{ "metadata": { "name": "", "signature": "sha256:c57d5061e28da12e72e8e85205826f9837a70fb76720c04f7e498cec94b97c21" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# GPy Introduction: Covariance Functions in GPy\n", "\n", "# Gaussian Process Summer School, Melbourne, Australia\n", "### 25th-27th February 2015\n", "### Neil D. Lawrence and Nicolas Durrande\n" ] }, { "cell_type": "code", "collapsed": false, "input": [ "%matplotlib inline\n", "from IPython.display import display\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "import pods\n", "import GPy" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stderr", "text": [ "/Users/neil/Library/Enthought/Canopy_64bit/User/lib/python2.7/site-packages/pytz/__init__.py:29: UserWarning: Module pods was already imported from /Users/neil/sods/ods/pods/__init__.pyc, but /Users/neil/Library/Enthought/Canopy_64bit/User/lib/python2.7/site-packages is being added to sys.path\n", " from pkg_resources import resource_stream\n" ] } ], "prompt_number": 1 }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Covariance Functions in GPy\n", "\n", "We've [introduced Gaussian processes](gaussian process introduction.ipynb) and built a simple class in python for fitting these models. In the last session we introduced Gaussian process models through constructing covariance functions in `numpy`. The `GPy` software is a BSD licensed software package for modeling with Gaussian processes in python. It is designed to make it easy for the user to construct models and interact with data. The software is BSD licensed to ensure that there are as few as possible constraints on its use. The `GPy` documentation is produced with Sphinx and is available [here](http://gpy.readthedocs.org/en/latest/).\n", "\n", "In the introduction to Gaussian processes we defined covariance functions (or kernels) as functions to which we passed objects in `GPy` covariance functions are objects.\n", "\n", "In `GPy` the covariance object is stored in `GPy.kern`. There are several covariance functions available. The exponentiated quadratic covariance is stored as `RBF` and can be created as follows." ] }, { "cell_type": "code", "collapsed": false, "input": [ "kern = GPy.kern.RBF(input_dim=1)\n", "display(kern)" ], "language": "python", "metadata": {}, "outputs": [ { "html": [ "\n", "\n", "\n", " \n", " \n", " \n", " \n", " \n", "\n", "\n", "\n", "
rbf.ValueConstraintPriorTied to
variance 1.0 +ve
lengthscale 1.0 +ve
" ], "metadata": {}, "output_type": "display_data", "text": [ "" ] } ], "prompt_number": 2 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here it's been given the name 'rbf' by default and some default values have been given for the lengthscale and variance, we can also name the covariance and change the initial parameters as follows," ] }, { "cell_type": "code", "collapsed": false, "input": [ "kern = GPy.kern.RBF(input_dim=1, name='signal', variance=4.0, lengthscale=2.0)\n", "display(kern)" ], "language": "python", "metadata": {}, "outputs": [ { "html": [ "\n", "\n", "\n", " \n", " \n", " \n", " \n", " \n", "\n", "\n", "\n", "
signal.ValueConstraintPriorTied to
variance 4.0 +ve
lengthscale 2.0 +ve
" ], "metadata": {}, "output_type": "display_data", "text": [ "" ] } ], "prompt_number": 3 }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Plotting the Kernel\n", "\n", "The covariance function expresses the covariation between two points. the `.plot()` method can be applied to the kernel to discover how the covariation changes as a function as one of the inputs with the other fixed (i.e. it plots `k(x, z)` as a function of a one dimensional `x` whilst keeping `z` fixed. By default `z` is set to `0.0`." ] }, { "cell_type": "code", "collapsed": false, "input": [ "kern.plot()" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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"text": [ "" ] } ], "prompt_number": 4 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here the title of the kernel is taken from the name we gave it (`signal`). \n", "\n", "## Changing Covariance Function Parameters\n", "\n", "When we constructed the covariance function we gave it particular parameters. These parameters can be changed later in a couple of different ways firstly, we can simple set the field value of the parameters. If we want to change the lengthscale of the covariance to 3.5 we do so as follows." ] }, { "cell_type": "code", "collapsed": false, "input": [ "kern.lengthscale = 3.5\n", "display(kern)" ], "language": "python", "metadata": {}, "outputs": [ { "html": [ "\n", "\n", "\n", " \n", " \n", " \n", " \n", " \n", "\n", "\n", "\n", "
signal.ValueConstraintPriorTied to
variance 4.0 +ve
lengthscale 3.5 +ve
