{ "metadata": { "name": "", "signature": "sha256:07536b850520cd632c3524fb4fa4ee43dda8c6b0334d3d6b8728bad88acf8264" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Multiple Outputs Gaussian Processes\n", "\n", "# Gaussian Process Summer School, Melbourne, Australia\n", "### 25th-27th February 2015\n", "### Neil D. Lawrence\n", "\n", "In this lab we are going to build on yestereday's work by looking at multiple output Gaussian processes\n", "\n", "## Getting started: Modelling Multiple Outputs\n", "\n", "Just as in the first lab, we firstly specify to include plots in the notebook and to import relevant libraries." ] }, { "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": 25 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "Running Example" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The first think we will look at is a multiple output model. Our aim is to jointly model all *sprinting* events from olympics since 1896. Data is provided by Rogers & Girolami's \"First Course in Machine Learning\". Firstly, let's load in the data." ] }, { "cell_type": "code", "collapsed": false, "input": [ "data = pods.datasets.olympic_sprints()\n", "X = data['X']\n", "y = data['Y']\n", "print data['info'], data['details']" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Olympics sprint event winning for men and women to 2008. Data is from Rogers and Girolami's First Course in Machine Learning. Data from the textbook 'A First Course in Machine Learning'. Available from http://www.dcs.gla.ac.uk/~srogers/firstcourseml/.\n" ] } ], "prompt_number": 26 }, { "cell_type": "markdown", "metadata": {}, "source": [ "When using data sets it's good practice to cite the originators of the data, you can get information about the source of the data from data['citation']" ] }, { "cell_type": "code", "collapsed": false, "input": [ "print data['citation']" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "A First Course in Machine Learning. Simon Rogers and Mark Girolami: Chapman & Hall/CRC, ISBN-13: 978-1439824146\n" ] } ], "prompt_number": 27 }, { "cell_type": "markdown", "metadata": {}, "source": [ "The data consists of all the male and female sprinting data for 100m, 200m and 400m since 1896 (six outputs in total). The ouput information can be found from: data['output_info']" ] }, { "cell_type": "code", "collapsed": false, "input": [ "print data['output_info']" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "{0: '100m Men', 1: '100m Women', 2: '200m Men', 3: '200m Women', 4: '400m Men', 5: '400m Women'}\n" ] } ], "prompt_number": 28 }, { "cell_type": "markdown", "metadata": {}, "source": [ "In GPy we deal with multiple output data in a particular way. We specify the output we are interested in for modelling as an additional *input*. So whilst for this data, normally, the only input would be the year of the event. We additionally have an input giving the index of the output we are modelling. This can be seen from examining data['X']." ] }, { "cell_type": "code", "collapsed": false, "input": [ "#print 'First column of X contains the olympic years.'\n", "#print data['X'][:, 0]\n", "#print 'Second column of X contains the event index.'\n", "#print data['X'][:, 1]" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 29 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now let's plot the data" ] }, { "cell_type": "code", "collapsed": false, "input": [ "markers = ['bo', 'ro', 'bx', 'rx', 'bs', 'rs']\n", "for i in range(6):\n", " # extract the event \n", " x_event = X[np.nonzero(X[:, 1]==i), 0]\n", " y_event = y[np.nonzero(X[:, 1]==i), 0]\n", " plt.plot(x_event, y_event, markers[i])\n", "plt.title('Olympic Sprint Times')\n", "plt.xlabel('year')\n", "plt.ylabel('time/s')" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 30, "text": [ "" ] }, { "metadata": {}, "output_type": 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"text": [ "" ] } ], "prompt_number": 30 }, { "cell_type": "markdown", "metadata": {}, "source": [ "In the plot above red is women's events, blue is men's. Squares are 400 m, crosses 200m and circles 100m. Not all events were run in all years, for example the women's 400 m only started in 1964.