{ "metadata": { "name": "", "signature": "sha256:d132a55f4fd06bd9bcfd3fce4e6a16df11818a010d327f7ad0a80eff9c24a96d" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Inroduction to Gaussian Processes\n", "\n", "## Machine Learning Summer School, Sydney, Australia\n", "### 23rd February 2015\n", "### Neil D. Lawrence\n", "\n", "When we form a Gaussian process we assume data is *jointly Gaussian* with a particular mean and covariance,\n", "$$\n", "\\mathbf{y}|\\mathbf{X} \\sim \\mathcal{N}(\\mathbf{m}(\\mathbf{X}), \\mathbf{K}(\\mathbf{X})),\n", "$$\n", "where the conditioning is on the inputs $\\mathbf{X}$ which are used for computing the mean and covariance. For this reason they are known as mean and covariance functions.\n" ] }, { "cell_type": "code", "collapsed": false, "input": [ "%matplotlib inline\n", "import numpy as np\n", "import scipy as sp\n", "import matplotlib.pyplot as plt\n", "import pods" ], "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__.py, 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": [ "## Marginal Likelihood\n", "\n", "To understand the Gaussian process we're going to build on our understanding of the marginal likelihood for Bayesian regression. In the session on [Bayesian regression](./week7.ipynb) we sampled directly from the weight vector, $\\mathbf{w}$ and applied it to the basis matrix $\\boldsymbol{\\Phi}$ to obtain a sample from the prior and a sample from the posterior. It is often helpful to think of modeling techniques as *generative* models. To give some thought as to what the process for obtaining data from the model is. From the perspective of Gaussian processes, we want to start by thinking of basis function models, where the parameters are sampled from a prior, but move to thinking about sampling from the marginal likelihood directly.\n", "\n", "## Sampling from the Prior\n", "\n", "The first thing we'll do is to set up the parameters of the model, these include the parameters of the prior, the parameters of the basis functions and the noise level. " ] }, { "cell_type": "code", "collapsed": false, "input": [ "# set prior variance on w\n", "alpha = 4.\n", "# set the order of the polynomial basis set\n", "degree = 5\n", "# set the noise variance\n", "sigma2 = 0.01" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 2 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now we have the variance, we can sample from the prior distribution to see what form we are imposing on the functions *a priori*. \n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's