" ], "metadata": {}, "output_type": "display_data", "text": [ "" ] } ], "prompt_number": 5 }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can even change the naming of the parameters, let's imagine that this covariance function was operating over time instead of space, we might prefer the name `timescale` for the `lengthscale` parameter." ] }, { "cell_type": "code", "collapsed": false, "input": [ "kern.lengthscale.name = 'timescale'\n", "display(kern)" ], "language": "python", "metadata": {}, "outputs": [ { "html": [ "\n", "\n", "\n", " \n", " \n", " \n", " \n", " \n", "\n", "\n", "\n", "
signal.ValueConstraintPriorTied to
variance 4.0 +ve
timescale 3.5 +ve
" ], "metadata": {}, "output_type": "display_data", "text": [ "" ] } ], "prompt_number": 6 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now we can set the time scale appropriately." ] }, { "cell_type": "code", "collapsed": false, "input": [ "kern.timescale = 10.\n", "display(kern)" ], "language": "python", "metadata": {}, "outputs": [ { "html": [ "\n", "\n", "\n", " \n", " \n", " \n", " \n", " \n", "\n", "\n", "\n", "
signal.ValueConstraintPriorTied to
variance 4.0 +ve
timescale 10.0 +ve
" ], "metadata": {}, "output_type": "display_data", "text": [ "" ] } ], "prompt_number": 7 }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Further Covariance Functions in GPy\n", "\n", "There are other types of basic covariance function in `GPy`. For example the `Linear` kernel,\n", "$$\n", "k(\\mathbf{x}, \\mathbf{z}) = \\alpha \\mathbf{x}^\\top \\mathbf{z}\n", "$$\n", "and the `Bias` kernel,\n", "$$\n", "k(\\mathbf{x}, \\mathbf{z}) = \\alpha\n", "$$\n", "where everything is equally correlated to each other. `Brownian` implements Brownian motion which has a covariance function of the form,\n", "$$\n", "k(t, t^\\prime) = \\alpha \\text{min}(t, t^\\prime).\n", "$$\n", "\n", "Broadly speaking covariances fall into two classes, *stationary* covariance functions, for which the kernel can always be written in the form\n", "$$\n", "k(\\mathbf{x}, \\mathbf{z}) = f(r)\n", "$$\n", "where $f(\\cdot)$ is a function and $r$ is the distance between the vectors $\\mathbf{x}$ and $\\mathbf{z}$, i.e.,\n", "$$\n", "r = ||\\mathbf{x} - \\mathbf{z}||_2 = \\sqrt{\\left(\\mathbf{x} - \\mathbf{z}\\right)^\\top \\left(\\mathbf{x} - \\mathbf{z}\\right)}.\n", "$$\n", "This partitioning is reflected in the object hierarchy in GPy. There is a base object `Kern` and this is inherited by `Stationary` to form the stationary covariance functions (like `RBF` and `Matern32`).\n", "\n", "## Computing the Covariance Function\n", "\n", "When using `numpy` to construct covariances we defined a function, `kern_compute` which returned a covariance matrix given the name of the covariance function. In `GPy`, the base object `Kern` implements a method `K`. That allows us to compute the associated covariance. Visualizing the structure of this covariance matrix is often informative in understanding whether we have appropriately captured the nature of the relationship between our variables in our covariance function. In `GPy` the input data is assumed to be provided in a matrix with $n$ rows and $p$ columns where $n$ is the number of data points and $p$ is the number of features we are dealing with. We can compute the entries to the covariance matrix for a given set of inputs `X` as follows." ] }, { "cell_type": "code", "collapsed": false, "input": [ "data = pods.datasets.olympic_marathon_men()\n", "# Load in the times of the olympics\n", "X = data['X']\n", "K=kern.K(X)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 8 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now to visualize this covariation between the time points we plot it as an image using the `imshow` command from matplotlib.\n", "```python\n", "plt.imshow(K, interpolation='None')\n", "```\n", "Setting the interpolation to `'None'` prevents the pixels being smoothed in the image. To better visualize the structure of the covariance we've also drawn white lines at the points where the First World War and the Second World War begin. At other points the Olympics are held every four years and the covariation is given by the computing the covariance function for two points which are four years apart, appropriately scaled by the time scale." ] }, { "cell_type": "code", "collapsed": false, "input": [ "def visualize_olympics(K):\n", " \"\"\"Helper function for visualizing a covariance computed on the Olympics training data.