\n", "\n", "We will look at modelling the data using coregionalization approaches described in this morning's lecture. We introduced these approaches through the Kronecker product. To indicate we want to construct a covariance function of this type in GPy we've overloaded the ** operator. Stricly speaking this operator means to the power of (like ^ in MATLAB). But for covariance functions we've used it to indicate a tensor product. The linear models of coregionalization we introduced in the lecture were all based on combining a matrix with a standard covariance function. We can think of the matrix as a particular type of covariance function, whose elements are referenced using the event indices. I.e. $k(0, 0)$ references the first row and column of the coregionalization matrix. $k(1, 0)$ references the second row and first column of the coregionalization matrix. Under this set up, we want to build a covariance where the first column from the features (the years) is passed to a covariance function, and the second column from the features (the event number) is passed to the coregionalisation matrix. Let's start by trying a intrinsic coregionalisation model (sometimes known as multitask Gaussian processes). Let's start by checking the help for the coregionalize covariance." ] }, { "cell_type": "code", "collapsed": false, "input": [ "GPy.kern.Coregionalize?" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 31 }, { "cell_type": "markdown", "metadata": {}, "source": [ "The coregionalize matrix, $\\mathbf{B}$, is itself is constructed from two other matrices, $\\mathbf{B} = \\mathbf{W}\\mathbf{W}^\\top + \\text{diag}(\\boldsymbol{\\kappa})$. This allows us to specify a low rank form for the coregionalization matrix. However, for our first example we want to specify that the matrix $\\mathbf{B}$ is not constrained to have a low rank form. " ] }, { "cell_type": "code", "collapsed": false, "input": [ "kern = GPy.kern.RBF(1, lengthscale=80)**GPy.kern.Coregionalize(1,output_dim=6, rank=5)\n", "display(kern)" ], "language": "python", "metadata": {}, "outputs": [ { "html": [ "\n", "\n", "\n", " \n", " \n", " \n", " \n", " \n", "\n", "\n", "\n", "\n", "\n", "
mul.ValueConstraintPriorTied to
rbf.variance 1.0 +ve
rbf.lengthscale 80.0 +ve
coregion.W (6, 5)
coregion.kappa (6,) +ve
" ], "metadata": {}, "output_type": "display_data", "text": [ "" ] } ], "prompt_number": 32 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Note here that the rank we specify is that of the $\\mathbf{W}\\mathbf{W}^\\top$ part. When this part is combined with the diagonal matrix from $\\mathbf{\\kappa}$ the matrix $\\mathbf{B}$ is totally general. This covariance function can now be used in a standard Gaussian process regression model. Let's build the model and optimize it." ] }, { "cell_type": "code", "collapsed": false, "input": [ "X" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 33, "text": [ "array([[ 1.89600000e+03, 0.00000000e+00],\n", " [ 1.90000000e+03, 0.00000000e+00],\n", " [ 1.90400000e+03, 0.00000000e+00],\n", " [ 1.90600000e+03, 0.00000000e+00],\n", " [ 1.90800000e+03, 0.00000000e+00],\n", " [ 1.91200000e+03, 0.00000000e+00],\n", " [ 1.92000000e+03, 0.00000000e+00],\n", " [ 1.92400000e+03, 0.00000000e+00],\n", " [ 1.92800000e+03, 0.00000000e+00],\n", " [ 1.93200000e+03, 0.00000000e+00],\n", " [ 1.93600000e+03, 0.00000000e+00],\n", " [ 1.94800000e+03, 0.00000000e+00],\n", " [ 1.95200000e+03, 0.00000000e+00],\n", " [ 1.95600000e+03, 0.00000000e+00],\n", " [ 1.96000000e+03, 0.00000000e+00],\n", " [ 1.96400000e+03, 0.00000000e+00],\n", " [ 1.96800000e+03, 0.00000000e+00],\n", " [ 1.97200000e+03, 0.00000000e+00],\n", " [ 1.97600000e+03, 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4.00000000e+00],\n", " [ 1.90800000e+03, 4.00000000e+00],\n", " [ 1.91200000e+03, 4.00000000e+00],\n", " [ 1.92000000e+03, 4.00000000e+00],\n", " [ 1.92400000e+03, 4.00000000e+00],\n", " [ 1.92800000e+03, 4.00000000e+00],\n", " [ 1.93200000e+03, 4.00000000e+00],\n", " [ 1.93600000e+03, 4.00000000e+00],\n", " [ 1.94800000e+03, 4.00000000e+00],\n", " [ 1.95200000e+03, 