def run_demo():
LG.basicConfig(level=LG.INFO)
random.seed(572)
#1. create toy data
[x, y] = create_toy_data()
feat_train = RealFeatures(transpose(x))
labels = RegressionLabels(y)
n_dimensions = 1
#2. location of unispaced predictions
X = SP.linspace(0, 10, 10)[:, SP.newaxis]
#new interface with likelihood parametres being decoupled from the covaraince function
likelihood = GaussianLikelihood()
covar_parms = SP.log([2])
hyperparams = {'covar': covar_parms, 'lik': SP.log([1])}
#construct covariance function
SECF = GaussianKernel(feat_train, feat_train, 2)
covar = SECF
zmean = ZeroMean()
inf = ExactInferenceMethod(SECF, feat_train, zmean, labels, likelihood)
gp = GaussianProcessRegression(inf, feat_train, labels)
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", SECF)
c1.append_child(c5)
c6 = ModelSelectionParameters("width")
c5.append_child(c6)
c6.build_values(0.001, 4.0, R_LINEAR)
crit = GradientCriterion()
grad = GradientEvaluation(gp, feat_train, labels, crit)
grad.set_function(inf)
gp.print_modsel_params()
root.print_tree()
grad_search = GradientModelSelection(root, grad)
grad.set_autolock(0)
best_combination = grad_search.select_model(1)
gp.set_return_type(GaussianProcessRegression.GP_RETURN_COV)
St = gp.apply_regression(feat_train)
St = St.get_labels()
gp.set_return_type(GaussianProcessRegression.GP_RETURN_MEANS)
M = gp.apply_regression()
M = M.get_labels()
#create plots
plot_sausage(transpose(x), transpose(M), transpose(SP.sqrt(St)))
plot_training_data(x, y)
PL.show()
def run_demo():
LG.basicConfig(level=LG.INFO)
random.seed(572)
x = np.linspace(0.0, 1.0, 80)
y = np.sin(3.0 * np.pi * x)
x = x[:, np.newaxis]
feat_train = RealFeatures(transpose(x));
labels = RegressionLabels(y);
n_dimensions = 1
#new interface with likelihood parametres being decoupled from the covaraince function
likelihood = GaussianLikelihood()
covar_parms = SP.log([2])
hyperparams = {'covar':covar_parms,'lik':SP.log([1])}
#construct covariance function
SECF = GaussianKernel(feat_train, feat_train,2)
covar = SECF
zmean = ZeroMean();
inf = ExactInferenceMethod(SECF, feat_train, zmean, labels, likelihood);
gp = GaussianProcessRegression(inf, feat_train, labels);
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", SECF);
c1.append_child(c5);
c6 = ModelSelectionParameters("width");
c5.append_child(c6);
c6.build_values(0.001, 4.0, R_LINEAR);
crit = GradientCriterion();
grad = GradientEvaluation(gp, feat_train, labels, crit);
grad.set_function(inf);
gp.print_modsel_params();
root.print_tree();
grad_search=GradientModelSelection(root, grad)
grad.set_autolock(0)
best_combination=grad_search.select_model(1);
x_test = np.linspace(0.0, 1.0, 100)
x_test = x_test[:, np.newaxis]
feat_test = RealFeatures(transpose(x_test));
gp.set_return_type(GaussianProcessRegression.GP_RETURN_COV)
St = gp.apply_regression(feat_test);
St = St.get_labels();
gp.set_return_type(GaussianProcessRegression.GP_RETURN_MEANS);
M = gp.apply_regression();
M = M.get_labels();
#create plots
pylab.figure()
# pylab.plot(x, y, 'rx')
pylab.plot(x_test, M, 'ro')
pylab.show()
def run_demo():
LG.basicConfig(level=LG.INFO)
random.seed(572)
#1. create toy data
[x,y] = create_toy_data()
feat_train = RealFeatures(transpose(x));
labels = RegressionLabels(y);
n_dimensions = 1
#2. location of unispaced predictions
X = SP.linspace(0,10,10)[:,SP.newaxis]
#new interface with likelihood parametres being decoupled from the covaraince function
likelihood = GaussianLikelihood()
covar_parms = SP.log([2])
hyperparams = {'covar':covar_parms,'lik':SP.log([1])}
#construct covariance function
SECF = GaussianKernel(feat_train, feat_train,2)
covar = SECF
zmean = ZeroMean();
inf = ExactInferenceMethod(SECF, feat_train, zmean, labels, likelihood);
gp = GaussianProcessRegression(inf, feat_train, labels);
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", SECF);
c1.append_child(c5);
c6 =ModelSelectionParameters("width");
c5.append_child(c6);
c6.build_values(0.001, 4.0, R_LINEAR);
crit = GradientCriterion();
grad=GradientEvaluation(gp, feat_train, labels,
crit);
grad.set_function(inf);
gp.print_modsel_params();
root.print_tree();
grad_search=GradientModelSelection(
root, grad);
grad.set_autolock(0);
best_combination=grad_search.select_model(1);
gp.set_return_type(GaussianProcessRegression.GP_RETURN_COV);
St = gp.apply_regression(feat_train);
St = St.get_labels();
gp.set_return_type(GaussianProcessRegression.GP_RETURN_MEANS);
M = gp.apply_regression();
M = M.get_labels();
#create plots
plot_sausage(transpose(x),transpose(M),transpose(SP.sqrt(St)));
plot_training_data(x,y);
PL.show();
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