now compute a range of values to make predictions at, spanning the *new* space of inputs," ] }, { "cell_type": "code", "collapsed": false, "input": [ "def polynomial(x, degree, loc, scale):\n", " degrees = np.arange(degree+1)\n", " return ((x-loc)/scale)**degrees" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 3 }, { "cell_type": "markdown", "metadata": {}, "source": [ "now let's build the basis matrices. First we load in the data\n" ] }, { "cell_type": "code", "collapsed": false, "input": [ "data = pods.datasets.olympic_marathon_men()\n", "x = data['X']\n", "y = data['Y']" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 4 }, { "cell_type": "code", "collapsed": false, "input": [ "plt.plot(x, y, 'rx')" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 7, "text": [ "[]" ] }, { "metadata": {}, "output_type": "display_data", "png": "iVBORw0KGgoAAAANSUhEUgAAAXwAAAEACAYAAACwB81wAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n", "text": [ "" ] } ], "prompt_number": 7 }, { "cell_type": "code", "collapsed": false, "input": [ "scale = np.max(x) - np.min(x)\n", "loc = np.min(x) + 0.5*scale\n", "\n", "num_data = x.shape[0]\n", "num_pred_data = 100 # how many points to use for plotting predictions\n", "x_pred = np.linspace(1880, 2030, num_pred_data)[:, None] # input locations for predictions\n", "Phi_pred = polynomial(x_pred, degree=degree, loc=loc, scale=scale)\n", "Phi = polynomial(x, degree=degree, loc=loc, scale=scale)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 13 }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Weight Space View\n", "\n", "To generate typical functional predictions from the model, we need a set of model parameters. We assume that the parameters are drawn independently from a Gaussian density,\n", "$$\n", "\\mathbf{w} \\sim \\mathcal{N}(\\mathbf{0}, \\alpha\\mathbf{I}),\n", "$$\n", "then we can combine this with the definition of our prediction function $f(\\mathbf{x})$,\n", "$$\n", "f(\\mathbf{x}) = \\mathbf{w}^\\top \\boldsymbol{\\phi}(\\mathbf{x}).\n", "$$\n", "We can now sample from the prior density to obtain a vector $\\mathbf{w}$ using the function `np.random.normal` and combine these parameters with our basis to create some samples of what $f(\\mathbf{x})$ looks like," ] }, { "cell_type": "code", "collapsed": false, "input": [ "num_samples = 10\n", "K = degree+1\n", "for i in xrange(num_samples):\n", " z_vec = np.random.normal(size=(K, 1))\n", " w_sample = z_vec*np.sqrt(alpha)\n", " f_sample = np.dot(Phi_pred,w_sample)\n", " plt.plot(x_pred, f_sample)\n" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": "iVBORw0KGgoAAAANSUhEUgAAAXoAAAEACAYAAAC9Gb03AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nFXoRkRz3X7a2o5nNYIsaAAAAAElFTkSuQmCC\n", "text": [ "" ] } ], "prompt_number": 14 }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Function Space View\n", "\n", "The process we have used to generate the samples is a two stage process. To obtain each function, we first generated a sample from the prior,\n", "$$\n", "\\mathbf{w} \\sim \\mathcal{N}(\\mathbf{0}, \\alpha \\mathbf{I})\n", "$$\n", "then if we compose our basis matrix, $\\boldsymbol{\\Phi}$ from the basis functions associated with each row then we get,\n", "$$\n", "\\mathbf{\\Phi} = \\begin{bmatrix}\\boldsymbol{\\phi}(\\mathbf{x}_1) \\\\ \\vdots \\\\ \\boldsymbol{\\phi}(\\mathbf{x}_n)\\end{bmatrix}\n", "$$\n", "then we can write down the vector of function values, as evaluated at\n", "$$\n", "\\mathbf{f} = \\begin{bmatrix} f_1 \\\\ \\vdots \\\\ f_n\\end{bmatrix}\n", "$$\n", "in the form\n", "$$\n", "\\mathbf{f} = \\boldsymbol{\\Phi} \\mathbf{w}.\n", "$$\n", "\n", "Now we can use standard properties of multivariate Gaussians to write down the probability density that is implied over $\\mathbf{f}$. In particular we know that if $\\mathbf{w}$ is sampled from a multivariate normal (or multivariate Gaussian) with covariance $\\alpha \\mathbf{I}$ and zero mean, then assuming that $\\boldsymbol{\\Phi}$ is a deterministic matrix (i.e. it is not sampled from a probability density) then the vector $\\mathbf{f}$ will also be distributed according to a zero mean multivariate normal as follows,\n", "$$\n", "\\mathbf{f} \\sim \\mathcal{N}(\\mathbf{0},\\alpha \\boldsymbol{\\Phi} \\boldsymbol{\\Phi}^\\top).\n", "$$\n", "\n", "The question now is, what happens if we sample $\\mathbf{f}$ directly from this density, rather than first sampling $\\mathbf{w}$ and then multiplying by $\\boldsymbol{\\Phi}$. Let's try this. First of all we define the covariance as\n", "$$\n", "\\mathbf{K} = \\alpha \\boldsymbol{\\Phi}\\boldsymbol{\\Phi}^\\top.\n", "$$" ] }, { "cell_type": "code", "collapsed": false, "input": [ "K = alpha*np.dot(Phi_pred, Phi_pred.T)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 15 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now we can use the `np.random.multivariate_normal` command for sampling from a multivariate normal with covariance given by $\\mathbf{K}$ and zero mean," ] }, { "cell_type": "code", "collapsed": false, "input": [ "for i in