{ "metadata": { "name": "", "signature": "sha256:a01415cbe268d3ebbc3fb35ee777a7ac91bddd76c775379630f05848049051db" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Non Gaussian Likelihoods\n", "\n", "# Gaussian Process Summer School, Melbourne, Australia\n", "### 25th-27th February 2015\n", "### Ricardo Andrade Pacheco, Max Zwiessele, James Hensman and Neil Lawrence\n", "\n", "In this lab we are going to consider approaches to dealing with non-Gaussian likelihoods." ] }, { "cell_type": "code", "collapsed": false, "input": [ "%matplotlib inline\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "import GPy\n", "import pods\n", "from IPython.display import display" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 1 }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "from matplotlib.patches import Polygon\n", "from matplotlib.collections import PatchCollection\n", "import cPickle as pickle\n", "import urllib\n", "\n", "urllib.urlretrieve('http://staffwww.dcs.sheffield.ac.uk/people/M.Zwiessele/gpss/lab2/EastTimor.pickle', 'EastTimor2.pickle')\n", "\n", "#Load the data\n", "with open(\"./EastTimor2.pickle\",\"rb\") as f:\n", " X,y,polygons = pickle.load(f)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 45 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now we will create a map of East Timor and, using GPy, plot the data on top of it. \n", "A classification model can be defined in a similar way to the regression model, but now using GPy.models.GPClassification. However, once we've define the model, we also need to update the approximation to the likelihood. This runs the Expectation propagation updates." ] }, { "cell_type": "code", "collapsed": false, "input": [ "print y.shape\n", "print X.shape" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "(67, 1)\n", "(67, 2)\n" ] } ], "prompt_number": 46 }, { "cell_type": "code", "collapsed": false, "input": [ "#Visualize a map of East-Timor\n", "fig = plt.figure()\n", "ax = fig.add_subplot(111)\n", "for p in polygons:\n", " ax.add_collection(PatchCollection([Polygon(p)],facecolor=\"#F4A460\"))\n", "ax.set_xlim(124.,127.5)\n", "ax.set_ylim(-9.6,-8.1)\n", "ax.set_xlabel(\"longitude\")\n", "ax.set_ylabel(\"latitude\")\n", "\n", "#Define the model\n", "kern = GPy.kern.RBF(2)\n", "model = GPy.models.GPClassification(X,y, kernel=kern)\n", "display(model)\n", "model.plot(ax=ax)" ], "language": "python", "metadata": {}, "outputs": [ { "html": [ "\n", "\n", "

\n", "Model: gp_classification
\n", "Log-likelihood: -115.594679675
\n", "Number of Parameters: 2
\n", "

\n", "\n", "\n", "\n", " \n", " \n", " \n", " \n", " \n", "\n", "\n", "\n", "
gp_classification.ValueConstraintPriorTied to
rbf.variance 1.0 +ve
rbf.lengthscale 1.0 +ve

\n", "Model: gp_classification
\n", "Log-likelihood: -107.199692241
\n", "Number of Parameters: 2
\n", "

\n", "\n", "\n", "\n", " \n", " \n", " \n", " \n", " \n", "\n", "\n", "\n", "
gp_classification.ValueConstraintPriorTied to
rbf.variance 1.66833160644 +ve
rbf.lengthscale 0.316603830844 +ve
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9K1LfhGI5xXvwjoeNMiCRAcqnV+TAilfhszHwQU/YORf6XAbX58GJ78PWb+G9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\nEGTt2e2OCLLw+GXZvO5RMAf48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g3PcfqK9wYPNRTyHHHchNSlgjmXFWQwsZOdBFB6lGFw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\n083cdVcW2dkW5s+PdCt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"text": [ "" ] } ], "prompt_number": 48 }, { "cell_type": "markdown", "metadata": {}, "source": [ "The optimization is based on the likelihood approximation that was made after we constructed the model. However, because we've now changed the model parameters the quality of that approximation has now probably deteriorated. To improve the model we should iterate between updating the Expectation propagation approximation and optimizing the model parameters. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Exercise 1\n", "\n", "Write a for loop to optimize the model by iterating between EP and kernel parameters optimization. What happens with the decision boundary after these iterations?" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Exercise 1 answer here" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 50 }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Robust Regression: A Running Example\n", "\n", "Yesterday we considered the olympic marathon data. In 1904 we noted there was an outlier example. Today we'll see if we can deal with that outlier by considering a non-Gaussian likelihood. Noise sampled from a Student-$t$ density is heavier tailed than that sampled from a Gaussian. However, it cannot be trivially assimilated into the Gaussian process. Below we use the *Laplace approximation* to incorporate this noise model." ] }, { "cell_type": "code", "collapsed": false, "input": [ "# redownload the marathon data from yesterday and plot\n", "data = pods.datasets.olympic_marathon_men()\n", "X = data['X']\n", "Y = data['Y']\n", "\n", "plt.plot(X, Y, 'bx')\n", "plt.xlabel('year')\n", "plt.ylabel('marathon pace min/km')" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 2, "text": [ "" ] }, { "metadata": {}, "output_type": "display_data", "png": 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WycnCzMwyOVmYmVmm/w++XZSdkl44NAAAAABJRU5ErkJggg==\n", "text": [ "" ] } ], "prompt_number": 2 }, { "cell_type": "code", "collapsed": false, "input": [ "# make a student t likelihood with standard parameters\n", "t_distribution = GPy.likelihoods.StudentT(deg_free=5, sigma2=2)\n", "laplace = GPy.inference.latent_function_inference.Laplace()\n", "\n", "kern = GPy.kern.RBF(1, lengthscale=50) + GPy.kern.Matern52(1, lengthscale=10) + GPy.kern.Bias(1)\n", "model = GPy.core.GP(X, Y, kernel=kern, inference_method=laplace, likelihood=t_distribution)\n", "model.constrain_positive('t_noise')\n", "\n", "model.optimize()\n", "model.plot()\n", "display(model)" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "WARNING: reconstraining parameters gp\n" ] }, { "html": [ "\n", "\n", "

\n", "Model: gp
\n", "Log-likelihood: -0.0708404207615
\n", "Number of Parameters: 7