 - a*x1 - return [a,b] # a*x + b - -def target_function(l): - # print 'Target function: %s x + %s' %(l[0], l[1] - f = lambda x: l[0]*x + l[1] - return f - -def sign(x,compare_to = 0): - 'returns +1 or -1 by comparing x to compare_to param (by default = 0)' - if x > compare_to: - return +1 - else: - return -1 - -def map_point(point,f): - 'maps a point (x1,x2) to a sign -+1 following function f ' - x1 = point[0] - y1 = point[1] - - y = f(x1) - compare_to = y1 - return sign(y,compare_to) - -def build_training_set(data, func): - t_set = [] - for i in range(len(data)): - point = data[i] - y = map_point(point,func) - t_set.append([ [ 1, point[0],point[1] ] , y ]) - return t_set -