np.arange(10):\n", " f_sample = np.random.multivariate_normal(mean=np.zeros(x_pred.size), \n", " cov=K)\n", " plt.plot(x_pred.flatten(), f_sample.flatten())" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": "iVBORw0KGgoAAAANSUhEUgAAAXoAAAEACAYAAAC9Gb03AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAALEgAACxIB0t1+/AAAIABJREFUeJzsvXd4XFed//+6UzV9VEbNklxkufduy06chASnkQ1ZSGgJ\nBLLwCwvZDSwskCUEWBYC+92EBQIEshASQklISMApxrET995tyUWy1aWRNJre5/7+OJrRuIQ48aj6\nvJ7n85w7kp65Z2Trfc79nE9RVFVFIpFIJGMXzXBPQCKRSCSDixR6iUQiGeNIoZdIJJIxjhR6iUQi\nGeNIoZdIJJIxjhR6iUQiGePocvEmiqKcBnxAEoirqrokF+8rkUgkkksnJ0IPqMBqVVV7c/R+EolE\nIskRuXTdKDl8L4lEIpHkiFwJvQr8TVGU3Yqi3JOj95RIJBJJDsiV66ZWVdV2RVFcwDpFUepUVd2U\no/eWSCQSySWQE6FXVbW9f3QrivI8sATYBKAoiiymI5FIJO8CVVVz4hK/ZNeNoihmRVFs/dcW4Drg\nUPbPqKo64u3BBx8c9jnIecp5jtY5ynnm3nJJLnb0JcDziqKk3+9pVVVfy8H7SiQSiSQHXLLQq6ra\nCMzLwVwkEolEMgjIzNh+Vq9ePdxTuCjkPHPLaJjnaJgjyHmOZJRc+4LOu4GiqIN9D4lEIhlrKIqC\nOlIOYyUSiUQyspFCL5FIJGMcKfQSiUQyxpFCL5FIJGMcKfQSiUQyxpFCL5FIJGMcKfQSiUQyxpFC\nL5FIJGMcKfQSiUQyxpFCL5FIJGMcKfQSiUQyxhkaoQ+Hh+Q2EolEIjmfoRH6z3wGZGEziUQiGRaG\nRuj374cf/WhIbiWRSCSSs8lJmWJFUbTAbqBFVdWbz/meqp48CStWwLPPwqpVl3w/iUQiGeuMxDLF\n9wFHgQuvGtXV8Otfw+23Q3Nzjm4pkUgkkoshF83BK4AbgF8Ab736rFkD//Iv8A//AKHQpd5WIpFI\nJBdJLnb0/wP8G5B625/8t3+D6dPh7rvl4axEIpEMEZfUHFxRlJuALlVV9ymKsvqtfu4b3/hG5nr1\nxz7G6gcegO9+F77ylUu5vUQikYwZNm7cyMaNGwflvS/pMFZRlO8AHwMSQB5gB55TVfXOrJ85v2ds\nayssXSoicf7hH971/SUSiWSsksvD2Jw1B1cU5UrgixeMurnQPXbtghtugNdeg/nzczIHiUQiGSuM\nxKibNBe/aixeDI89BrfcAm1tOZ6GRCKRSNLkbEf/ljd4qx19mu98B55/Ht54A8zmQZ2LRCKRjBZG\npOvmLW/wdkKvqvDxj4PPJxKqtNpBnY9EIpGMBkay6+adoyjw+OPg9cIXvjDcs5FIJJIxx/ALPYDB\nAH/6E6xbB48+OtyzkUgkkjHFJcXR5xSnE9auFTVxqqrg1luHe0YSiUQyJhg5Qg8wfjy89JIol+By\nwcqVwz0jiUQiGfWMDNdNNgsWwNNPw223wZEjwz0biUQiGfUMf9TNW/HUU/C1r8GWLVBRkfuJSSSS\nd42qqsRTcRKpBPGkGJNqkmQqSVJNklJTZP/dK4qCgoJG0aDVaNEqWnQaHQatAYPWgE6jQ1FyEmAy\nZshl1M3Ict1k89GPQkcHvPe98OabUFg43DOSSEYViVQCX9SHN+LFF/WdZf6YH3/UTyAWyFgwHiQU\nD2XGcDxMKB4ikohkLJqMEkvGiCVjaBVtRqR1Gl1GwLUaLRpFg4KSFitUVFRVJaWmMgtCIpUgnooT\nS8ZIpBIYtUbydHnk6fIw680Zsxqs2I12bEYbdoMdZ54zY4XmQgpMBRSZiyi2FFNoKkSrkSHa5zJy\nd/RpvvxlkUz1t7+B1Zq7iUkko4CUmsIb8dIT7qEn1ENvuPc880Q8eCIe+iJ99EX68ITFdTgRxmaw\n4chz4DA6cOQ5hGAabNgMNqwGKzajGC16ixgNFsx6MyadKSO0afHN0+Vh1Bkxao3otXo0Su48vyk1\nRSwZI5KIEI6HCSfCBGNBgvEggVgAf9SPP+bPLFx9kT48EU/m99Id6sYdcuMJeygwFVBqLaXMVkaZ\ntYxxtnFUOiqpsFdQ5ahignMCdqM9Z3MfLMZWwtTboapwzz3Q1CQOao3G3E1OIhligrEg7pAbd9BN\nV7ArI1Ddoe7zrCfcgyfswWqwUmgupNAkdq9py8/LF6MpP3Od3uk68hxYDdacivFoIJFK0B3qpiPQ\nQbu/nfZAOy2+Flp8LTT7mmnyNnG67zR5ujwmOidSXVDN5