4.00000000e+00],\n", " [ 1.95600000e+03, 4.00000000e+00],\n", " [ 1.96000000e+03, 4.00000000e+00],\n", " [ 1.96400000e+03, 4.00000000e+00],\n", " [ 1.96800000e+03, 4.00000000e+00],\n", " [ 1.97200000e+03, 4.00000000e+00],\n", " [ 1.97600000e+03, 4.00000000e+00],\n", " [ 1.98000000e+03, 4.00000000e+00],\n", " [ 1.98400000e+03, 4.00000000e+00],\n", " [ 1.98800000e+03, 4.00000000e+00],\n", " [ 1.99200000e+03, 4.00000000e+00],\n", " [ 1.99600000e+03, 4.00000000e+00],\n", " [ 2.00000000e+03, 4.00000000e+00],\n", " [ 2.00400000e+03, 4.00000000e+00],\n", " [ 2.00800000e+03, 4.00000000e+00],\n", " [ 1.96400000e+03, 5.00000000e+00],\n", " [ 1.96800000e+03, 5.00000000e+00],\n", " [ 1.97200000e+03, 5.00000000e+00],\n", " [ 1.97600000e+03, 5.00000000e+00],\n", " [ 1.98000000e+03, 5.00000000e+00],\n", " [ 1.98400000e+03, 5.00000000e+00],\n", " [ 1.98800000e+03, 5.00000000e+00],\n", " [ 1.99200000e+03, 5.00000000e+00],\n", " [ 1.99600000e+03, 5.00000000e+00],\n", " [ 2.00000000e+03, 5.00000000e+00],\n", " [ 2.00400000e+03, 5.00000000e+00],\n", " [ 2.00800000e+03, 5.00000000e+00]])" ] } ], "prompt_number": 33 }, { "cell_type": "code", "collapsed": false, "input": [ "model = GPy.models.GPRegression(X, y, kern)\n", "model.optimize()" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 9 }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can plot the results using the ability to 'fix inputs' in the model.plot() function. We can specify that column 1 should be fixed to event number 2 by passing fixed_inputs = [(1, 2)] to the model. To plot the results for all events on the same figure we also specify fignum=1 in the loop as below. " ] }, { "cell_type": "code", "collapsed": false, "input": [ "for i in range(6):\n", " model.plot(fignum=1,fixed_inputs=[(1, i)])\n", "plt.xlabel('years')\n", "plt.ylabel('time/s')" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 10, "text": [ "" ] }, { "metadata": {}, "output_type": "display_data", "png": 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ooL8DBoHHgcjw/VLK3vc8aJKc7xDRYYZh7Uz1ztEW3j3SwuHa9hFXd5oQlBdn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"text": [ "" ] } ], "prompt_number": 10 }, { "cell_type": "markdown", "metadata": {}, "source": [ "There is a lot we can do with this model. First of all, each of the races is a different length, so the series have a different mean. We can include another coregionalization term to deal with the mean. Below we do this and reduce the rank of the coregionalization matrix to 1." ] }, { "cell_type": "code", "collapsed": false, "input": [ "kern1 = GPy.kern.RBF(1, lengthscale=80)**GPy.kern.Coregionalize(1,output_dim=6, rank=1)\n", "kern2 = GPy.kern.Bias(1)**GPy.kern.Coregionalize(1,output_dim=6, rank=1)\n", "kern = kern1 + kern2" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 11 }, { "cell_type": "code", "collapsed": false, "input": [ "model = GPy.models.GPRegression(X, y, kern)\n", "model.optimize()" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 12 }, { "cell_type": "code", "collapsed": false, "input": [ "for i in range(6):\n", " model.plot(fignum=1,fixed_inputs=[(1, i)])\n", "plt.xlabel('years')\n", "plt.ylabel('time/s')" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 13, "text": [ "" ] }, { "metadata": {}, "output_type": "display_data", "png": 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dnAxVwzgzojGDtTsa6eqLEIoalORnkOZzEQhGWLe1jlWb9rN+Wz3hSDy5T7rP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\nT7myZiRRGOXtKGLnhKvu4+pTxxJpj+fXN01GADecNU59w45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"text": [ "" ] } ], "prompt_number": 13 }, { "cell_type": "markdown", "metadata": {}, "source": [ "This is a simple form of the linear model of coregionalization. Note how confident the model is about what the women's 400 m performance would have been. You might feel that the model is being over confident in this region. Perhaps we are forcing too much sharing of information between the sprints. We could return to the intrinsic coregionalization model and force the two base covariance functions to share the same coregionalization matrix." ] }, { "cell_type": "code", "collapsed": false, "input": [ "kern1 = GPy.kern.RBF(1, lengthscale=80) + GPy.kern.Bias(1)\n", "kern1.name = 'rbf_plus_bias'\n", "kern2 = GPy.kern.Coregionalize(1,output_dim=6, rank=5)\n", "kern = kern1**kern2\n", "kern.name = 'product'\n", "display(kern)" ], "language": "python", "metadata": {}, "outputs": [ { "html": [ "\n", "\n", "\n", " \n", " \n", " \n", " \n", " \n", "\n", "\n", "\n", "\n", "\n", "\n", "
