def regression_gaussian_process_modular (n=100,n_test=100, \
x_range=6,x_range_test=10,noise_var=0.5,width=1, seed=1):
from modshogun import RealFeatures, RegressionLabels, GaussianKernel, Math
try:
from modshogun import GaussianLikelihood, ZeroMean, \
ExactInferenceMethod, GaussianProcessRegression
except ImportError:
print("Eigen3 needed for Gaussian Processes")
return
# reproducable results
random.seed(seed)
Math.init_random(17)
# easy regression data: one dimensional noisy sine wave
X = random.rand(1, n) * x_range
X_test = array([[float(i) / n_test * x_range_test for i in range(n_test)]])
Y_test = sin(X_test)
Y = sin(X) + random.randn(n) * noise_var
# shogun representation
labels = RegressionLabels(Y[0])
feats_train = RealFeatures(X)
feats_test = RealFeatures(X_test)
# GP specification
shogun_width = width * width * 2
kernel = GaussianKernel(10, shogun_width)
zmean = ZeroMean()
lik = GaussianLikelihood()
lik.set_sigma(noise_var)
inf = ExactInferenceMethod(kernel, feats_train, zmean, labels, lik)
# train GP
gp = GaussianProcessRegression(inf)
gp.train()
# some things we can do
alpha = inf.get_alpha()
diagonal = inf.get_diagonal_vector()
cholesky = inf.get_cholesky()
# get mean and variance vectors
mean = gp.get_mean_vector(feats_test)
variance = gp.get_variance_vector(feats_test)
# plot results
#plot(X[0],Y[0],'x') # training observations
#plot(X_test[0],Y_test[0],'-') # ground truth of test
#plot(X_test[0],mean, '-') # mean predictions of test
#fill_between(X_test[0],mean-1.96*sqrt(variance),mean+1.96*sqrt(variance),color='grey') # 95% confidence interval
#legend(["training", "ground truth", "mean predictions"])
#show()
return alpha, diagonal, round(variance, 12), round(mean, 12), cholesky
def regression_gaussian_process_modular (n=100,n_test=100, \
x_range=6,x_range_test=10,noise_var=0.5,width=1, seed=1):
from modshogun import RealFeatures, RegressionLabels, GaussianKernel, Math
try:
from modshogun import GaussianLikelihood, ZeroMean, \
ExactInferenceMethod, GaussianProcessRegression
except ImportError:
print("Eigen3 needed for Gaussian Processes")
return
# reproducable results
random.seed(seed)
Math.init_random(17)
# easy regression data: one dimensional noisy sine wave
X=random.rand(1,n)*x_range
X_test=array([[float(i)/n_test*x_range_test for i in range(n_test)]])
Y_test=sin(X_test)
Y=sin(X)+random.randn(n)*noise_var
# shogun representation
labels=RegressionLabels(Y[0])
feats_train=RealFeatures(X)
feats_test=RealFeatures(X_test)
# GP specification
shogun_width=width*width*2
kernel=GaussianKernel(10, shogun_width)
zmean = ZeroMean()
lik = GaussianLikelihood()
lik.set_sigma(noise_var)
inf = ExactInferenceMethod(kernel, feats_train, zmean, labels, lik)
# train GP
gp = GaussianProcessRegression(inf)
gp.train()
# some things we can do
alpha = inf.get_alpha()
diagonal = inf.get_diagonal_vector()
cholesky = inf.get_cholesky()
# get mean and variance vectors
mean = gp.get_mean_vector(feats_test)
variance = gp.get_variance_vector(feats_test)
# plot results
#plot(X[0],Y[0],'x') # training observations
#plot(X_test[0],Y_test[0],'-') # ground truth of test
#plot(X_test[0],mean, '-') # mean predictions of test
#fill_between(X_test[0],mean-1.96*sqrt(variance),mean+1.96*sqrt(variance),color='grey') # 95% confidence interval
#legend(["training", "ground truth", "mean predictions"])
#show()
return alpha, diagonal, round(variance,12), round(mean,12), cholesky
def regression_gaussian_process_modelselection(n=100, n_test=100, x_range=5, x_range_test=10, noise_var=0.4):
from modshogun import RealFeatures, RegressionLabels
from modshogun import GaussianKernel
from modshogun import GradientModelSelection, ModelSelectionParameters
from modshogun import (
GaussianLikelihood,
ZeroMean,
ExactInferenceMethod,
GaussianProcessRegression,
GradientCriterion,
GradientEvaluation,
)
# easy regression data: one dimensional noisy sine wave
X_train = random.rand(1, n) * x_range
X_test = array([[float(i) / n_test * x_range_test for i in range(n_test)]])
y_test = sin(X_test)
y_train = sin(X_train) + random.randn(n) * noise_var
# shogun representation
labels = RegressionLabels(y_train[0])
