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example ML2 parameter selection for GP Regression
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examples/undocumented/python_modular/regression_gaussian_process_modelselection.py
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#!/usr/bin/env python | ||
from numpy import * | ||
from pylab import plot, show, legend | ||
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parameter_list=[[20,100,6,10,0.5,1, 1], [20,100,6,10,0.5,1, 2]] | ||
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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): | ||
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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 | ||
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# Reproducable results | ||
random.seed(seed) | ||
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# 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 | ||
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# shogun representation | ||
labels=RegressionLabels(Y_train[0]) | ||
feats_train=RealFeatures(X_train) | ||
feats_test=RealFeatures(X_test) | ||
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# 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) | ||
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# Paramter tree for model selection | ||
root=ModelSelectionParameters() | ||
c1=ModelSelectionParameters("inference_method", inf) | ||
root.append_child(c1) | ||
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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) | ||
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c4 = ModelSelectionParameters("sigma") | ||
c3.append_child(c4) | ||
c4.build_values(0.001, 4.0, R_LINEAR) | ||
c5 = ModelSelectionParameters("kernel", kernel) | ||
c1.append_child(c5) | ||
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c6 = ModelSelectionParameters("width") | ||
c5.append_child(c6) | ||
c6.build_values(0.001, 4.0, R_LINEAR) | ||
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# Criterion for Gradient Search | ||
crit = GradientCriterion() | ||
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# Evaluate our inference method for its derivatives | ||
grad=GradientEvaluation(gp, feats_train, labels, crit) | ||
grad.set_function(inf) | ||
gp.print_modsel_params() | ||
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root.print_tree() | ||
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grad_search=GradientModelSelection(root, grad) | ||
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# Set autolocking to false to get rid of warnings | ||
grad.set_autolock(False) | ||
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# Search for best parameters | ||
best_combination=grad_search.select_model(True) | ||
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#inference | ||
gp.set_return_type(GaussianProcessRegression.GP_RETURN_COV) | ||
sigma = gp.apply_regression(feats_test) | ||
sigma = sigma.get_labels() | ||
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gp.set_return_type(GaussianProcessRegression.GP_RETURN_MEANS) | ||
mean = gp.apply_regression(feats_test) | ||
mean = mean.get_labels() | ||
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# some things we can do | ||
alpha = inf.get_alpha() | ||
diagonal = inf.get_diagonal_vector() | ||
cholesky = inf.get_cholesky() | ||
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# 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"]) | ||
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show() | ||
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return gp, alpha, labels, diagonal, covariance, mean, cholesky | ||
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if __name__=='__main__': | ||
print('Gaussian Process Regression') | ||
regression_gaussian_process_modelselection(*parameter_list[1]) |