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Created July 12, 2013 07:43
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{
"metadata": {
"name": "shogun_gp_regression"
},
"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"Gaussian Process Regression with Shogun"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Import all necessary modules from Shogun"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from modshogun import RealFeatures, RegressionLabels, GaussianKernel, Math\n",
"from modshogun import GaussianLikelihood, ZeroMean, ExactInferenceMethod, GaussianProcessRegression"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 1
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Generate some data, a 1d noisy sine wave, evaluated at random points"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"n=15\n",
"x_range=4*pi\n",
"y_noise_variance=0.1\n",
"y_amplitude=1\n",
"y_frequency=1\n",
"\n",
"X=random.rand(1,n)*x_range\n",
"Y=sin(X*y_frequency)*y_amplitude+randn(n)*sqrt(y_noise_variance)\n",
"X_test=linspace(0,x_range, 200)\n",
"Y_true=sin(X_test)\n",
"\n",
"plot(X_test,Y_true, 'b-')\n",
"plot(X,Y, 'ro')\n",
"_=legend(['data generating model', 'noisy observations'])\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "display_data",
"png": 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vXqLTEE16vkE8c+bMWm9Dre4dV1dXZGVlyb/PysqCm5tbpcdYW1vD0tISANCn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\nAAAASUVORK5CYII=\n"
}
],
"prompt_number": 2
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Convert data into Shogun representation, print dimensions to be sure data was passed in correct "
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"labels=RegressionLabels(Y.ravel())\n",
"feats_train=RealFeatures(X)\n",
"feats_test=RealFeatures(reshape(X_test, (1, len(X_test))))\n",
"\n",
"print feats_train.get_num_vectors()\n",
"print feats_train.get_num_features()\n",
"print feats_test.get_num_vectors()\n",
"print feats_test.get_num_features()"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"15\n",
"1\n",
"200\n",
"1\n"
]
}
],
"prompt_number": 3
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Specify a Shogun GP (exact GP-regression) with fixed hyper-parameters and pass it the data"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"kernel_sigma=1\n",
"gp_obs_noise=0.5\n",
"\n",
"kernel=GaussianKernel(10, kernel_sigma)\n",
"mean=ZeroMean()\n",
"lik=GaussianLikelihood(gp_obs_noise)\n",
"inf=ExactInferenceMethod(kernel, feats_train, mean, labels, lik)\n",
"gp = GaussianProcessRegression(inf)"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 4
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Train GP and plot its predictions"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"_=gp.train()"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 5
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Perform inference and plot predictions on full range"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"predictions=gp.apply(feats_test)\n",
"Y_test=predictions.get_labels()\n",
"\n",
"plot(X_test,Y_true, 'b')\n",
"plot(X_test, Y_test, 'r-')\n",
"plot(X,Y, 'ro')\n",
"_=legend(['data generating model', 'mean predictions', 'noisy observations'])\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "display_data",
"png": 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M6JtvvpFE73z77bdkY2NDtWvXJkdHR9qwYYPkuISEBPL29iYLCwsyMzOjbt26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\nY2yB8NBnjLEFwkOfMcYWCA99xhhbID8ADEnnDJCXjPUAAAAASUVORK5CYII=\n"
}
],
"prompt_number": 6
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"So far so good. The nice thing is: we have a distribution over the predictions"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"mean = gp.get_mean_vector(feats_test)\n",
"variance = gp.get_variance_vector(feats_test)\n",
"\n",
"# print 95% confidence region\n",
"plot(X_test,Y_true, 'b')\n",
"plot(X_test, Y_test, 'r-')\n",
"plot(X,Y, 'ro')\n",
"error=1.96*sqrt(variance)\n",
"fill_between(X_test,mean-error,mean+error,color='grey')\n",
"\n",
"ylim([-y_amplitude,y_amplitude+1])\n",
"_=legend(['data generating model', 'mean predictions', 'noisy observations'])"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "display_data",
"png": 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+cHGR2/a+iwsWvPWWWtt4FgPL/3V0dKCxsRF2dnaDjg0NDcWvv/6K+vp6rFq1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\nT3hzMx++/LIs2y3cT3h4uNQSzGb27NmSH0APuLhwKC+P9/r+kc7LGs6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}
