example ML2 parameter selection for GP Regression

examples/undocumented/python_modular/graphical/regression_gaussian_process_modelselection.py

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+#!/usr/bin/env python
+from numpy import * 
+from pylab import plot, show, legend
+import scipy
+
+parameter_list=[[20,100,10,10,0.25,1, 1], [20,100,6,10,0.5,1, 2]]
+
+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
+
+if __name__=='__main__':
+	print('Gaussian Process Regression')
+	regression_gaussian_process_modelselection(*parameter_list[1])