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 shogun.Features import RealFeatures, RegressionLabels
from shogun.Kernel import GaussianKernel
try:
from shogun.Regression import GaussianLikelihood, ZeroMean, \
ExactInferenceMethod, GaussianProcessRegression
except ImportError:
print("Eigen3 needed for Gaussian Processes")
return
# reproducable results
random.seed(seed)
# easy regression data: one dimensional noisy sine wave
n = 15
n_test = 100
x_range_test = 10
noise_var = 0.5
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
width = 1
shogun_width = width * width * 2
kernel = GaussianKernel(10, shogun_width)
zmean = ZeroMean()
lik = GaussianLikelihood()
inf = ExactInferenceMethod(kernel, feats_train, zmean, labels, lik)
gp = GaussianProcessRegression(inf, feats_train, labels)
# some things we can do
alpha = inf.get_alpha()
diagonal = inf.get_diagonal_vector()
cholesky = inf.get_cholesky()
# inference
gp.set_return_type(GaussianProcessRegression.GP_RETURN_MEANS)
mean = gp.apply_regression(feats_test)
gp.set_return_type(GaussianProcessRegression.GP_RETURN_COV)
covariance = gp.apply_regression(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.get_labels(), '-') # mean predictions of test
#legend(["training", "ground truth", "mean predictions"])
#show()
return gp, alpha, labels, diagonal, covariance, mean, 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 shogun.Features import RealFeatures, RegressionLabels
from shogun.Kernel import GaussianKernel
try:
from shogun.Regression import GaussianLikelihood, ZeroMean, \
ExactInferenceMethod, GaussianProcessRegression
except ImportError:
print("Eigen3 needed for Gaussian Processes")
return
# reproducable results
random.seed(seed)
# easy regression data: one dimensional noisy sine wave
n=15
n_test=100
x_range_test=10
noise_var=0.5;
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
width=1
shogun_width=width*width*2
kernel=GaussianKernel(10, shogun_width)
zmean = ZeroMean()
lik = GaussianLikelihood()
inf = ExactInferenceMethod(kernel, feats_train, zmean, labels, lik)
gp = GaussianProcessRegression(inf, feats_train, labels)
# some things we can do
alpha = inf.get_alpha()
diagonal = inf.get_diagonal_vector()
cholesky = inf.get_cholesky()
# inference
gp.set_return_type(GaussianProcessRegression.GP_RETURN_MEANS)
mean = gp.apply_regression(feats_test)
gp.set_return_type(GaussianProcessRegression.GP_RETURN_COV)
covariance = gp.apply_regression(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.get_labels(), '-') # mean predictions of test
#legend(["training", "ground truth", "mean predictions"])
#show()
return gp, alpha, labels, diagonal, covariance, mean, cholesky
def regression_gaussian_process_modular(
traindata_real=traindat, testdata_real=testdat, trainlab=label_traindat, width=2.1
):
from numpy.random import randn
from shogun.Features import RealFeatures, RegressionLabels
from shogun.Kernel import GaussianKernel
try:
from shogun.Regression import GaussianLikelihood, ZeroMean, ExactInferenceMethod, GaussianProcessRegression
except ImportError:
print "Eigen3 needed for Gaussian Processes"
return
labels = RegressionLabels(trainlab)
feats_train = RealFeatures(traindata_real)
feats_test = RealFeatures(testdata_real)
kernel = GaussianKernel(feats_train, feats_train, width)
zmean = ZeroMean()
lik = GaussianLikelihood()
inf = ExactInferenceMethod(kernel, feats_train, zmean, labels, lik)
gp = GaussianProcessRegression(inf, feats_train, labels)
alpha = inf.get_alpha()
diagonal = inf.get_diagonal_vector()
cholesky = inf.get_cholesky()
gp.set_return_type(GaussianProcessRegression.GP_RETURN_COV)
covariance = gp.apply_regression(feats_test)
gp.set_return_type(GaussianProcessRegression.GP_RETURN_MEANS)
predictions = gp.apply_regression()
print ("Alpha Vector")
print (alpha)
print ("Labels")
print (labels.get_labels())
print ("sW Matrix")
print (diagonal)
print ("Covariances")
print (covariance.get_labels())
print ("Mean Predictions")
print (predictions.get_labels())
print ("Cholesky Matrix L")
print (cholesky)
return gp, alpha, labels, diagonal, covariance, predictions, cholesky
def regression_gaussian_process_modular (traindata_real=traindat, \