PzJTC6YzLSiaUwrmka+KX+4PwZwuQk9\nQCIhulNpNPDMM6AbuR4nyeVFLBnDHXTTGeykK9h1QXOHhKi7g25UVIotxbjMLlwWFy6ziyJz0XlW\naCqkyFxEgakAvVY/3B9zTKGqKu6Qm0ZPIyd7T3LKc4rjPcep76mnrrsOs97MTNdMZhXPYlbxLOaW\nzGV2yWzM+qEt0XL5CT1ANArvex+UlcETTwjRl0gGgWAsSGewk85AZ0bAz7rO+l4gFsBldlFsKabY\nUkyJtUSIuNlFibUkI+rFlmJcFhcWvUUeOo5gVFWlzd/GEfcRDncd5lDXIQ50HKCuu47xzvEsKFvA\n4vLFLCpfxIKyBYMq/pen0INoQbhmDcyeLWrZyz8YyUWgqir+mD8jzueN53wtqSYpsZRQYi2hxCLE\nOv06+7rEUkK+Kf+yc49cjsSTcY51H2NP2x52t+1mV9sujriPMK1oGssrlnPb9Nu4auJVOb3n5Sv0\nIIqfXXMNXHUVfO97UuwvU1JqCk/Yc+Ed9wUEXKtoM+KcGbOvs0abwSZ33ZK3JZKIsLd9L9uatzHB\nOYHbZtyW0/e/vIUeoLdXCP3NN8O3viXFfowQSUQG/Nr9h5VpV8m51+6gG4vBcv5OO70DP0fALQbL\ncH88ieQdIYUewO0WYv+BD8CDD+b+/SWXTCgewh10ZyJL3EH3WeO5B5XRZDTj6z7L720pwWVxZUQ8\nbUadjMCSjF1GTMKUoih5wBuAETAAf1ZVdWg6frtcsH49rF4tonC+9rUhue3lSigeoifUk4lbzo5f\n7g510x3upifUc1aoYDKVzESWZEeYuMwuJuVPynwtfYBpN9qly0QiGQQueUevKIpZVdWQoig6YDOi\nb+zmrO8Pzo4+TXu72Nl/9KPwwAODd58xQDKVxBf1iQSbsOesMZN8E/bQGxHX6QSdnnAPqqpmYrkL\nzSL0r8hUNHDdHxLosgyEC8oIE4nk3TNidvQAqqqG+i8NgBbovdT3fEeUlcGGDXD11ZBMjlk3TiwZ\nE6nrWRmCaUunuHujXrwRL96oyBxMj32RPrwRL4FYAJvRhjPPSX5efibRJp1sU2AqoDq/OpNWXmAq\nyAj7UMcQSySS3HHJQq8oigbYC1QDj6mqevTcn3F930V+Xn4mY89hFGYz2jIp2VaDNWNmvfmsVOw8\nXR4mvRiNWiNGnfHskLayMti4cUDsH3poSA5ok6kksWSMaDJKNBE9a8yuD5JO6U7XDgknxBiKhwjG\nRF2RQDxwVsp3tvmjfoCzfl92o/2s+h/p32tNYU0m3d1hdJBv6v+9939NhgJKJJcfudjRp4B5iqI4\ngFcVRVmtqurG7J/5uOfjhBNhIokIUxdOZfzM8Xgj3kxhpY5Ax1kClxbBtJ1bVCmaiKLViIJKeo0+\nU1ip5HaFZ376Xd7c+r/8v1uK0Wp1aBTNWQWW0mP/3MWIKLaUtnQFvvSYSCUyVfriqXhmVFUVo86I\nXqPP1AAx6oyZxSl9nV6k0guXSWfCYhC1RUosJZmFzaK3YDFYMgtf+tpmtGHQGi71n0oikYxgNm7c\nyMaNGwflvXMadaMoyn8AYVVVf5D1tZz76NMlUtOCm65+l0glSLq7KPvHjxNaNJe2b3+ZlEKmal66\ngh4Icc8W/fSCoFE0mQp86VKq6cp8eo0evVafGXUaWYpBIpEMDiMmvFJRlCIgoapqn6IoJuBV4CFV\nVddn/czgHsZeCK8XbrwRpkwRjce1smypRCIZXeRS6C/VYVsGvK4oyn5gB/BStsgPGw4HvPoqNDfD\nhz4Esdhwz0gikUiGjdGbMHUxRCLw4Q9DMAjPPSfr2UskklHDSNrRj2zy8uAPfxCtCK+9VpROkEgk\nksuMsS30ILJmf/ELWLkSVq0S7hyJRCK5jLg8wkYUBb7/fSgthdpaePllmDlzuGclkUgkQ8LlIfRp\nvvAFkVx19dXw7LNihy+RSCRjnLHvujmXD38Ynn4abrsNfv/74Z6NRCKRDDpjO+rm73HggKhn/9nP\nwpe+JGvaSySSEcWISZi6qBuMVKEHaGkRiVXLlonWhHrZhFkikYwMZHhlrqiogE2boKlJCH5f33DP\nSCKRSHLO5S30AHY7vPQSTJ8Oy5fDqVPDPSOJRCLJKVLoQcTaP/oofO5zIvxyw4bhnpFEIpHkDCn0\n2dx7r4jIueMO+MlPYKSeLUgkEsk74PI+jH0rTp2CW24Ru/v//V8wyFrwEolkaJFRN0OB3w8f+xh0\ndYnkqvLy4Z6RRCL5OyQSEA5DKATRqLBYTHw9kRDN50BEUisKaDQi0E6vB6MRTCYwm4XpRkAqqRT6\noSKVgu98Bx57DH73O5lJK5EMMskkdHeL/VVXF7jd4nVPjzCPRwTH9fWJthN+P/h8EAgIMTebhWAb\njcIMBiHkWu1AW4q0HCWTEI8Li0bFIpFeKAwGEadht0NBARQVQWEhlJSISiqlpSJor6oKxo0bnMhs\nKfRDzcsvw