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paper_F_noise.py
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paper_F_noise.py
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from matplotlib import pyplot as plt
import matplotlib.gridspec as gridspec
import numpy as np
import scipy as sp
from scipy.linalg import cholesky, cho_solve, solve_triangular
import math
import time
import copy
import sys
from sklearn.gaussian_process import GaussianProcessRegressor
from sklearn.gaussian_process.kernels import RBF, Matern, RationalQuadratic,ExpSineSquared, DotProduct, ConstantKernel, WhiteKernel
from math import pi
from GP_module import GP
from models_module import *
import subprocess
command = ['rm PRELIMINARY_PAPER_F/*']
subprocess.call(command, shell=True)
def basis_function(x, return_variance= False):
# basis = np.ones((1, len(x)));
# for i in range(len(x)):
# basis[0][i] = x[i] + x[i]*np.sin(x[i]);
# if return_variance is True:
# return basis, np.zeros(( len(x), len(x) ));
# else:
# return basis;
if return_variance is True:
return np.ones((1, len(x) )), np.zeros((len(x), len(x) ));
else:
return np.ones((1, len(x) ));
plt.rc('font',family='Times New Roman')
Rnd_seed = 49;
RandomDataGenerator = np.random.RandomState();
RandomDataGenerator.seed( Rnd_seed );
col = ['r', 'b', 'm'];
FONTSIZE = 14
Mode_Opt_labels= ['ML', 'LOO', 'DL', 'WA', 'AWLL', 'LS'];
Mode_Opt_list = ['MLL', 'LOO', 'MLLD', 'MLLW', 'MLLA', 'MLLS'];
LASSO_list = [False, False, True, False, False, False];
Mode='G'#Don't touch this for the paper
Nobs_array = [ 6, 9, 12, 15 ];
#Nobs_array = [ 6 ];
NdataRandomization= 10;
Nested= False;
Matching = False;
Equal_size= True;
Deterministic= False;
Activate_histogram_plot=False
x_min = 0.0;
x_max = 1.0;
Np = 1000;
xx = np.linspace(x_min, x_max, Np);
# Complex Function
models = [model_1, model_2, model_6, model_3, model_4];
truth = model_4
Nmod = len(models);
Tychonov_regularization_coeff= 1e-4;
gp_restart = 10;
kernel = ConstantKernel(1.0**2, (1.0e-1**2, 1.0e1**2)) * RBF(length_scale=1.0, length_scale_bounds=(1.0e-1, 1.0e1)) \
+ WhiteKernel(noise_level=1.0e-2, noise_level_bounds=(1.0e-8, 1.0e-0));
Mode_Opt = Mode_Opt_list[ 0 ];
LASSO= LASSO_list[0];
nOrdering = 1;
N_columns = 2;
if Activate_histogram_plot: N_columns += 1;
class PerformanceRecord:
regression_param = [];
kernel_param = [];
LOGL = [];
score = [];
MF_performance = [];
SF_performance = [];
LG_performance = [];
for iDataRandomization in range(NdataRandomization):
Train_points = [];
for iOrdering in range(nOrdering):
MF_performance.append([PerformanceRecord() for i in range(len(Nobs_array))]);
SF_performance.append([PerformanceRecord() for i in range(len(Nobs_array))]);
LG_performance.append([PerformanceRecord() for i in range(len(Nobs_array))]);
fig_frame = [];
for iOrdering in range( len(Nobs_array) ):
fig_frame.append(plt.figure(figsize=(14, 8)));
outer = gridspec.GridSpec( nOrdering, N_columns, wspace= 0.2, hspace= 0.3 );
for nn in range(len(Nobs_array)):
Nobs = Nobs_array[nn];
model_order = [];
tmp = np.arange(Nmod-1);
np.random.shuffle(tmp)
tmp = np.append(tmp, [Nmod-1], axis=0);
model_order.append(tmp);
print("Number of observations " + str(Nobs) + " iRand " + str(iDataRandomization));