product.ValueConstraintPriorTied to
rbf_plus_bias.rbf.variance 1.0 +ve
rbf_plus_bias.rbf.lengthscale 80.0 +ve
rbf_plus_bias.bias.variance 1.0 +ve
coregion.W (6, 5)
coregion.kappa (6,) +ve
" ], "metadata": {}, "output_type": "display_data", "text": [ "" ] } ], "prompt_number": 14 }, { "cell_type": "code", "collapsed": false, "input": [ "model = GPy.models.GPRegression(X, y, kern)\n", "model.optimize()" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 15 }, { "cell_type": "code", "collapsed": false, "input": [ "for i in range(6):\n", " model.plot(fignum=1,fixed_inputs=[(1, i)])\n", "plt.xlabel('years')\n", "plt.ylabel('time/s')" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 16, "text": [ "" ] }, { "metadata": {}, "output_type": "display_data", "png": 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Q/W39bG3sIm461M0owjek6XJEITCZCCHk1oNu5UBKSSxu0dzZj2M76WDICXiZ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\nxvMOamdCO/P3j2PZTtQrffCGX9HUQeMo6zecQ8+4gXQ6zdT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"text": [ "" ] } ], "prompt_number": 16 }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Exercise 1\n", "\n", "Can you fix the issue with over confidence in this model? Some things you might try include (a) adding additional covariance functions to handle shorter lengthscale effects. (b) Changing the rank of the coregionalization matrix. (c) Adding a coregionalized noise model using GPy.kern.white()." ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Question 1 answer here" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 19 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Predictions in the multioutput case can be very effected by our covariance function *design*. This reflects the themes we saw on the first day where the importance of covariance function choice was emphasized at design time. \n", "\n", "Can you build a covariance matrix that coregionalizes separately over the sex of the athletes and the event identity? Does this matrix perform better?" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# set up the inputs to index sex and event separately.\n", "X2 = np.zeros((X.shape[0], 3))\n", "X2[:, 0] = X[:, 0]\n", "X2[:, 1] = np.remainder(X[:, 1],2) == 1\n", "X2[:, 2] = np.floor(X[:, 1]/2)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 17 }, { "cell_type": "code", "collapsed": false, "input": [ "kern1 = (GPy.kern.RBF(1, lengthscale=80, active_dims=0)\n", " *GPy.kern.Coregionalize(1, output_dim=2, rank=1, active_dims=1, name='coregion1')\n", " *GPy.kern.Coregionalize(1, output_dim=3, rank=1, active_dims=2, name='coregion2'))\n", " \n", "kern2 = (GPy.kern.Bias(1, active_dims=0)\n", " *GPy.kern.Coregionalize(1, output_dim=2, rank=0, active_dims=1)\n", " *GPy.kern.Coregionalize(1, output_dim=3, rank=0, active_dims=2)\n", " )\n", "\n", "kern = kern1+ kern2\n", "\n", "\n", "\n", "display(kern)\n", "#print \"First coregion:\", [(k.name, k.active_dims) for k in kern.parts[0].parts]\n", "#print \"Second \", [(k.name, k.active_dims) for k in kern.parts[0].parts[1].parts]\n", "\n", "model = GPy.models.GPRegression(X2, y, kern) \n", "display(model.optimize('scg', messages=1))\n" ], "language": "python", "metadata": {}, "outputs": [ { "html": [ "\n", "\n", "\n", " \n", " \n", " \n", " \n", " \n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "
mul_1.rbf.variance 1.0 +ve
mul_1.rbf.lengthscale 80.0 +ve
mul_1.coregion1.W (2, 1)
mul_1.coregion1.kappa (2,) +ve
mul_1.coregion2.W (3, 1)
mul_1.coregion2.kappa (3,) +ve
mul_2.bias.variance 1.0 +ve
mul_2.coregion_1.W []
mul_2.coregion_1.kappa (2,) +ve
mul_2.coregion_2.W []
mul_2.coregion_2.kappa (3,) +ve
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\n", "Model: GP regression
\n", "Log-likelihood: -130.482376392
