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paper_A_ctime.py
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paper_A_ctime.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 *
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 = [ 15 ];
NdataRandomization= 100;
Nested= False;
Matching = False;
Equal_size= False;
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;
for iDataRandomization in range(NdataRandomization):
Train_points = [];
for nn in range(len(Nobs_array)):
Nobs = Nobs_array[nn];
model_order = [];
model_order.append(np.arange(Nmod).flatten());
print("Number of observations " + str(Nobs) + " iRand " + str(iDataRandomization));
print("Generating synthetic data")
if Equal_size:
Nobs_model = [Nobs for i in range(Nmod)];
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]);
for iOrdering in range(nOrdering):
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), Tychonov_regularization_coeff, 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), Tychonov_regularization_coeff, Opt_Mode= Mode_Opt, LASSO=LASSO);
# 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), Tychonov_regularization_coeff, 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), Tychonov_regularization_coeff, Opt_Mode= Mode_Opt, LASSO=LASSO);
# GP_single = GP(kernel, mode=Mode);
# GP_single.fit(Train_points[-1].reshape(-1, 1), observations[-1][:, 0].reshape(-1, 1), Tychonov_regularization_coeff, Opt_Mode= Mode_Opt, LASSO=LASSO);
exit()