print("Generating synthetic data")
if Equal_size:
# Nobs_model = [Nobs for i in range(Nmod)];
Nobs_model = [2*Nobs for i in range(Nmod)];
Nobs_model[-1] = Nobs;
else:
if not Deterministic:
Nobs_model = [(Nmod - i)*Nobs for i in range(Nmod)];
#Nobs_model = [10*Nobs for i in range(Nmod)];
#Nobs_model[-1] = Nobs;
else:
Nobs_model = [ (Nobs - 1) *2**(Nmod - i - 1) + 1 for i in range(Nmod)];
if Matching:
if not Equal_size: print("Matching must have equal sized data sets!"); exit();
Train_points = [];
if Deterministic:
for i in range(Nmod):
Train_points.append( np.linspace(x_min, x_max, Nobs_model[i]) );
else:
for i in range(Nmod):
RandomDataGenerator.seed( Rnd_seed );
Train_points.append( RandomDataGenerator.uniform(x_min, x_max, Nobs_model[i]) );
elif Nested and nn != 0:
for i in range(Nmod):
if Deterministic:
Train_points[i] = np.concatenate( (Train_points[i], np.linspace(x_min, x_max, Nobs_model[i]-len(Train_points[i])) ), axis=None)
else:
Train_points[i] = np.concatenate( (Train_points[i], RandomDataGenerator.uniform(x_min, x_max, Nobs_model[i]-len(Train_points[i])) ), axis=None)
else:
Train_points = [];
for i in range(Nmod):
if Deterministic:
Train_points.append( np.linspace(x_min, x_max, Nobs_model[i]) );
else:
Train_points.append( RandomDataGenerator.uniform(x_min, x_max, Nobs_model[i]) );
observations = [];
for i in range(Nmod):
observations.append([]);
for j in range(Nobs_model[i]):
observations[i].append(models[i](Train_points[i][j]));
for i in range(Nmod):
observations[i] = np.array(observations[i]);
it_frame = fig_frame[nn];
it_frame.suptitle('N points ' + str(Nobs) );
for iOrdering in range(nOrdering):
inner = gridspec.GridSpecFromSubplotSpec(Nmod, 1, subplot_spec= outer[N_columns*iOrdering], wspace=0.1, hspace=0.1)
print(model_order[iOrdering])
Mfs = [];
print('IR regression param');
for Nm in model_order[iOrdering]:
if not Mfs:
Mfs.append(GP(kernel, mode=Mode));
Mfs[-1].fit(Train_points[Nm].reshape(-1, 1), observations[Nm][:, 0].reshape(-1, 1), observations[Nm][:, 1].reshape(-1, 1), Opt_Mode= Mode_Opt, LASSO=LASSO);
else:
Mfs.append( GP(kernel, [Mfs[i].predict for i in range( len(Mfs) )], mode=Mode) );
Mfs[-1].fit(Train_points[Nm].reshape(-1, 1), observations[Nm][:, 0].reshape(-1, 1), observations[Nm][:, 1].reshape(-1, 1), Opt_Mode= Mode_Opt, LASSO=LASSO);
print(len(Train_points[Nm]), Mfs[-1].regression_param)
MGs = [];
print('LeGratiet regression param');
for Nm in model_order[iOrdering]:
if not MGs:
MGs.append(GP(kernel, mode=Mode));
MGs[-1].fit(Train_points[Nm].reshape(-1, 1), observations[Nm][:, 0].reshape(-1, 1), observations[Nm][:, 1].reshape(-1, 1), Opt_Mode= Mode_Opt, LASSO=LASSO);
else:
MGs.append( GP(kernel, [MGs[-1].predict], mode=Mode) );
MGs[-1].fit(Train_points[Nm].reshape(-1, 1), observations[Nm][:, 0].reshape(-1, 1), observations[Nm][:, 1].reshape(-1, 1), Opt_Mode= Mode_Opt, LASSO=LASSO);
print(len(Train_points[Nm]), MGs[-1].regression_param)
for Nm in model_order[iOrdering]:
ax = plt.Subplot(it_frame, inner[ np.where(np.array(model_order[iOrdering]) == Nm )[0][0] ])
yy, vv = Mfs[ np.where(np.array(model_order[iOrdering]) == Nm )[0][0] ].predict(xx.reshape(-1, 1), return_variance= True)
yy = yy.flatten();
ss = np.sqrt(np.diag(vv))
ax.plot(xx, yy, color='r', label='GP')