],
"prompt_number": 7
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We can even visualise it more fancy"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from scipy.stats import norm\n",
"\n",
"means = gp.get_mean_vector(feats_test)\n",
"variances = gp.get_variance_vector(feats_test)\n",
"\n",
"y_values=linspace(-y_amplitude-2*y_noise_variance, y_amplitude+2*y_noise_variance)\n",
"D=zeros((len(y_values), len(X_test)))\n",
"\n",
"# evaluate normal distribution at every prediction point (column)\n",
"for i in range(shape(D)[1]):\n",
" norm.pdf(y_values, means[i], variances[i])\n",
" D[:,i]=norm.pdf(y_values, means[i], variances[i])\n",
" \n",
"pcolor(X_test,y_values,D)\n",
"plot(X_test,Y_true, 'b')\n",
"plot(X_test, Y_test, 'r-')\n",
"_=plot(X,Y, 'ro')\n",
" "
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "display_data",
"png": 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W0JsIbzRWxvLt4vHcGPkyBxbkgTW8nt8tl/6bdVunsq8yYPV3JgpH2ROlMhHO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\nIulAyE5fIpFIOhCy05dIJJIOxP8Dpe/qxCv8icYAAAAASUVORK5CYII=\n"
}
],
"prompt_number": 8
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now lets learn the best model parameters with Maximum Likelihood II"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from shogun.ModelSelection import GradientModelSelection, ModelSelectionParameters, R_LINEAR, R_EXP\n",
"from shogun.Regression import GradientCriterion, GradientEvaluation\n",
"\n",
"kernel=GaussianKernel(10, kernel_sigma)\n",
"mean=ZeroMean()\n",
"lik=GaussianLikelihood(gp_obs_noise)\n",
"inf=ExactInferenceMethod(kernel, feats_train, mean, labels, lik)\n",
"gp = GaussianProcessRegression(inf)\n",
"\n",
"# construct model selection parameter tree\n",
"root=ModelSelectionParameters();\n",
"c1=ModelSelectionParameters(\"inference_method\", inf);\n",
"root.append_child(c1);\n",
"\n",
"c2=ModelSelectionParameters(\"likelihood_model\", lik);\n",
"c1.append_child(c2);\n",
"\n",
"c3=ModelSelectionParameters(\"sigma\");\n",
"c2.append_child(c3);\n",
"c3.build_values(-1.0, 1.0, R_EXP);\n",
"\n",
"c4=ModelSelectionParameters(\"scale\");\n",
"c1.append_child(c4);\n",
"c4.build_values(-1.0, 1.0, R_EXP);\n",
"\n",
"c5=ModelSelectionParameters(\"kernel\", kernel);\n",
"c1.append_child(c5);\n",
"\n",
"c6=ModelSelectionParameters(\"width\");\n",
"c5.append_child(c6);\n",
"c6.build_values(-1.0, 1.0, R_EXP);\n",
"\n",
"\n",
"# Criterion for Gradient Search\n",
"crit = GradientCriterion()\n",
"\n",
"# Evaluate our inference method for its derivatives\n",
"grad = GradientEvaluation(gp, feats_train, labels, crit)\n",
"\n",
"grad.set_function(inf) \n",
"gp.print_modsel_params() \n",
"root.print_tree() \n",
"\n",
"# gradient descent on marginal likelihood\n",
"grad_search = GradientModelSelection(root, grad) \n",
"\n",
"# Set autolocking to false to get rid of warnings\t\n",
"grad.set_autolock(False) \n",
"\n",
"# Search for best parameters\n",
"best_combination = grad_search.select_model(True)\n",
"\n",
"# apply them to gp\n",
"best_combination.apply_to_machine(gp)\n",
"\n",
"# training and inference with learned parameters\n",
"gp.train()\n",
"predictions=gp.apply(feats_test)\n",
"Y_test=predictions.get_labels()\n",
"\n",
"# visualise\n",
"means = gp.get_mean_vector(feats_test)\n",
"variances = gp.get_variance_vector(feats_test)\n",
"\n",
"y_values=linspace(-y_amplitude-2*y_noise_variance, y_amplitude+2*y_noise_variance)\n",
"D=zeros((len(y_values), len(X_test)))\n",
"\n",
"# evaluate normal distribution at every prediction point (column)\n",
"for i in range(shape(D)[1]):\n",
" norm.pdf(y_values, means[i], variances[i])\n",
" D[:,i]=norm.pdf(y_values, means[i], variances[i])\n",
" \n",
"pcolor(X_test,y_values,D)\n",
"plot(X_test,Y_true, 'b')\n",
"plot(X_test, Y_test, 'r-')\n",
"_=plot(X,Y, 'ro')\n",
"\n",
"# print best parameters\n",
"print \"kernel width\", kernel.get_width()\n",
"print \"kernel scalling\", inf.get_scale()\n",
"print \"noise level\", lik.get_sigma()\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"kernel width 3.6679925725\n",
"kernel scalling 0.785651526209\n",
"noise level 0.5\n"
]
},
{
"output_type": "display_data",
"png": 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UIOYLeirttJja+M7Uv/LnEsOWIRRQdzwBV1zM6c/gn0GsWfoUT21f47vRhJjQ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}
],
"prompt_number": 9
},
{
"cell_type": "code",
"collapsed": false,
"input": [],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 9
}
],
"metadata": {}
}
]
}
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