\"\"\"\n", " fig, ax = plt.subplots(figsize=(8,8))\n", " im = ax.imshow(K, interpolation='None')\n", "\n", " WWI_index = np.argwhere(X==1912)[0][0]\n", " WWII_index = np.argwhere(X==1936)[0][0]\n", "\n", " ax.axhline(WWI_index+0.5,color='w')\n", " ax.axvline(WWI_index+0.5,color='w')\n", " ax.axhline(WWII_index+0.5,color='w')\n", " ax.axvline(WWII_index+0.5,color='w')\n", " plt.colorbar(im)\n", " \n", "visualize_olympics(kern.K(X))" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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" ], "metadata": {}, "output_type": "pyout", "prompt_number": 10, "text": [ "\u001b[1msignal.timescale\u001b[0;0m:\n", "Param([ 10.])" ] } ], "prompt_number": 10 }, { "cell_type": "markdown", "metadata": {}, "source": [ "of 10 is ensuring that neighbouring Olympic years are correlated, but there is only weak dependency across the period of each of the world wars. If we increase the timescale to 20 we obtain stronger dependencies between the wars." ] }, { "cell_type": "code", "collapsed": false, "input": [ "kern.timescale = 20\n", "visualize_olympics(kern.K(X))" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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"text": [ "" ] } ], "prompt_number": 11 }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Covariance Matrices and Covariance Functions\n", "\n", "A Gaussian process specifieds that any finite set of realizations of the function will jointly have a Gaussian density. In other words, if we are interested in the joint distribution of function values at a set of particular points, realizations of those functions can be sampled according to a Gaussian density. The Gaussian process provides a prior over an infinite dimensional object: the function. For our purposes we can think of a function as being like an infinite dimensional vector. The mean of our Gaussian process is normally specified by a vector, but is now itself specified by a *mean function*. The covariance of the process, instead of being a matrix is also a *covariance function*. But to construct the infinite dimensional matrix we need to make it a function of two arguments, $k(\\mathbf{x}, \\mathbf{z})$. When we compute the covariance matrix using `k.K(X)` we are computing the values of that matrix for the different entries in $\\mathbf{X}$. `GPy` also allows us to compute the cross covariance between two input matrices, $\\mathbf{X}$ and $\\mathbf{Z}$.\n", "\n", "## Sampling from a Gaussian Process\n", "\n", "We cannot sample a full function from a process because it consists of infinite values, however, we can obtain a finite sample from a function as described by a Gaussian process and visualize these samples as functions. This is a useful exercise as it allows us to visualize the type of functions that fall within the support of our Gaussian process prior. Careful selection of the right covariance function can improve the performance of a Gaussian process based model in practice because the covariance function allows us to bring domain knowledge to bear on the problem. If the input domain is low dimensional, then we can at least ensure that we are encoding something reasonable in the covariance through visualizing samples from the Gaussian process. \n", "\n", "For a one dimensional function, if we select a vector of input values, represented by `X`, to be equally spaced, and ensure that the spacing is small relative to the lengthscale of our process, then we can visualize a sample from the function by sampling from the Gaussian (or a multivariate normal) with the `numpy` command\n", "```python\n", "F = np.random.multivariate_normal(mu, K, num_samps).T\n", "```\n", "where `mu` is the mean (which we will set to be the zero vector) and `K` is the covariance matrix computed at the points where we wish to visualize the function. The transpose at the end ensures that the the matrix `F` has `num_samps` columns and $n$ rows, where $n$ is the dimensionality of the *square* covariance matrix `K`. \n", "\n", "Below we build a simple helper function for sampling from a Gaussian process and visualizing the result. " ] }, { "cell_type": "code", "collapsed": false, "input": [ "def sample_covariance(kern, X, num_samps=10):\n", " \"\"\"Sample a one dimensional function as if its from a Gaussian process with the given covariance function.\"\"\"\n", " from IPython.display import HTML\n", " display(HTML('

Samples from a Gaussian Process with ' + kern.name + ' Covariance

'))\n", " display(kern)\n", " K = kern.K(X) \n", "\n", " # Generate samples paths from a Gaussian with zero mean and covariance K\n", " F = np.random.multivariate_normal(np.zeros(X.shape[0]), K, num_samps).T\n", "\n", " fig, ax = plt.subplots(figsize=(8,8))\n", " ax.plot(X,F)\n", "\n" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 12 }, { "cell_type": "markdown", "metadata": {}, "source": [ "We are now in a position to define a vector of inputs, a covariance function, and then to visualize the samples from the process." ] }, { "cell_type": "code", "collapsed": false, "input": [ "# create an input vector\n", "X = np.linspace(-2, 2, 200)[:, None]\n", "\n", "# create a covariance to visualize\n", "kern = GPy.kern.RBF(input_dim=1)\n", "\n", "# perform the samples.\n", "sample_covariance(kern, X)" ], "language": "python", "metadata": {}, "outputs": [ { "html": [ "

Samples from a Gaussian Process with rbf Covariance

" ], "metadata": {}, "output_type": "display_data", "text": [ "" ] }, { "html": [ "\n", "\n", "\n", " \n", " \n", " \n", " \n", " \n", "\n", "\n", "\n", "