ax.fill_between(xx, yy-ss, yy+ss, facecolor='r', alpha=0.3, interpolate=True)
ax.scatter(Train_points[Nm], observations[Nm][:, 0])
ax.plot(xx, models[Nm](xx)[:][0], color='k', label='T')
if Nm == Nmod-1:
ax.tick_params(axis='both', labelsize=FONTSIZE)
ax.yaxis.set_major_formatter(plt.NullFormatter())
ax.set_ylabel('T', fontsize=FONTSIZE)
else:
ax.yaxis.set_major_formatter(plt.NullFormatter())
ax.set_ylabel('M ' + str(Nm+1), fontsize=FONTSIZE)
it_frame.add_subplot(ax)
MF_performance[-(nOrdering-iOrdering)][nn].regression_param = np.copy( Mfs[-1].regression_param.flatten() );
MF_performance[-(nOrdering-iOrdering)][nn].kernel_param = np.copy( np.exp(Mfs[-1].kernel.theta) );
MF_performance[-(nOrdering-iOrdering)][nn].LOGL = np.copy( Mfs[-1].compute_loglikelihood(xx.reshape(-1, 1), truth(xx)[0].reshape(-1, 1)) )
MF_performance[-(nOrdering-iOrdering)][nn].score = np.copy( Mfs[-1].score(xx.reshape(-1, 1), truth(xx)[0].reshape(-1, 1)) )
LG_performance[-(nOrdering-iOrdering)][nn].regression_param = np.copy( MGs[-1].regression_param.flatten() );
LG_performance[-(nOrdering-iOrdering)][nn].kernel_param = np.copy( np.copy( np.exp(MGs[-1].kernel.theta) ) );
LG_performance[-(nOrdering-iOrdering)][nn].LOGL = np.copy( MGs[-1].compute_loglikelihood(xx.reshape(-1, 1), truth(xx)[0].reshape(-1, 1)) )
LG_performance[-(nOrdering-iOrdering)][nn].score = np.copy( MGs[-1].score(xx.reshape(-1, 1), truth(xx)[0].reshape(-1, 1)) )
yy, vv = Mfs[-1].predict(xx.reshape(-1, 1), return_variance= True)
yy = yy.flatten();
ss = np.sqrt(np.diag(vv))
yg, vg = MGs[-1].predict(xx.reshape(-1, 1), return_variance= True)
yg = yg.flatten();
sg = np.sqrt(np.diag(vg))
GP_single = GP(kernel, mode=Mode);
GP_single.fit(Train_points[-1].reshape(-1, 1), observations[-1][:, 0].reshape(-1, 1), observations[Nm][:, 1].reshape(-1, 1), Opt_Mode= Mode_Opt, LASSO=LASSO);
SF_performance[-(nOrdering-iOrdering)][nn].regression_param = np.copy( GP_single.regression_param.flatten() );
SF_performance[-(nOrdering-iOrdering)][nn].kernel_param = np.copy( np.exp(GP_single.kernel.theta) );
SF_performance[-(nOrdering-iOrdering)][nn].LOGL = np.copy( GP_single.compute_loglikelihood(xx.reshape(-1, 1), truth(xx)[0].reshape(-1, 1)) )
SF_performance[-(nOrdering-iOrdering)][nn].score = np.copy( GP_single.score(xx.reshape(-1, 1), truth(xx)[0].reshape(-1, 1)) )
yy_s, vv_s = GP_single.predict(xx.reshape(-1, 1), return_variance= True)
yy_s = yy_s.flatten();
ss_s = np.sqrt(np.diag(vv_s))
inner = gridspec.GridSpecFromSubplotSpec(1, 1, subplot_spec= outer[N_columns*iOrdering+1], wspace=0.1, hspace=0.1)
ax = plt.Subplot(it_frame, inner[0])
ax.scatter(Train_points[-1], observations[-1][:, 0])
ax.plot(xx, truth(xx)[0], color='k', label='T')
ax.plot(xx, yy, color='r', label='IR')
ax.fill_between(xx, yy-ss, yy+ss, facecolor='r', alpha=0.3, interpolate=True)
ax.plot(xx, yy_s, color='g', label='SF')
ax.fill_between(xx, yy_s-ss_s, yy_s+ss_s, facecolor='g', alpha=0.3, interpolate=True)
ax.plot(xx, yg, color='b', label='SR')
ax.fill_between(xx, yg-sg, yg+sg, facecolor='b', alpha=0.3, interpolate=True)
ax.legend(prop={'size': FONTSIZE}, frameon=False)
ax.tick_params(axis='both', labelsize=FONTSIZE)
it_frame.add_subplot(ax)
if Activate_histogram_plot:
inner = gridspec.GridSpecFromSubplotSpec(1, 1, subplot_spec= outer[N_columns*iOrdering+2], wspace=0.1, hspace=0.3)
ax = plt.Subplot(it_frame, inner[0])
print(["M " + str(j+1) for j in model_order[iOrdering] ])
for i in range( len(Mfs) ):
if (len(Mfs[i].regression_param) == 0): continue;
ax.bar(i, np.absolute( Mfs[i].regression_param ).max() +0.1, 0.95, color='gainsboro', edgecolor='k');
l = len(Mfs[i].regression_param.flatten());
w = 1.0/(l);
bar_chart_width= 0.7/(Nmod-1);
w = 1.0/(Nmod-1);
ax.bar([(i-0.5)+w/2 +j*w for j in model_order[iOrdering][0:l]], np.absolute( Mfs[i].regression_param ).flatten(), bar_chart_width, color=[ 'r' if j else 'k' for j in (Mfs[i].regression_param > 0) ] )
ax.tick_params(axis='both', labelsize=FONTSIZE)
ax.set_xticks([j for j in range( len(model_order[iOrdering]) )])
ax.set_xticklabels(["M " + str(j+1) for j in model_order[iOrdering]]);
ax.legend(prop={'size': FONTSIZE}, frameon=False)
it_frame.add_subplot(ax)
model_order.append(np.arange(Nmod).flatten());
model_order[-1][2] = 3;
model_order[-1][3] = 2;
string_save = 'PRELIMINARY_PAPER_F/' + str(iDataRandomization) + '_' + Mode + '_' + Mode_Opt + '_';
if LASSO: string_save+= 'LASSO_';
if Matching: string_save+= 'matching_';
if Nested: string_save+= 'nested_';
if Equal_size: string_save+= 'equal_';
for nn in range(len(Nobs_array)):
fig_frame[nn].tight_layout()
fig_frame[nn].savefig( string_save + str(nn) + '.pdf')
av_score_IR = np.zeros((nOrdering, len(Nobs_array)));
st_score_IR = np.zeros((nOrdering, len(Nobs_array)));
av_score_SR = np.zeros((nOrdering, len(Nobs_array)));
st_score_SR = np.zeros((nOrdering, len(Nobs_array)));
av_score_SF = np.zeros((nOrdering, len(Nobs_array)));
st_score_SF = np.zeros((nOrdering, len(Nobs_array)));
for j in range(len(Nobs_array)):
for iOrdering in range(nOrdering):
f_IR = open('PRELIMINARY_PAPER_F/regression_params_IR_' + Mode + '_' + Mode_Opt + '_n'+ str(Nobs_array[j]) + '_o' + str(iOrdering) + '.dat', 'w')
f_SR = open('PRELIMINARY_PAPER_F/regression_params_SR_' + Mode + '_' + Mode_Opt + '_n'+ str(Nobs_array[j]) + '_o' + str(iOrdering) + '.dat', 'w')
f_SF = open('PRELIMINARY_PAPER_F/regression_params_SF_' + Mode + '_' + Mode_Opt + '_n'+ str(Nobs_array[j]) + '_o' + str(iOrdering) + '.dat', 'w')
reg_IR = []; reg_SR = []; reg_SF = [];
sco_IR = []; sco_SR = []; sco_SF = [];
kp_IR = []; kp_SR = []; kp_SF = [];
for i in MF_performance[iOrdering::nOrdering]: reg_IR.append(i[j].regression_param); sco_IR.append(i[j].score); kp_IR.append(i[j].kernel_param);
for i in LG_performance[iOrdering::nOrdering]: reg_SR.append(i[j].regression_param); sco_SR.append(i[j].score); kp_SR.append(i[j].kernel_param);
for i in SF_performance[iOrdering::nOrdering]: reg_SF.append(i[j].regression_param); sco_SF.append(i[j].score); kp_SF.append(i[j].kernel_param);
f_IR.write('Mean: ' + str( np.array(reg_IR).mean(axis=0) ) + '\n');
f_IR.write('Std: ' + str( np.array(reg_IR).std(axis=0) ) + '\n');
f_IR.write('Mean score: ' + str( np.array(sco_IR).mean(axis=0) ) + ' Std score: ' + str( np.array(sco_IR).std(axis=0) ) + '\n');
f_IR.write('Mean ker p: ' + str( np.array(kp_IR ).mean(axis=0) ) + ' Std reg p: ' + str( np.array(kp_IR ).std(axis=0) ) + '\n');
av_score_IR[iOrdering, j] = np.array(sco_IR ).mean(axis=0); st_score_IR[iOrdering, j] = np.array(sco_IR ).std(axis=0);
