{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Heteroscedastic Regression" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Updated on 27th November 2015" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### by Ricardo Andrade" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In this Ipython Notebook we will look at how to implement a GP regression with different noise terms using GPy.\n", "\n", "$\\bf N.B.:$ There is currently no implementation to predict the noise for outputs that are not part of the training set." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Usually, a GP regression model assumes that a set of targets $\\{ y_1,\\ldots,y_n \\}$ is related to a set of inputs $\\{ {\\bf x }_1,\\ldots, {\\bf x }_n \\}$ through the relation:\n", "$$ y_i = f({\\bf x}_i) + \\epsilon_i, $$\n", "where $f \\sim \\mathcal{GP}$ and $\\epsilon_i \\sim \\mathcal{N}(0,\\sigma^2)$ for all $i$.. An heteroscedastic model works in the same way, but allows different variances for the noise terms of the observations, i.e., $\\epsilon_i \\sim \\mathcal{N}(0,\\sigma_i^2)$. By adding this assumption, the model will now give different weights to each observation. Hence, it will try to fit better those observations with smaller noise and will be free not to fit very well those observations with larger noise." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Before using GPy, we need to perform some setup." ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Populating the interactive namespace from numpy and matplotlib\n" ] } ], "source": [ "import numpy as np\n", "import pylab as pb\n", "import GPy \n", "%pylab inline" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As an example we will use the following function, which has a peak around 0." ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "def f(X):\n", " return 10. + .1*X + 2*np.sin(X)/X\n", "\n", "fig,ax = pb.subplots()\n", "ax.plot(np.linspace(-15,25),f(np.linspace(-10,20)),'r-')\n", "ax.grid()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We will draw some points $( {\\bf x},y)$ from the function above, and add some noise on $y$." ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "X = np.random.uniform(-10,20, 50)\n", "X = X[~np.logical_and(X>-2,X<3)] #Remove points between -2 and 3 (just for illustration) \n", "X = np.hstack([np.random.uniform(-1,1,1),X]) #Prepend a point between -1 and 1 (just for illustration)\n", "error = np.random.normal(0,.2,X.size)\n", "Y = f(X) + error\n", "fig,ax = pb.subplots()\n", "ax.plot(np.linspace(-15,25),f(np.linspace(-10,20)),'r-')\n", "ax.plot(X,Y,'kx',mew=1.5)\n", "ax.grid()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We will use a combination of an MLP and Bias kernels. Although other kernels can be used as well." ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": false }, "outputs": [], "source": [ "kern = GPy.kern.MLP(1) + GPy.kern.Bias(1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "For the moment, we will assume that we already know the error on each observation.\n", "To call the model we just need to run these lines." ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": false }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ " /home/maxz/anaconda/lib/python2.7/site-packages/matplotlib/axes/_axes.py:2651: MatplotlibDeprecationWarning:Use of None object as fmt keyword argument to suppress plotting of data values is deprecated since 1.4; use the string \"none\" instead.\n" ] }, { "data": { "text/plain": [ "[]" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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a8H6YBOrkI2h+hIQSYaIxxlUJEAN+Is/rgffp2rB77OstCDCge3gySrNGorQi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\nTJ/UBPKKKth76Cwntv2L/P1ZTJ/0E3q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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "m = GPy.models.GPHeteroscedasticRegression(X[:,None],Y[:,None],kern)\n", "m['.*het_Gauss.variance'] = abs(error)[:,None] #Set the noise parameters to the error in Y\n", "m.het_Gauss.variance.fix() #We can fix the noise term, since we already know it\n", "m.optimize()\n", "\n", "m.plot_f() #Show the predictive values of the GP.\n", "pb.errorbar(X,Y,yerr=np.array(m.likelihood.flattened_parameters).flatten(),fmt=None,ecolor='r',zorder=1)\n", "pb.grid()\n", "pb.plot(X,Y,'kx',mew=1.5)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In the following example we show how the magnitud of the noise of a specific observation modifines the model fit." ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": false }, "outputs": [], "source": [ "def noise_effect(noise):\n", " m.het_Gauss.variance[:1] = noise\n", " m.het_Gauss.variance.fix()\n", " m.optimize()\n", " \n", " m.plot_f() \n", " pb.errorbar(X.flatten(),Y.flatten(),yerr=np.array(m.likelihood.flattened_parameters).flatten(),fmt=None,ecolor='r',zorder=1) \n", " pb.plot(X[1:],Y[1:],'kx',mew=1.5)\n", " pb.plot(X[:1],Y[:1],'ko',mew=.5)\n", " pb.grid()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Scroll the bar to see how the GP fitted changes." ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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U1up+/JkXMVvsdIrXkZIUfBhmjTBBqtU9qTTQGzZsqLF/yZIlQRnvaLxHWor2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\nxei4qF9gpW7KzVb6d4tDra6ryiXFG8k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mpHjNfUx8FLyoJcoqLqWPmaqiWq1hYSYXa/IG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\nlFJM4EREKcUETkSUUkzgREQp9T9Rk+JiTAcBjQAAAABJRU5ErkJggg==\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from IPython.html.widgets import *\n", "interact(noise_effect, noise=(0.1,2.))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "If we set all the noise terms to be equal, then we have just a homoscedastic GP regression model. The code below shows a comparison between the heteroscedastic and the homoscedastic models when the noise terms are fixed to the same value." ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Kernel parameters (optimized) in the heteroscedastic model\n", " \u001b[1msum. \u001b[0;0m | value | constraints | priors\n", " \u001b[1mmlp.variance \u001b[0;0m | 6.74905510673 | +ve | \n", " \u001b[1mmlp.weight_variance\u001b[0;0m | 4.51460469888 | +ve | \n", " \u001b[1mmlp.bias_variance \u001b[0;0m | 11.4561726893 | +ve | \n", " \u001b[1mbias.variance \u001b[0;0m | 116.301919585 | +ve | \n", "\n", "Kernel parameters (optimized) in the homoscedastic model\n", " \u001b[1msum. \u001b[0;0m | value | constraints | priors\n", " \u001b[1mmlp.variance \u001b[0;0m | 6.74905510673 | +ve | \n", " \u001b[1mmlp.weight_variance\u001b[0;0m | 4.51460469888 | +ve | \n", " \u001b[1mmlp.bias_variance \u001b[0;0m | 11.4561726893 | +ve | \n", " \u001b[1mbias.variance \u001b[0;0m | 116.301919585 | +ve | \n" ] }, { "data": { "image/png": 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T3SLgQt04boBZQcBffP0aAO+4pY/33L4TgG/98EJNxzcNE9eTolZCDtcLuHh1ktcvj+P4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\nz13g+Z9dZTLl0BK3uW3/Vj5y5E3s3Dq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8sZVXzujrq6MqIeQKLzUTM6ksw2MpYrEo8djCieJv/uAsf/71H+MHIfv72vnU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\nPvK+a4FcqODATok8ErYfcsf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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "#Heteroscedastic model\n", "m1 = GPy.models.GPHeteroscedasticRegression(X[:,None],Y[:,None],kern)\n", "m1.het_Gauss.variance = .05\n", "m1.het_Gauss.variance.fix()\n", "m1.optimize()\n", "\n", "# Homoscedastic model\n", "m2 = GPy.models.GPRegression(X[:,None],Y[:,None],kern)\n", "m2['.*Gaussian_noise'] = .05\n", "m2['.*noise'].fix()\n", "m2.optimize()\n", "\n", "m1.plot_f()\n", "pb.title('Homoscedastic model')\n", "m2.plot_f()\n", "pb.title('Heteroscedastic model')\n", "\n", "print \"Kernel parameters (optimized) in the heteroscedastic model\"\n", "print m1.kern\n", "print \"\\nKernel parameters (optimized) in the homoscedastic model\"\n", "print m2.kern" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can also learn the noise for each observation. \n", "In this case I found useful to set a lower bound on the noise terms of $10^{-6}$ or to add a white noise kenel.\n", "In this case, I found useful to add a white noise kernel." ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "collapsed": false }, "outputs": [], "source": [ "kern = GPy.kern.MLP(1) + GPy.kern.Bias(1)" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "collapsed": true }, "outputs": [], "source": [ "m = GPy.models.GPHeteroscedasticRegression(X[:,None],Y[:,None],kern)\n", "m.optimize()" ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "collapsed": false }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ " /home/maxz/Documents/gpy/GPy/likelihoods/gaussian.py:101: RuntimeWarning:invalid value encountered in sqrt\n", " /home/maxz/Documents/gpy/GPy/likelihoods/gaussian.py:359: RuntimeWarning:invalid value encountered in sqrt\n" ] }, { "data": { "image/png": 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V1/7+UT30N184LWyVfP4B2XNr9JnIsU3fVXY5vPTSS2rYsyfuM4pL1as5eeY3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\nFAAAJBo9oAAAAACApEMABWKgNwNOQS3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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(1,1,figsize=(13,5))\n", "m.plot_f(ax=ax)\n", "m.plot_data(ax=ax)\n", "m.plot_errorbars_trainset(ax=ax, alpha=1)\n", "fig.tight_layout()\n", "pb.grid()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Predictions of $y$ at new points $\\bf x$ would need a estimate of the noise term, however we just have those for the training set. At the moment we don't have a rotine to estimate heteroscedastic noise at new points. Estimates for the GP at new poinst are still available using the following command:" ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "collapsed": false }, "outputs": [], "source": [ "mu, var = m._raw_predict(m.X)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### plot density\n", "The new GPy release allows us to plot the density of the GP more fine-grained. This is shown below:" ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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8krx0nVOSrfasdXqsr12/V3Wl0jxD+ubfPaotf/WVM8JW0ZcflD2vUl9wjm3i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\nAElFTkSuQmCC\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(1,1,figsize=(13,5))\n", "m.plot_f(ax=ax, plot_density=True)\n", "m.plot_data(ax=ax)\n", "m.plot_errorbars_trainset(ax=ax, alpha=1)\n", "fig.tight_layout()\n", "pb.grid()" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 2", "language": "python", "name": "python2" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 2 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython2", "version": "2.7.11" } }, "nbformat": 4, "nbformat_minor": 0 }