testdata_real=testdat, \
trainlab=label_traindat, width=2.1):
from numpy.random import randn
from shogun.Features import RealFeatures, RegressionLabels
from shogun.Kernel import GaussianKernel
try:
from shogun.Regression import GaussianLikelihood, ZeroMean, \
ExactInferenceMethod, GaussianProcessRegression
except ImportError:
print "Eigen3 needed for Gaussian Processes"
return
labels=RegressionLabels(trainlab)
feats_train=RealFeatures(traindata_real)
feats_test=RealFeatures(testdata_real)
kernel=GaussianKernel(feats_train, feats_train, width)
zmean = ZeroMean()
lik = GaussianLikelihood()
inf = ExactInferenceMethod(kernel, feats_train, zmean, labels, lik)
gp = GaussianProcessRegression(inf, feats_train, labels)
alpha = inf.get_alpha()
diagonal = inf.get_diagonal_vector()
cholesky = inf.get_cholesky()
gp.set_return_type(GaussianProcessRegression.GP_RETURN_COV)
covariance = gp.apply_regression(feats_test)
gp.set_return_type(GaussianProcessRegression.GP_RETURN_MEANS)
predictions = gp.apply_regression()
print("Alpha Vector")
print(alpha)
print("Labels")
print(labels.get_labels())
print("sW Matrix")
print(diagonal)
print("Covariances")
print(covariance.get_labels())
print("Mean Predictions")
print(predictions.get_labels())
print("Cholesky Matrix L")
print(cholesky)
return gp, alpha, labels, diagonal, covariance, predictions, cholesky
def regression_gaussian_process_modelselection (n=100,n_test=100, \
x_range=6,x_range_test=10,noise_var=0.5,width=1, seed=1):
from shogun.Features import RealFeatures, RegressionLabels
from shogun.Kernel import GaussianKernel
from shogun.ModelSelection import GradientModelSelection, ModelSelectionParameters, R_LINEAR
from shogun.Regression import GaussianLikelihood, ZeroMean, \
ExactInferenceMethod, GaussianProcessRegression, GradientCriterion, \
GradientEvaluation
# Reproducable results
random.seed(seed)
# 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
width=1
shogun_width=width*width*2
kernel=GaussianKernel(10,shogun_width)
kernel.init(feats_train,feats_train)
zmean = ZeroMean()
likelihood = GaussianLikelihood()
inf = ExactInferenceMethod(kernel, feats_train, zmean, labels, likelihood)
gp = GaussianProcessRegression(inf, feats_train, labels)
# Paramter tree for model selection
root = ModelSelectionParameters()
c1 = ModelSelectionParameters("inference_method", inf)
root.append_child(c1)
c2 = ModelSelectionParameters("scale")
c1.append_child(c2)
c2.build_values(0.01, 4.0, R_LINEAR)
c3 = ModelSelectionParameters("likelihood_model", likelihood)
c1.append_child(c3)
c4 = ModelSelectionParameters("sigma")
c3.append_child(c4)
c4.build_values(0.001, 4.0, R_LINEAR)
c5 = ModelSelectionParameters("kernel", kernel)
c1.append_child(c5)
c6 = ModelSelectionParameters("width")
c5.append_child(c6)
c6.build_values(0.001, 4.0, R_LINEAR)
# Criterion for Gradient Search
crit = GradientCriterion()
# Evaluate our inference method for its derivatives
grad = GradientEvaluation(gp, feats_train, labels, crit)
grad.set_function(inf)
gp.print_modsel_params()
root.print_tree()
# Handles all of the above structures in memory
grad_search = GradientModelSelection(root, grad)
# Set autolocking to false to get rid of warnings
grad.set_autolock(False)
# Search for best parameters
best_combination = grad_search.select_model(True)
# Outputs all result and information
best_combination.print_tree()
best_combination.apply_to_machine(gp)
result = grad.evaluate()
result.print_result()
#inference
gp.set_return_type(GaussianProcessRegression.GP_RETURN_COV)
covariance = gp.apply_regression(feats_test)
covariance = covariance.get_labels()
gp.set_return_type(GaussianProcessRegression.GP_RETURN_MEANS)
mean = gp.apply_regression(feats_test)
mean = mean.get_labels()
# some things we can do
alpha = inf.get_alpha()
diagonal = inf.get_diagonal_vector()
cholesky = inf.get_cholesky()
# plot results
plot(X_train[0],Y_train[0],'x') # training observations
plot(X_test[0],Y_test[0],'-') # ground truth of test
plot(X_test[0],mean, '-') # mean predictions of test
legend(["training", "ground truth", "mean predictions"])
show()
return gp, alpha, labels, diagonal, covariance, mean, cholesky