f_SR.write('Mean: ' + str( np.array(reg_SR).mean(axis=0) ) + '\n');
f_SR.write('Std: ' + str( np.array(reg_SR).std(axis=0) ) + '\n');
f_SR.write('Mean score: ' + str( np.array(sco_SR).mean(axis=0) ) + ' Std score: ' + str( np.array(sco_SR).std(axis=0) ) + '\n');
f_SR.write('Mean ker p: ' + str( np.array(kp_SR ).mean(axis=0) ) + ' Std reg p: ' + str( np.array(kp_SR ).std(axis=0) ) + '\n');
av_score_SR[iOrdering, j] = np.array(sco_SR ).mean(axis=0); st_score_SR[iOrdering, j] = np.array(sco_SR ).std(axis=0);
f_SF.write('Mean: ' + str( np.array(reg_SF).mean(axis=0) ) + '\n');
f_SF.write('Std: ' + str( np.array(reg_SF).std(axis=0) ) + '\n');
f_SF.write('Mean score: ' + str( np.array(sco_SF).mean(axis=0) ) + ' Std score: ' + str( np.array(sco_SF).std(axis=0) ) + '\n');
f_SF.write('Mean ker p: ' + str( np.array(kp_SF ).mean(axis=0) ) + ' Std reg p: ' + str( np.array(kp_SF ).std(axis=0) ) + '\n');
av_score_SF[iOrdering, j] = np.array(sco_SF ).mean(axis=0); st_score_SF[iOrdering, j] = np.array(sco_SF ).std(axis=0);
f_IR.write('N reg param, score, kern params\n');
f_SR.write('N reg param, score, kern params\n');
f_SF.write('N reg param, score, kern params\n');
for i in MF_performance[iOrdering::nOrdering]:
reg_IR.append(i[j].regression_param);
for k in i[j].regression_param:
f_IR.write( str(k) + ' ');
f_IR.write( str(i[j].score) + ' ');
for k in i[j].kernel_param:
f_IR.write( str(k) + ' ');
f_IR.write('\n')
for i in LG_performance[iOrdering::nOrdering]:
for k in i[j].regression_param:
f_SR.write( str(k) + ' ');
f_SR.write( str(i[j].score) + ' ');
for k in i[j].kernel_param:
f_SR.write( str(k) + ' ');
f_SR.write('\n')
for i in SF_performance[iOrdering::nOrdering]:
for k in i[j].regression_param:
f_SF.write( str(k) + ' ');
f_SF.write( str(i[j].score) + ' ');
for k in i[j].kernel_param:
f_SF.write( str(k) + ' ');
f_SF.write('\n')
f_IR.close()
f_SR.close()
for iOrdering in range(nOrdering):
string_save = 'PRELIMINARY_PAPER_F/' + Mode + '_' + Mode_Opt + '_o' + str(iOrdering) + '_';
if LASSO: string_save+= 'LASSO_';
if Matching: string_save+= 'matching_';
if Nested: string_save+= 'nested_';
if Equal_size: string_save+= 'equal_';
plt.figure()
plt.plot(av_score_IR[iOrdering, :], color='r', label='IR')
plt.plot(av_score_SR[iOrdering, :], color='b', label='SR')
plt.plot(av_score_SF[iOrdering, :], color='g', label='SF')
plt.xlabel(r'$N^l$', fontsize=FONTSIZE);
plt.ylabel(r'$score_{AVG}$', fontsize=FONTSIZE);
plt.xticks(np.arange(0, len(Nobs_array)), [str(j) for j in Nobs_array], fontsize=FONTSIZE);
plt.yticks(fontsize=FONTSIZE);
plt.legend(prop={'size': FONTSIZE}, frameon=False)
plt.tight_layout()
plt.savefig( string_save + 'nPoints_behavior_AVG.pdf');
plt.figure()
plt.plot(st_score_IR[iOrdering, :], color='r', label='IR')
plt.plot(st_score_SR[iOrdering, :], color='b', label='SR')
plt.plot(st_score_SF[iOrdering, :], color='g', label='SF')
plt.xlabel(r'$N^l$', fontsize=FONTSIZE);
plt.ylabel(r'$score_{STD}$', fontsize=FONTSIZE);
plt.xticks(np.arange(0, len(Nobs_array)), [str(j) for j in Nobs_array], fontsize=FONTSIZE);
plt.yticks(fontsize=FONTSIZE);
plt.legend(prop={'size': FONTSIZE}, frameon=False)
plt.tight_layout()
plt.savefig( string_save + 'nPoints_behavior_STD.pdf');
exit()