{ "metadata": { "name": "", "signature": "sha256:7ebb3e1c06b3cc29183d75f7da1608e810832f602d443a57fbfa8b0d7faefdbb" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# GPy Introduction: Covariance Functions in GPy\n", "\n", "## Machine Learning Summer School, Sydney, Australia\n", "\n", "### 23rd February 2015\n", "\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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DYYxVE0SE7YmJ6BoQgL5WVrjRpUu1SNpVwS1u9jerV6+Gl5cXzp8/z/t3M8Y06rFCgZnh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eUK//c/7jD2/vsmmQekyj1ucLIOB1AZQB4AwQBqv7JNJwAH0z5vCuBkBvv61zsRnV5HzVY1o1Vn\nVxnx/Y1IV2Qkkb09v8PMwfxv+VOpeaXor9t/GfyY1Gep9OCPBxTcNpj8ivtR6NBQivGJ+adnciq/\niXdw4H9TU00VvekkJBD17EnUsqVFtzZWhSZaQ1c/vUp/lfmL7q+9T3qdld33MMC5++eo1LhSVHp6\nadp/bb9q/eZNSq8n8vfnX3R7eyInJ6KmTYmSjD+35WXI4og7u0PZJgDCiSiSiFIBbAXg+so2HwJY\nl5aZgwAUVxTF8U07tlPssKTjEkz+czJik2KzGaZ4rbfeApydeT1jDhX8MBg9tvfAhu4b0l3XmpHc\nRXOjzJAycPJxQuMrjVGofiHcnHATgZUCETg4HD3qxePwIUJQEBdTyW1lqxwfPgRat+YqaN7eQHHj\nVuS0WqQj3P/tPk7VOQW7fHZoHNoYZYeWhWJnOTPGjaVB2QY48tERaA5oMN5rPJzXOcP/tr/aYRlH\naiqXfm7ShMugtmrFaxzPnePXxYEDuba4hclu4i4P4M5LX99N+96btjFokVujco3Qq04vfHvk22wF\nKQwwdixXz9Dr1Y7E7MJiwtBpUycs7bQU7au3z/J+8pXNh4pfVkRd//fwZycnbN5lhzHRlzHnwWnk\n3noLSRFJRoza9EJCgGbNuNTq+vX/VG/L6Z799Qznmp3Do42P4OTthBq/1kCe4rZdKq5+/fpwqeyC\nIYlDMMRpCAbvHoz2G9sj6G6Q2qFlTUwMlyesUgVYtQr47jsuSjVmDHfvsbPjX/qnT4HPP+cCKxYk\nu+//DT2aV9+Gpvu4adOmvfi8devWaN26NWa3mY06y+og4E5ApkZCIpNatAAKF+YbmJ07qx2N2dx5\ndgftNrTDTOeZ6FWnV7b3d/w48MknwLvvFsKvN6rC0bEK4gLj8GjjI5xrcg4FahaA40BHlO5TGnkc\nLPfF3ssLGDwY+PlnHnQIIDEsETe/vYn4s/GoMrsKHAda1ppsU5s6dSqcnZ1xY9QNDKw/EGvPr0Xv\nHb1R37E+ZjjPQMOyDdUO8c1CQ7lYyrZtQLduwIEDGa/dzpeP+9K2bAnMmcMt+bLJ19cXvr6+2d5P\ndu9xNwNw+KWvJwKY8Mo2KwD0e+nrqwAc09lXhvcBtl7aSu8se4c0WuPO6BOv+OMPIhcXtaMwm8fP\nH1PNxTVp/l/zs72vJ0+IPvmEqEIFoj170t9Gl6KjqH1RFNI3hE4UPUEXu16kR1sfWdzs42XLiBwd\nifz81I7EMqQ8TqFro6+Rf0l/uvXjLdImWtb5Mqf+/fvT7NmzX3ydlJpEv578lcr+VJa6b+1O5x+c\nVzG6DOj1RIcPE3XowL/YU6cSPXhg+OPv3yeqUoWXixkZ1FgOBh6x3wBPTsuLN09OawYDJ6e9TK/X\nU7sN7Wie/zyj/GeJDCQn8y92NosKWINnyc+o4W8NadKRSdne165dvLzT3Z3o6VPDHvNiUptLMJ0o\ndoKuDL5C0YeiSZeqy3Y8WaXVEn35JVHNmkTh4aqFYTG0CVqKnB1Jfg5+FPZ5GKVEWXYRFXMIDQ2l\nUqVKUdwrE1kTNYm0IGABlV9QntptaEdHbx5VfxJbYiLRb78R1a5NVK8e0Zo1WZ9sdu0aF17Yt8+o\nIaqSuPl50RHANfDs8olp3xsBYMRL2yxJ+/kFAA0z2M9rD/B6zHVymOtAkU8is/2fJV5j6lReZGzD\nEjWJ1HJtSxp1YFS2Xlzu3SPq0YMT3YkTb94+I8kPkunOL3foTNMz5F/an8I+C6OnAU/N+sL39ClR\np05Ezs7Wt77c2HTJOrq77C4FVAigkF4hlHA9Qe2QLErfvn1p7ty56f4sOTWZVp9bTTUX16T3fn+P\ndlzeQVqdma9Q3LtHNGkSl/br2pXo6FHjVDkKCiIqWZIoICD7+0qjWuI21sebEjcR0czjM6nr5q7q\nv5OzZQ8ecDm/GOup+JQZGq2GOm/qTAM8BpBOn7XRrV5P9Pvv/Dc8ZYpxV4wkhidSxMwICqoVRIGV\nA+nGpBv0POS58Z4gHdeucc2J0aONXl/CquhSdHRvxT0KqBRAFzpeoGdBz9QOySJdunSJHB0d6fnz\njH8vdXod7Q7dTc1WNaMav9ag3878RokaE1dfO32aaOBAohIliD77jCgs7M2PyayDB/mqpJFqFOeI\nxJ2cmkw1F9ekXVd2ZeG/SBhs8GCiH39UOwqj0+l1NMBjAHXZ3CXL8yXCwrjyYZMmRBcvGjnAl+j1\neoo7H0fhX4dTQIUAOlX/FN368RYl3TLuulIvLy5f+ttvRt2tVdEmaunu8rsU8FYABbcLpqeBBt7v\nyMF69uxJCxYseON2er2ejkcepy6bu1DJeSVpvNd4uhFrxCqNWi3Rzp1ELVoQVarExRJMfclo3Tou\njXr3brZ3lSMSNxHR8cjjVG5BOXqSJJUgTObMGa5raY3VQjKg1+vJ/YA7tVrbKkvv/DUaoh9+4EIq\nP//Mrxfmotfp6YnvE7r66VXyc+Byq3cWZ69mul7Px1GmTM6tOa6J0VDEzAjyd/Sni10v0tO/JGEb\n6vz581SmTJlM1TC/EXuDvvb+mkrOK0mdN3Wmg2EHs3zVi2Jjuf7uW28RNW9OtH27eV+vfvyR6J13\nsl2RKKuJ26Laehoai/sBd2j1Wqz8cKWJo8rBPviA1y/27q12JEYx+ejkLLfnPHsWGD4cKF0a+O03\noHJl08RoCL1Gj1ivWETtjELM/hgUrFUQpXqWQskeJVGgSoE37wBASgqXXz1/Hti7l+tM5CSJYYm4\nt/QeHm14hJLdS6LiuIooVKeQ2mFZnW7duqFNmzb4/PPMtWBOTE3E1pCtWHJqCeI18RjZaCQGOw3+\nTz/wdF2+DCxezMu5unTh16jGjbN4BNlAxKVQg4O5MlEWixzYTFtPQzxLfkYVFlagozePGvwYkUk7\ndhD93/+pHYVRzP9rPtVaUouiEqIy9biEBKLx4/lSsiV28dKl6Cj6UDRdHX6V/Ev50+mGpylydiQ9\nD8343uO9ezxA6dmT+8vkFLpUHT3e9ZiC2waTf2l/ujHxRra7vOV0Z86cofLly1NSFid56PV6Crgd\nQB/t/oiK/VCMXLe40u7Q3f+9jaXV8mzutm35EtG0aZlbzmUqOh1Rr15EAwZk+cUBOWnEDQD7r+3H\nl15f4qL7RRTMU9CEkeVQWi1QrRqwaxfQqJHa0WTZqnOrMOvELPi7+aNCUYMK9gEAjh4FPv2UK4f9\n/DOPti2ZXqvHM79niPKIQvSuaOQukRslXUvCvqM9ijYvCrvcdjh+HOjfn3soTJzIxaFsXWJYIh5t\neISHfzxEvrfyofyo8ijVsxTs8uWAgzeDLl26