rbf.ValueConstraintPriorTied to
variance 1.0 +ve
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gFxwsQMLyBLhPcUevT3uhdXfj5sE7ckRUfH18gG7d5Lh8eSEMhlIMGrTv+mxb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bAAAg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\ne0cSHDybI0cetdoxbaXDCVkpt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Samples from a Gaussian Process with poly Covariance

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poly.ValueConstraintPriorTied to
variance 1.0 +ve
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pa+P/4uK4KS6OMDt1PMnOhkcfhY8+gssu00/7GjjQLk8lhN0pm6LskTLKHisj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\nn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"text": [ "" ] } ], "prompt_number": 14 }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Combining Covariance Functions\n", "\n", "Covariance functions can be combined in various ways to make new covariance functions. \n", "\n", "### Adding Covariance Functions\n", "\n", "Perhaps simplest thing you can do to combine covariance functions is to add them. The sum of two Gaussian random variables is also Gaussian distributed, with a covariance equal to the sum of the covariances of the original variables (similarly for the mean). This implies that if we add two functions drawn from Gaussian processes together, then the result is another function drawn from a Gaussian process, and the covariance function is the sum of the two covariance functions of the original process.\n", "$$\n", "k(\\mathbf{x}, \\mathbf{z}) = k_1(\\mathbf{x}, \\mathbf{z}) + k_2(\\mathbf{x}, \\mathbf{z}).\n", "$$\n", "Here the domains of the two processes don't even need to be the same, so one of the covariance functions could perhaps depend on time and the other on space,\n", "$$\n", "k\\left(\\left[\\mathbf{x}\\quad t\\right], \\left[\\mathbf{z}\\quad t^\\prime\\right]\\right) = k_1(\\mathbf{x}, \\mathbf{z}) + k_2(t, t^\\prime).\n", "$$\n", "\n", "In `GPy` the addition operator is overloaded so that it is easy to construct new covariance functions by adding other covariance functions together." ] }, { "cell_type": "code", "collapsed": false, "input": [ "k1 = GPy.kern.RBF(1, variance=4.0, lengthscale=10., name='long term trend')\n", "k2 = GPy.kern.RBF(1, variance=1.0, lengthscale=2., name='short term trend')\n", "kern = k1 + k2\n", "kern.name = 'signal'\n", "kern.long_term_trend.lengthscale.name = 'timescale'\n", "kern.short_term_trend.lengthscale.name = 'timescale'\n", "display(kern)" ], "language": "python", "metadata": {}, "outputs": [ { "html": [ "\n", "\n", "\n", " \n", " \n", " \n", " \n", " \n", "\n", "\n", "\n", "\n", "\n", "
signal.ValueConstraintPriorTied to
long term trend.variance 4.0 +ve
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" ], "metadata": {}, "output_type": "display_data", "text": [ "" ] } ], "prompt_number": 15 }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Multiplying Covariance Functions\n", "\n", "An alternative is to multiply covariance functions together. This also leads to a valid covariance function (i.e. the kernel is within the space of Mercer kernels), although the interpretation isn't as straightforward as the additive covariance. " ] }, { "cell_type": "code", "collapsed": false, "input": [ "k1 = GPy.kern.Linear(1)\n", "k2 = GPy.kern.RBF(1)\n", "kern = k1*k2\n", "display(kern)\n", "fig, ax = plt.subplots(figsize=(8,8))\n", "im = ax.imshow(kern.K(X), interpolation='None')\n", "plt.colorbar(im)" ], "language": "python", "metadata": {}, "outputs": [ { "html": [ "\n", "\n", "\n", " \n", " \n", " \n", " \n", " \n", "\n", "\n", "\n", "\n", "
mul.ValueConstraintPriorTied to
linear.variances 1.0 +ve
rbf.variance 1.0 +ve
rbf.lengthscale 1.0 +ve
" ], "metadata": {}, "output_type": "display_data", "text": [ "" ] }, { "metadata": {}, "output_type": "pyout", "prompt_number": 16, "text": [ "" ] }, { "metadata": {}, "output_type": "display_data", "png": 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dmFwNqzSnhG0JlEu/AocEWUrX7tu44/gW5OR5nMa0rXemsdK+1MdKZNQYmnGX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"text": [ "" ] } ], "prompt_number": 16 }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Exercise 3\n", "\n", "Now try a range of different covariance functions and values and plot the corresponding sample paths for each using the same approach given above." ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Try plotting sample paths here" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 17 }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Exercise 4\n", "\n", "Can you tell the covariance structures that have been used for generating the\n", "sample paths shown in the figures below?\n", "
\n", "
\n", "\n", "\n", "
\n", "\"Figure\"Figure\"Figure
\"Figure\"Figure\"Figure
\n", "
\n" ] }, { "cell_type": "raw", "metadata": {}, "source": [ "# Exercise 4 answer" ] } ], "metadata": {} } ] }