feats_train = RealFeatures(X_train)
feats_test = RealFeatures(X_test)
# GP specification
kernel = GaussianKernel(10, 0.05)
mean = ZeroMean()
likelihood = GaussianLikelihood(0.8)
inf = ExactInferenceMethod(kernel, feats_train, mean, labels, likelihood)
inf.set_scale(2.5)
gp = GaussianProcessRegression(inf)
means = gp.get_mean_vector(feats_test)
variances = gp.get_variance_vector(feats_test)
# plot results
figure()
subplot(2, 1, 1)
title("Initial parameter's values")
plot(X_train[0], y_train[0], "bx") # training observations
plot(X_test[0], y_test[0], "g-") # ground truth of test
plot(X_test[0], means, "r-") # mean predictions of test
fill_between(X_test[0], means - 1.96 * sqrt(variances), means + 1.96 * sqrt(variances), color="grey")
legend(["training", "ground truth", "mean predictions"])
# evaluate our inference method for its derivatives
grad = GradientEvaluation(gp, feats_train, labels, GradientCriterion(), False)
grad.set_function(inf)
# handles all of the above structures in memory
grad_search = GradientModelSelection(grad)
# search for best parameters
best_combination = grad_search.select_model(True)
# outputs all result and information
best_combination.apply_to_machine(gp)
means = gp.get_mean_vector(feats_test)
variances = gp.get_variance_vector(feats_test)
# plot results
subplot(2, 1, 2)
title("Selected by gradient search parameter's values")
plot(X_train[0], y_train[0], "bx") # training observations
plot(X_test[0], y_test[0], "g-") # ground truth of test
plot(X_test[0], means, "r-") # mean predictions of test
fill_between(X_test[0], means - 1.96 * sqrt(variances), means + 1.96 * sqrt(variances), color="grey")
legend(["training", "ground truth", "mean predictions"])
show()
def regression_gaussian_process_modelselection (n=100, n_test=100, \
x_range=5, x_range_test=10, noise_var=0.4):
from modshogun import RealFeatures, RegressionLabels
from modshogun import GaussianKernel
from modshogun import GradientModelSelection, ModelSelectionParameters
from modshogun import GaussianLikelihood, ZeroMean, \
ExactInferenceMethod, GaussianProcessRegression, GradientCriterion, \
GradientEvaluation
# easy regression data: one dimensional noisy sine wave
X_train = random.rand(1, n) * x_range
X_test = array([[float(i) / n_test * x_range_test for i in range(n_test)]])
y_test = sin(X_test)
y_train = sin(X_train) + random.randn(n) * noise_var
# shogun representation
labels = RegressionLabels(y_train[0])
feats_train = RealFeatures(X_train)
feats_test = RealFeatures(X_test)
# GP specification
kernel = GaussianKernel(10, 0.05)
mean = ZeroMean()
likelihood = GaussianLikelihood(0.8)
inf = ExactInferenceMethod(kernel, feats_train, mean, labels, likelihood)
inf.set_scale(2.5)
gp = GaussianProcessRegression(inf)
means = gp.get_mean_vector(feats_test)
variances = gp.get_variance_vector(feats_test)
# plot results
figure()
subplot(2, 1, 1)
title('Initial parameter\'s values')
plot(X_train[0], y_train[0], 'bx') # training observations
plot(X_test[0], y_test[0], 'g-') # ground truth of test
plot(X_test[0], means, 'r-') # mean predictions of test
fill_between(X_test[0],
means - 1.96 * sqrt(variances),
means + 1.96 * sqrt(variances),
color='grey')
legend(["training", "ground truth", "mean predictions"])
# evaluate our inference method for its derivatives
grad = GradientEvaluation(gp, feats_train, labels, GradientCriterion(),
False)
grad.set_function(inf)
# handles all of the above structures in memory
grad_search = GradientModelSelection(grad)
# search for best parameters
best_combination = grad_search.select_model(True)
# outputs all result and information
best_combination.apply_to_machine(gp)
means = gp.get_mean_vector(feats_test)
variances = gp.get_variance_vector(feats_test)
# plot results
subplot(2, 1, 2)
title('Selected by gradient search parameter\'s values')
plot(X_train[0], y_train[0], 'bx') # training observations
plot(X_test[0], y_test[0], 'g-') # ground truth of test
plot(X_test[0], means, 'r-') # mean predictions of test
fill_between(X_test[0],
means - 1.96 * sqrt(variances),
means + 1.96 * sqrt(variances),
color='grey')
legend(["training", "ground truth", "mean predictions"])
show()