\n", "Number of Parameters: 19
\n", "

\n", "\n", "\n", "\n", " \n", " \n", " \n", " \n", " \n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "
GP_regression.ValueConstraintPriorTied to
Gaussian_noise.variance 0.322503741245 +ve
" ], "metadata": {}, "output_type": "display_data", "text": [ "" ] } ], "prompt_number": 19 }, { "cell_type": "code", "collapsed": false, "input": [ "model.add.mul_1.coregion1.W" ], "language": "python", "metadata": {}, "outputs": [ { "html": [ "\n", "\n", "\n", "\n", " \n", " \n", " \n", " \n", " \n", "\n", "\n", "\n", "\n", "
[0 0]-2.4773371925N/A
[1 0]-5.00748406387N/A
[2 0]-11.1726954204N/A

\n", "Model: GP regression
\n", "Log-likelihood: -130.482376392
\n", "Number of Parameters: 19
\n", "

\n", "\n", "\n", "\n", " \n", " \n", " \n", " \n", " \n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "
GP_regression.ValueConstraintPriorTied to
Gaussian_noise.variance 0.322503741245 +ve
" ], "metadata": {}, "output_type": "display_data", "text": [ "" ] } ], "prompt_number": 24 }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Low Rank Approximations\n", "\n", "In the worst case, inference in a Gaussian process is $\\mathcal{O}(n^3)$ computational complexity and $\\mathcal{O}(n^2)$ storage. For efficient inference in larger data sets we need to consider approximations. One approach is low rank approximation of the covariance matrix (also known as sparse approximations or perhaps more accurately parsimonious approximations). We'll study these approximations by first creating a simple data set by sampling from a GP." ] }, { "cell_type": "code", "collapsed": false, "input": [ "X = np.sort(np.random.rand(50,1)*12,0)\n", "k = GPy.kern.RBF(1)\n", "K = k.K(X)\n", "K+= np.eye(50)*0.01 # add some independence (noise) to K\n", "y = np.random.multivariate_normal(np.zeros(50), K).reshape(50,1)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 25 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Build a straightforward GP model of our simulation. We\u2019ll also plot the posterior of $f$." ] }, { "cell_type": "code", "collapsed": false, "input": [ "model = GPy.models.GPRegression(X,y)\n", "model.optimize()\n", "fig = plt.figure()\n", "ax = fig.add_subplot(111)\n", "model.plot_f(ax=ax)\n", "model._raw_predict?\n", "mu, var = model._raw_predict(X) # this fetches the posterior of f\n", "\n", "plt.vlines(X[:,0], mu[:,0]-2.*np.sqrt(var[:,0]), mu[:,0]+2.*np.sqrt(var[:,0]),color='r',lw=2)" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 28, "text": [ "" ] }, { "metadata": {}, "output_type": "display_data", "png": 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5syJXLcrgrlvXAvDLh/fSOzA86XvMStJ+6Bc/uvjf0UMHZuw5mSkxvDWLlSTd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\n9vUF/O4776PZEkX5vlK2r77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"text": [ "" ] } ], "prompt_number": 28 }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Exercise 2\n", "\n", "One thought that occurs is as follows. Do we need all the data to create this posterior estimate? Are any of the data points redundant? What happens to the model if you remove some data?\n", "\n", "*Hint:* \n", "python\n", "X2 = np.delete(X,range(8),0)\n", "y2 = np.delete(y,range(8),0)\n", "" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Exercise 2 answer here" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 29 }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Building the Low Rank Approximation\n", "\n", "Now we\u2019ll consider a GP that uses a low rank approximation to fit the data." ] }, { "cell_type": "code", "collapsed": false, "input": [ "Z = np.random.rand(3,1)*12\n", "model = GPy.models.SparseGPRegression(X,y,Z=Z)\n", "display(model)" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "clang: warning: argument unused during compilation: '-fopenmp'\n", "In file included from /Users/neil/.cache/scipy/python27_compiled/sc_1790bf65208b11355ffcfd4b65a5f1092.cpp:11:\n", "In file included from /Users/neil/Library/Enthought/Canopy_64bit/User/lib/python2.7/site-packages/scipy/weave/blitz/blitz/array.h:26:\n", "In file included from /Users/neil/Library/Enthought/Canopy_64bit/User/lib/python2.7/site-packages/scipy/weave/blitz/blitz/array-impl.h:37:\n", "/Users/neil/Library/Enthought/Canopy_64bit/User/lib/python2.7/site-packages/scipy/weave/blitz/blitz/range.h:120:34: warning: '&&' within '||' [-Wlogical-op-parentheses]\n", " return ((first_ < last_) && (stride_ == 1) || (first_ == last_));\n", " ~~~~~~~~~~~~~~~~~^~~~~~~~~~~~~~~~~ ~~\n", "/Users/neil/Library/Enthought/Canopy_64bit/User/lib/python2.7/site-packages/scipy/weave/blitz/blitz/range.h:120:34: note: place parentheses around the '&&' expression to silence this warning\n", " return ((first_ < last_) && (stride_ == 1) || (first_ == last_));\n", " ^\n", " ( )\n", "In file included from /Users/neil/.cache/scipy/python27_compiled/sc_1790bf65208b11355ffcfd4b65a5f1092.cpp:23:\n", "In file included from /Users/neil/Library/Enthought/Canopy_64bit/User/lib/python2.7/site-packages/numpy/core/include/numpy/arrayobject.h:4:\n", "In file included from /Users/neil/Library/Enthought/Canopy_64bit/User/lib/python2.7/site-packages/numpy/core/include/numpy/ndarrayobject.h:17:\n", "In file included from /Users/neil/Library/Enthought/Canopy_64bit/User/lib/python2.7/site-packages/numpy/core/include/numpy/ndarraytypes.h:1761:\n", "/Users/neil/Library/Enthought/Canopy_64bit/User/lib/python2.7/site-packages/numpy/core/include/numpy/npy_1_7_deprecated_api.h:15:2: warning: \"Using deprecated NumPy API, disable it by \" \"#defining NPY_NO_DEPRECATED_API NPY_1_7_API_VERSION\" [-W#warnings]\n", "#warning \"Using deprecated NumPy API, disable it by \" \\\n", " ^\n", "/Users/neil/.cache/scipy/python27_compiled/sc_1790bf65208b11355ffcfd4b65a5f1092.cpp:24:10: fatal error: 'omp.h' file not found\n", "#include \n", " ^\n", "2 warnings and 1 error generated.\n", "\n", " Weave compilation failed. Falling back to (slower) numpy implementation\n", "\n" ] }, { "html": [ "\n", "\n", "

\n", "Model: sparse gp mpi
\n", "Log-likelihood: -89.690592049
\n", "Number of Parameters: 6
\n", "

\n", "\n", "\n", "\n", " \n", " \n", " \n", " \n", " \n", "\n", "\n", "\n", "\n", "\n", "
sparse_gp_mpi.ValueConstraintPriorTied to
inducing inputs (3, 1)
rbf.variance 1.0 +ve
rbf.lengthscale 1.0 +ve
Gaussian_noise.variance 1.0 +ve
" ], "metadata": {}, "output_type": "display_data", "text": [ "" ] } ], "prompt_number": 30 }, { "cell_type": "markdown", "metadata": {}, "source": [ "In GPy, the sparse inputs $\\mathbf{Z}$ are abbreviated 'iip' , for inducing input. Plot the posterior\n", "of $u$ in the same manner as for the full GP:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "mu, var = model._raw_predict(Z) \n", "plt.vlines(Z[:,0], mu[:,0]-2.*np.sqrt(var[:,0]), mu[:,0]+2.*np.sqrt(var[:,0]),color='r')" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 31, "text": [ "" ] }, { "metadata": {}, "output_type": "display_data", "png": 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"text": [ "" ] } ], "prompt_number": 31 }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Exercise 3\n", "\n", "Optimise and plot the model. The inducing inputs are marked \u2013 how\n", "are they placed? You can move them around with e.g. m['iip_2_0'] = 100 . What\n", "happens to the likelihood? What happens to the fit if you remove an input?" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Exercise 3 answer" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 32 }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Exercise 4\n", "\n", "How does the fit of the sparse compare with the full GP? Play around\n", "with the number of inducing inputs, the fit should improve as $M$ increases. How many\n", "inducing points are needed? What do you think happens in higher dimensions?" ] }, { "cell_type": "raw", "metadata": {}, "source": [ "# Exercise 4 answer" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Exercise 5\n", "\n", "Can you build a low rank Gaussian process with the intrinsic model of coregionalization? Do you have to treat the 2nd input (which specifies the event number) in a special way?" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Exercise 5 answer" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 33 } ], "metadata": {} } ] }