oHPnznB3d8/WfuJT4rHjyg6sDV6LsJgwDKw3EG5V\ne+Idz9M8wra35+qOvXtbVgm/pCSgTRugbVtg5sxMPzyrI26rTdwA0N+jPyoUqYD57eabKKocbt48\nrnu5fr3akWTJjss7MPbwWBwfehw1HGoY9JjYWK4pfvQosHw50KmTiYM0AdIT4oLiEOMZg9iDsUiK\nSMb+t6rjj4hSWPu7Hp37Wm7FNmPQRGnweNtjPNrwCCm3U1C6f2mUGVoGhesXVjs0mxMUFITevXsj\nPDwcefPmNco+bwV548EPk1DL+xwC6xZDlFs/tOg7HlXtqxll/0b3+DHQvDkwZQowbFimHpojE/fj\nhMeot7weDvQ/gMblVbjPYetiY3nUfeUKULas2tFkiiHtOV9GBOzcyW/qe/UCZs/mksXW7vlzYNgA\nHcIu6jC/dgQKBD5GgeoFUMK5BIq1KoZiLYrZRJ3tpJtJiN4bjei90Xh+/jkcujjAcbAjSrQtAbvc\nMro2pQ4dOqBnz5745JNPsr4TjYYnXKxYwYOFTz6BbsSn8NdFYNvlbfAI9UClYpXQt25f9KnbB5WK\nVTLeARjD1avcoGTzZm4FaqAcmbgBYOPFjZj31zyc+fQM8uYyzjs+8ZKRIwFHR2D6dLUjMZjfLT/0\n2N4De/vtNai+/d27fPk4PJz7DTRvboYgzeDaNaB7d24lvGQJkD8/oE/VIy4wDk99n+Lp8aeIPxWP\nAjUKoHir4ijWqhiKf1Dcomuo/00br8Uz/2d4euwpYg/HQvNIA4euDijpWhIl2pbIsC+6ML6AgAAM\nHDgQYWFhyJMnk787kZHAypXAmjVArVr8etO9O/DK6F2r18I30hdbQ7Zi99XdqOlQEz1q94BrTVeD\nr6aZ3PHjfCn/2DGgbl2DHpJjEzcRwXWrK+qVrofZ/5ttgshyuCtX+B7OrVuWdW8pA+cenEOHjR2w\nqccmuFRzee22ej3PEv/+e+Czz4Bvv7WKQzTIrl3AiBHcAGn48Iy302v0iD8Tj6fHOZHHBcYhj0Me\nFHmvyIuPQvUKIW8p9d4UExGSI5MRfzYe8Wfi8ez4Mzy/9BxF3iuCEs4lUMKlBIo2LQolV85p+GFp\n2rZti4EDB2KYIZeKdTpuZrRiBRAYyN1sRowAatc26Lk0Og2O3jyKPVf3YF/YPpTIXwKuNV3hWssV\nTco3gZ2i4hWWTZu4GcnJk0CZMm/cPMcmbgB4+PwhnFY4YV+/fWhaoamRIxNo3x4YMID71Vqw0KhQ\ntFnfBss6LUP32t1fu+2VK9zFCwB+/93gN8gWT6vl141t24AdOzK/Uob0hKTrSYg/E//iIyEkAUpu\nBQXrFEShOoVQoGYB5H8r/4uP3Pa5jdIlS6/VI+VWChKvJyIpPAlJ4UlIvJyI+HPxsMtvhyKNiqBw\nw8Io3rI4ijYvKqNqC3LixAm4ubnh6tWryJ1R0/kHD4DVq3mEXaYM4O4O9OkDFMz65GI96XH63mns\nvbYXe6/tRWxSLLq+3RWdanRCmyptMr300yhmzgT27QN8fYFCr19mmKMTN8ATkaYcm4LzI87LLHNj\nO3iQJ16cPQtYaBvDyKeR+GDtB5jlPAtD3s34DUZKCnfoW7YMmDGD3+jbyuzqhw+5BWeuXHyrrWRJ\n4+yXiKB5qEFiaCISriQg6VoSkm8lI/l2MlJupUCfqkfeUnmR2yE38jjkQR77PMhVLBfs8tpByavw\nv3kUUCpBn6yHPkUPfbIeungdNI81SI1KRerjVGifapGvQj4UqF4ABWoUQIHqBVCwVkEUblgY+crY\nyKUQG9aqVSsMHz4cgwcP/uebOh3g48P3oI4e5UQ9YgTQ0DQtQMNjw7H/2n4cvnEYAXcC0KhsI7Sv\n1h4dqneAUxkn84zGiQA3N+7l7eHx2heYHJ+4AZ5l7ljIEYs6LDJSVAIAX1OuXZv/+D74QO1o/uNB\n/AN8sPYDjG06FmOajslwOz8/XuJVqxbf8y1f3oxBmtjRo8BHHwEffwxMncrJ21y0cVpOvrGpSI1J\nhTZGC+0zLSfqVD1IQ9Br9LDLYwe7/C99FLJD3tJ5kad0Hv7XIY9c7rZiR48exahRo3DlyhXkunUL\nWLsW+OMPHl27ufG7yqLmGwEnpibieORxHA4/jMM3DuNZ8jO0r94eHap1gEs1F5QsaKR3tunRaHiJ\n2Acf8EzXDEjiBhCbFIt6y+thY/eNcK7ibKTIBADOdMeO8TtICxKbFItWf7RC37p9MaXllHS3efoU\nmDAB8PQEfv0V6NHDzEGakFbLVw5WrQI2bMjUhFYhjIoSEjCjQQOMzJMHjlFRnKiHDQPq11c7NADA\nzSc34RXuBa8bXjgWeQxvO7wNl6oucKnqgvcrvo98uY18VScqCmjaFJg1i281pkMSd5qD1w9i9MHR\nuDDygjr3N2xVfDzX+jx7Vt2any+JT4mHywYXtKjUAvNd5v/nPisRT9L6/HOga1fgxx+B4sVVCtYE\n7t/ngip58gAbNxo0F0YI4yICzpzhe9fbtyOqenXMvn8fC69fh10Bw0rwqkGj0+Dk3ZPwueED75ve\nCI0KRYtKLdCuWju4VHVBnVJ1jDJvAyEhPLl3/35O4q+QxP2ST/d/ihRdCtZ1W2eU/Yk048bx/Zr5\n6he8SdYmo/PmzqhavCp+7/r7f/7I7t3jJV7XrvHkMwu8wp8thw/zYObvKmjmvPvw93MAACAASURB\nVDQuBKKi+N3imjVAYiJfCh8yBFS+PJo1a4Zx48ahT58+akdpsNikWPwZ8eeLRK7RaeBS1QXtqrVD\n26ptDaujnpH9+3mZW1AQUOHf1Rslcb8kQZOARr83wvetvseAeulfohBZEBHB05Rv3XrjbElT0ug0\n6Lm9JwrmKYjNPTYjl90/WUuv51UmU6f+k9RsZYkXAKSm8vK1jRv5o1UrtSMSOYZOxw01Vq8GjhwB\nPvyQE3bLlv+agOXp6YmJEyciODgYdlY485OIcOPJDXjf8IbPTR/4RvqicvHKLy6rt6jUAgXyZPJq\nwrx5vNTDz+9fs+glcb/i/IPzaLexHYKGB6FqiapG22+O17070K4dL+VQQaouFf08+kGn12FH7x3I\nk+ufgg+XL/MSL0XhFSd16qgSosncuQP068fze9avB0qVUjsikSOEh/NEs3XreEanmxv/IhYrlu7m\nRIT33nsP3333Hbp162bmYI1Pq9fi1L1TL0bjFx9dRPMKzV9cVq/vWP/Nl9WJeDltcjKwdeuLNzqS\nuNOx6OQibAnZAv9h/v96gRfZ4OvLSfvyZbOvo9LpdRi0exDiUuKwq8+uF5NJEhN5/sfKlba3xOtv\nHh7AqFHAV18BX39te8cnLExCAtcAXrOGy3kOGsT3Zt55x6CH79mzBzNmzMDZs2eNc6/YgjxLfoZj\nkcdeJPL4lHi0rdqWR+TVXFCuSLn0H5icDDg7Ax068CVBSOJOFxGhy5YucHJ0wpz/zTHqvnMsIuDd\nd4G5c/kX0Ez0pMewvcNwP/4+9vffj/y58wMADhwAxozhLl4LF1pdSfU3ev6c2/76+nJRpnTmtwhh\nHERcyWzNGn6n2KIFj647d/5PCdI30ev1aNCgAebMmYPOnTubKGDLEPEkAj43feBz0wdHbx5FuSLl\nXozGW77VEoXyvnRb8eFD/iNesADo1UsSd0YeJzxGg98aYEP3DWhTpY3R958jrV0LbN/OZQvNQE96\njNg/AmGxYTg08BAK5imI27e5Icjly8DSpYDL66ubWqXTp3kVyQcfAL/8YhtNT4QFevCA1xKuWcNf\nu7lxGdJsvgvesWMHfvrpJ5w8edLmRt0Z0el1OPvg7IvR+LkH59C4XOMXibxB2QawOx/M1Sj//BNK\n/fqSuDPic8MHw/YOw5lPz6BMYVkzk23JycBbb3FR/Vq1TPpURITPDn6G8w/Pw2uQF/LbFcGiRTzg\n//xz4JtvuHmGLdHp+Ph++YWXz/furXZEwuZoNFzYYM0awN8f6NmTE3bz5karjqjX61GvXj0sXLgQ\n7du3N8o+rU18SjyO3zr+IpFHJUShbdW26BRVHJ0XH0bJ0FuSuF9n6rGpOH7rOI58dAS57TKopSsM\n99133PZz6VKTPQURYZz3OPjf9ofPYB9cOlMM7u48P2bJEqB6dZM9tWpu3eLBTq5cPAGtYkW1IxI2\n5e/1kRs38ptuNzdO2oVN06t88+bNWLp0Kfz9/XPMqPt17jy7A5+bPjgQdgBHQz0RN10jift1dHod\nOm/ujHql62F+O/XXIVu9+/e5M0dEhEmqmhARvvb5GkcjjmJrx6OYO80e3t7Azz9zv2xbfA3YsoWv\nInz9NS+Zl7XZwig0GmDPHl4neeUKTzJzcwNqmL4dpk6nQ506dbB8+XK0aSO3Kl+WlBSPggWLZilx\n55i5qbnscmFTj03YGboTHlcsq2ynVSpXDujUidd0GhkR4YvDX+BYhC96JRxFi0b2KFGCX3N697a9\npP30KY+yp03jwirffCNJWxhBZCQwaRJQqRKwfDkvt7h9m3u9miFpA0CuXLkwadIkzJw50yzPZ00K\nFMj6pJUck7gBwKGgA3b03gF3T3dci76mdjjWb+xYYPFiLphtJHrSY/TB0fC+EoTny47ghJc9Tpzg\nSZhm7E9gNl5eQL16fGznzgGNGqkdkbBqOh0vtejcGXjvPSApiZckHDsG9O2b6dnhxjBgwADcvn0b\nfn5+Zn9uW5VjLpW/bOXZlVgUtAhBw4NQOK9p7u3kGO+/D4wfb5TOHXrSY8CWETgSHIrCew/il3lF\n8eGHtjfCBrj0+/jxPMJevZobCQmRZU+ecCGDpUt5NvjIkdnudW1Mq1evxrZt2+Dt7a12KBYlq8vB\nctSI+2/DGw5Hs/LNMHj3YOhJr3Y41m3sWJ7+nE3xz3VoON0NHr5hGFX0MK5eKApXV9tM2r6+3DBJ\nqwUuXpSkLbLh+nXgs8+AatWAS5e4q87Jk8DQoRaTtAFg8ODBCAsLQ2BgoNqh2IQcOeIGgBRtClw2\ncDu3H9v+aLbntTmpqUDVqlxI/913M/1wImDrdi2Gew5BkTKPcHzkXtSsql4ddFNKTOTa6Tt38sRe\nG69LIUyFiJdi/vwzEBDATeZHj+Z5JxZsxYoV2LdvHw4ePKh2KBZDRtyZlC93Puzquws7ruzA2vNr\n1Q7HeuXJw7U4szDqDgwEmrfQwP3IQNR9LwYRs/fbbNIODOT3NdHRPDCSpC0yTa/nimbvvcdlhzt1\n4vWDs2dbfNIGgGHDhuHixYs4c+aM2qFYvRw74v5baFQoWv3RCjt670CrytJqKUtiYnhR9bVrQOk3\nt78LD+eRZ8CZBDi490KVivmwrffWF2VMbUlSEs8WX7+ebz8aYSqAyGm0Wm5MMWcOr7eePJkbzFth\nwfrFixfjyJEj2Lt3r9qhWAQZcWdR7VK1sanHJvTd2RfhseFqh2OdHBx4cfVvv712s5gYrrvdrBlQ\n891YVJzkgkY1y8Cj706bTNp/38uOjAQuXJCkLTJJowFWrQJq1uSJZ7/8wj2dXV2tMmkDwPDhw3H6\n9GkEBwerHYpVs86zb2Qu1VwwrfU0dN7cGVEJUWqHY53GjgWWLeMXm1ckJwM//cSFmlJTgT9P38de\n+1b4v0rNsfrD1TZXye7pU24vOngwL2Pbts2gCxFCsNRULpZSvTpPiPjjD76n7eJi9bM1CxQogPHj\nx2PWrFlqh2LVJHGnGfneSPSq3QsdN3VEXEqc2uFYn3fe4Upq27e/+JZeD2zeDNSuzf3j/fyAL2eG\no9u+FhjwzgD81O4n2Cm29Su4axf/N+TNyw1QPvxQ7YiE1dDr+V1enTrA7t2ctA8f5i4zNmTEiBHw\n9/dHSEiI2qFYrRx/j/tlRIRRnqNwNeYqDg08ZJOXb01q/35gxgxQ0Cns26/gu++AAgWAefOAVq2A\nwDuB6L6tO2Y4z8CnjT5VO1qjun+fV+VcucJXN1u0UDsiYVV8fIBvv+VL4HPnAjZeHnTu3LkIDg7G\nli1b1A5FVdLW00h0eh0G7hqIJG0SPPp42NxlXFMinR5JFd/GmGLrcSbv+5g5k+fQKAqwK3QXRhwY\ngXXd1qFTjU5qh2o0ej0n6smTuebF5Mm2161MmNDp0zxT884dnh3es6fVXw43RHx8PKpVq4YTJ06g\nlok7DFoySdxGpNFp4LrVFY6FHLHGdY3NXc41BT8/YMoUoN3VXzC4agAq/LXtxfyZRScXYX7AfOzv\nvx8NyzZUN1AjunyZV8IlJ3PyrldP7YiE1bh3D5gwgUuRTp3KjT/y5FE7KrOaNWsWwsLCsH79erVD\nUY3MKjeivLnywqOPB8JjwzHKc5RUV3uN06eBDh2Ajz7i154JocNQ6ZoP7O7dgVavxdhDY7Hy3EoE\nuAXYTNJ+/pw7eLVuzU1PAgIkaQsDJSdzkw8nJ6ByZV5C+emnOS5pA8CYMWNw8OBBhIfLap7MspkR\nNxH/TeTKxX8DxrjaFJ8Sj86bO6OafTWs6roKueykZdPfzp4FZs4Ezpzhy8Mff/xS/4IvvkBSbsKH\nTlegQMH23ttRPL/xW3+aGxHPF/rqK74FOW8e4OiodlTCahw4wOsh33mHlxtUq6Z2RKqbOnUq7t69\ni9Um6DJoDWz6UrlOB4SG8pvTmzeBGzf43/v3gbg4btgQH89Jm4hXU+TNyx9FigBlynDd/bJlucDQ\n22/zxM1atd5czjdBkwDXra4oVagU1ndbjzy5ct4745f5+/OtuEuXeNT56ac8Ae1lYacOoWSbLvhp\n02jM6LrQJuYJhIXx5LMHD3jVm41N9BWmdO8eN1q/dAlYsgRo107tiCxGbGwsatSogbNnz6Jy5cpq\nh2N2NpW4nz3je6aBgVwv//RpTrq1a/Ob1KpV+aNCBW6HWKQIf/x9tUmv5+SdksKJ/eFDfsF98ID/\nhsLCePbv9euc1OvX56IgzZpxNcHCrzQMS0pNQs/tPZE/d35s7bUVeXOZvzWemoiAI0c4Yd++zZNf\nhwwB8uX777a7Q3fj0wOf4ox3FbzVdRC/YFmx+Hi+svn779zaeMyYHHlVU2SFTsd9sKdP58kQEyfK\nzMV0TJo0CbGxsVixYoXaoZidTSTu+fMJ+/cD588DTZtyx8hmzYAmTbg4l7FptUBEBD/fyZP8RuHi\nRR6Rt2nD9Q5atuRReYo2BX139oVGp8H23ttzRDtQIl7hNXs2J7BJk4B+/YDc6QygtXotph6big0X\nN8Cjjwca39Vz/9/w8PQfYOH0emDdOr4N4OLC1SbLl1c7KmE1QkL4/lG+fFxRsHZttSOyWNHR0Xj7\n7bdx4cIFVKxYUe1wzMomEvennxK6deNJP69efjWXlBS+f3v0KC+tPH8eaNwY6NgR6OKaigVX3XH2\nwVns778fFYpWUCdIE9Nq+V7uDz/wstIpU4Du3TOusng37i4GeAxAgTwFsKH7BpQulFYmrFUrXiPV\nv7/5gjeC48eBL7/k38FFi/j8C2EQrZbLBC5YwO/2Pv7YasuTmtM333yDpKQkLF68WO1QzMomErel\nxPKy+Hh+Iff0BPbsAUqWIpTpMR+XCi7GwUH70LBcA7VDNJq4OGD1ai6JXLEiX9nr2PH1E/08wzzx\n8b6PMbbpWExoMeHfS+cOHAC+/57fCVnB2tSbN4FvvuEJd/Pm8YxxKwhbWIrQUO6DXbQo/yFVqqR2\nRFbj0aNHqF27NkJCQlDOCjqdGUtWEzeIyCI+OBTLptUS+fsTjRtHVLr1TrKbUIpcv9lLp04R6fVq\nR5d1t2/zMdnbE/XtS3Tq1Jsfk5SaROO8xlHFhRXJ75Zf+hvpdER16hD5+Bg3YCN7/Jjoyy+JHByI\nZs8mSkxUOyJhVXQ6ogULiEqWJFq+3LpfDFT0xRdf0BdffKF2GGaVlvcynS9lxJ1FRMDm46fh7tsN\neS6OhP3lSRg8MBcGDrSeVR5nz/IVPS8vHih8/jnw1ltvftzpe6cxdO9Q1HSoid+7/o6SBUtmvPHa\ntdyS0MvLaHEbS1wcsHAhT/Tt35/vZ5cpo3ZUwqo8fMgzNZ8/BzZs4FmzIkvu37+Pd955B6GhoXDM\nIesspQCLmSkKMLB1Y1wddxpOrsdQ7DMXRMbcR/PmPKlu6VIgygIbjel0wL59PI+ge3egUSO+RLxg\nwZuTdoo2BZOPTkaXLV3wXcvv4NHH4/VJGwAGDOCJOhbUxi8piY+3Rg2enHj6NLB4sSRtkUmenkCD\nBjyD9vhxSdrZVK5cOQwYMAALFixQOxSLJyNuI9DpdZjjNwfLzizD753XINfNjti4ETh4kOdnffQR\n0KVL+sunzCU6mm+7rVjBRUO++ILLIhu6tCnobhCG7x+OaiWqYUWXFShTOBNZbt48nq6/cWPWgjcS\njYZnis+YwW9YZs3iWhhCZEpKCk+G2LOHf6dlUb/R3LlzB05OTggLC0PJkm8YFNgAs9/jBmAPwAdA\nGABvAMUz2C4SwEUA5wGces3+THAHwbxORJ6gigsr0peHv6QETQLFxRGtXUvk7Mz3T93diQIDzXsL\n7NQpoo8+IipenGjoUKLTpzP3+IfxD2nonqFU9qeytPHCRtJnJfinT/kGemRk5h9rBImJRL/+SlSx\nIlHbtnwOhMiSiAii994j6tGDKDZW7Whs0ogRI2jChAlqh2EWyOI97uwk7nkAvkn7fAKAHzPYLgKA\nvQH7M9X/jVlFJ0RTv539qNov1ejPm3+++H5kJNGsWUQ1ahC9/TZ/bqo8lpRE9McfRI0bE1WuTDR3\nLlFUVOb2odFqaEHAAnKY60DjvcbTs+Rn2Qtq/HgiM088efaM6IcfiBwdiVxdiYKCzPr0wtZ4ehKV\nLk20cKFMQDOh27dvU4kSJejRo0dqh2JyaiTuqwAc0z4vA+BqBttFAHAwYH+m+r9Rxb6r+6jCwgo0\nwGMA3X1298X39Xoe8bm78yjc2ZlH5XFx2X/Oq1eJvvmGqFQpovbtifbt45nwmaHVaWnLpS1Uc3FN\nar+hPYVGhWY/MCKiO3eISpQwyyglKopoyhT+/x0wgOjiRZM/pbBlWi3R5MlE5csT+WWwgkIY1Wef\nfUZfffWV2mGYnBqJ+8lLnysvf/3KdjfTLpOfAfDJa/Znsv8ctcSnxNPko5PJYa4Dff/n9/8ZtSYn\nE+3cSfThh0TFihENGkTk7Z25ZBsXR7RqFdH77/PIcvx4omvXMh/r3wm79pLa1GxVM/IK98raZfHX\n+egjXm9lIpcuEX3yCd8WGD6c6Pp1kz2VyCliYohcXIjatCF6+FDtaHKMe/fuUYkSJejevXtqh2JS\nWU3cr52cpiiKT9po+lWTAawjohIvbRtLRPbp7KMsET1QFKVU2j3xMUTkl852NHXq1Bdft27dGq1b\nt84wNmsS8SQC045Pw6Hrh/Blsy/h3tj9P92yoqKALVuA9et5hcmgQTyprU6d/+6PiGu5r1nD82Na\ntwbc3LhYSmbraCdoErA1ZCsWBC5AsfzFML31dLhUdYFiisojly5xg4WICKPVbNbpeHLvL79w/YuR\nI4ERI6RrlzCCK1cAV1fgww+BuXOtsnSvNfvqq6+g1Wrx66+/qh2K0fj6+sLX1/fF19OnTweZeXLa\nVQBl0j4viwwulb/ymKkAxmXwM+O/nbEwIY9CaNCuQWQ/156+OvwVhUWHpb9dCF/yLleOqFEjnlj1\n+DFfbZ41i6haNa5r8tNPWR8EhDwKoTEHx5D9XHvqurmraUbY6enYkej337O9m4gIou+/J6pQgahJ\nE6KNG4lSUrIfnhBERLR/PxdU+eMPtSPJsR4+fEglSpSg27dvqx2KycDcBVgURZkHIIaI5iqK8i14\nVvm3r2xTEEAuIopXFKUQePb5dCLyTmd/lNVYrM2tp7ew5NQSrLuwDvUd62NQ/UHoVqvbf0bhOh1w\n+DDw44/cBEVReOXJpEncBCWzg+LrMdex99pe7L66GxFPIjC84XAMbzgclYqZsTTj8ePA8OHA1avc\nhzUTEhO56cmaNVw8ZsAALgXt5GSiWEXOQ8Sj68WLAQ8PXqMtVDNhwgTExcVh+fLlaodiEmavVa4o\nij2A7QAqgZd89SGip4qilAOwkog6K4pSFcCutIfkBrCJiH7IYH85JnH/LUWbgr3X9mJryFYcjTiK\npuWbomP1jvhf1f9Bc68u1q3NhS1bODH1788dqw4cAHx9+fWke3e+kpdRad/4lHgE3QvCkZtHsO/a\nPjxJfoIP3/4QrrVc4VLVRZ3e4kRAixbcH7NfvzdurtEA3t58G8HTkzvFDR3Kx65WIxphozQabjAf\nEgLs3Svt4CxAdHQ0atasabP9uqXJiJWLS4nDngtHseLoIZyLOQ5Nvod4K08jtKxVF02q1kLFYhVR\nvkh5lChQAkpqYZzwzYMDB/TwOZaCSjWfoJlzDCrVuw0qFokr0Zdx6dElRD6NRIOyDdCyUkt8WPND\nNC7f+N9NQNRy8CA39b5wId3LBs+ecbLev583rVWL37j07g2ULq1CvML2PX0K9OjBDUI2bQIKFVI7\nIpFmypQpePjwIVatWqV2KEYnidtK6XScpNas4TainTvzRLP6TWNw/tFZXIm6gtCoUNyNv4v78ffx\nLPkZ4jXx0Oq1sFPskMcuD/Lp7ZEaZ4/n9ypCG/MW6perjQ4N6qN/2zp4u2o+y+twRcSlImfNArp0\ngU7HhdWOHeNEfeoUD8q7dAG6duVOZUKYTGQk0KkT0L49t+TM5C0cYVpPnjxBjRo1cPLkSVSvXl3t\ncIxKEreVuX6d+2+sX8+Xut3c+Mpx8eJvfuzr3L7NbwC8vYETJ7gV8PvvA//3f0Dz5kD9+upfYn7+\nHLi7cDuKrvkZ7vUDcMJPQZkyPDu+fXugbVugcGF1YxQ5xOnTfL9p4kS+fSMs0vTp03Hjxg2sX79e\n7VCMShK3FXj+HNixgxP2tWu85GvYMNPVyybilVd//QUEBACBgfy8lStzAndyAmrX5t4IVarwVUJj\nSkoCbtwAwsP5jcqFC8C5czzAqV9Xh73X6+DK5ytQe5SzNPgQ5ufjAwwcCKxaxUu+hMV69uwZqlev\nDj8/P9SqVUvtcIxGEreFIuLEuXYtsGsXzwp3c+Mrc3nzmj8ejYYndF+4wB9hYZzcb94EChbkDmGl\nSwOlSgElS/K/hQtzrPny8b+5cnGfheTkfz6ePAEePwYePeJ/79/ntemVK3MXrurVgXr1gIYNgbp1\n09abr10LbN7ML6BCmNOOHcBnn/HM8RYt1I5GGGDOnDm4dOkStmzZonYoRiOJ28Lcv8+Xwdes4UTn\n5gYMHmy5rSOJOOFGRnLCjY7mf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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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MOu/rTHq6xpQpakmOJGpjWDtZA1z2Kwi7FxICy5bB9ddD69bqEkIIO1GZV0nc2DiiPonC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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
long term trend.timescale 10.0 +ve
short term trend.variance 1.0 +ve
short term trend.timescale 2.0 +ve
" ], "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": {} } ] }