8c/Dl/9Knz+8zK5SiJ5h6iqEOrmZpG+0toqrK1NWHs7dHSIn3E6haC6XMLSIltYCPn5\nwpzOASG22YQZjbn501RVIfg+n1hM0otMegFqbxfW2gpnzkBnp6iu8l//den3zkYK/XDQ0AD/+I8w\nebKohmm3D/eMJJIRQzIpBPv0aWhsFAKYtqYmIfB5eWIXXFkpdsHjxgmPaHm5KEFVViaEfSS4Td4J\n8bhofWGz5fZ9R5TQK4pSCTwJFAMq8HNVVX+Y9X119+7dLFy48JLuMyKIROC++0T45XPPwezZwz0j\niWTICAREnEK2NTQIYW9uFjvuCRMGbPx4YVVVQtxl3593xkgT+lKgVFXV/YqiWIE9wD+oqnqs//tq\nUVERDz74IJ/97GczzbhHNb/5Ddx/v/Dff+pT0pUjGTP4/XDixICdPDlgPh9MmiQeaidNElZdLcbx\n48WOXZI7RpTQn/eGivIC8L/p3rGKoqgnTpzggx/8IJMmTeLxxx8nPz8/p/ccFo4dg9tvhxkz4Oc/\nl64cyaghFhO78ePHzzevVwh5Tc2AVVeLsaxMRKpIhoYRK/SKokwA3gBmqqoa6P+aqqoqkUiEf/u3\nf+Oll17i6aefpra2Nmf3HTbCYfjXf4V16+C3v4WlS4d7RhIJIA4UOzuhrg7q68+2lhbhSpkyBaZO\nFWPaysulmI8URqTQ97ttNgLfVlX1hayvqw8++GDm5wwGAz/84Q+59957+epXv4putJ28XIjnnhNZ\ntZ//PPz7vw/EcUkkg0w0Ktwq9fVC1NNWXy9CBKdOPd8mTZI5gCORjRs3snHjxszrhx56aGQJvaIo\neuAvwMuqqj5yzvfOi7ppa2vjzjvvJBQK8Zvf/Ibq6upLnsOw09IiEqxSKXjySeG0lEhyRHf3+UJe\nVycOQcePh2nThIhPmzZwXVg43LOWXAojakeviNPVXwM9qqr+6wW+f8HwylQqxaOPPsp3vvMdvvvd\n73L33XeP/oPaZBL++7/hBz8QPWrvvFMe1EoumkRCRLGkXSzZwp5MXljMq6vl7nysMtKEfiXwJnAQ\nEV4J8BVVVV/p//7fjaM/fPgwH/3oR6mqquJnP/sZZWVllzSfEcGBA2J3P3ky/PSnUFw83DOSjCB6\ne88W8/TY2Ch85BcS9JISuWe43BhRQv+2N7iIhKlYLMY3v/lNHn/8cR555BHuuOOO0b+7j0bh61+H\nX/9aFEb7wAeGe0aSISQWO3t3nm3R6Nk+87SgT54s0vclEhiDQp9m165d3HXXXUybNo0f//jHY2N3\nv22bKJ8wb55oV+hyDfeMJDkilRJp8BcKU2xuFpEt6aiWbGEvLZW7c8nbM2aFHiASifCtb32Lxx9/\nnIcffpi77rpr9O/uw2H4j/+Ap56C//kfUe9+tH+mywRVFTVYspOITpwQYn7qlKi5kg5NrKkZEHYZ\n2SK5VMa00KfZt28fd999Ny6Xi8cee2xsRObs3Amf/KQIk3jsMbHlkww76Z35yZNCvLOzQU+eFO6U\n7ASimhoh5pMn576+iUSS5rIQeoB4PM7//M//8PDDD/PFL36RL3zhC+gHox7oUBKLwXe/Cz/8odjl\n//M/y7j7ISAcFoedDQ3Csuu1nD4tKiJWVwvxnjx5IBt08mRwOIZ79pLLkctG6NM0NjZy77330tLS\nwk9+8hNWjYW68PX18JnPiOIiP/sZjIWib8NIIiFSGRobL2wej3iQmjQJJk4UQp6u0zJpElgsQzfX\neDJOKB4iFA8RToQJx8NEEhGiySjRRJRoMkosGSOejJNIJYin4iRTSZJqkmQqSUpNkVJTqJz/d6VR\nNBnTaXRoFS06jQ6D1oBeq8egNWDQGjBqjRh1RvJ0eZh0JvJ0eZj1ZiwGCwat9DldLPFUit1+P3pF\nYVGOy6CMOqHfu1dlzpxL27iqqsqzzz7L/fffz9VXX83DDz9MSUlJ7iY6HKiqiMr593+H226Db39b\nbC0l5xGNigPO7PK3aWtsFPXBi4uFiGdbWthzkdqvqiqheIiecA+94V56w714wh48EQ+esIe+SB/e\nqBdv1Isv6sMf9Ysx5icYCxKIBQjGgwCY9WZMOhNmvZk8XR55ujyMOmNGgA1aA3qNHr1Wf5ZgaxQN\nWkWLoigoKGedX6mqiopKSk2RSCUyC0N6sYglYxlLLyiRRIRwPJxZcNLzs+gt2Iw2rAYrNoMNu9GO\n3WjHkefAYXTgzHPizHNSYCrIWKGpkCJzEfmmfDTK2KyjEO0X9jf6+nijr49tPh+TTSY+P24cH89x\n8MioE/rp01VaW0UpmGx7NwEofr+fb37zm/zqV7/igQce4N577x397pzeXvja1+CFF4Rb52Mfu6wK\njiSToi5Lc/OApWuYp8feXlG/PF32NrsM7oQJ4rjj3Rx+JlNJuoJdtAfa6Qh00BnopDPYSWegk65Q\nF+6gG3fITXeom+5QNwoKhebCjLjl5+WTn5efEb60EKaF0Wa0YTPYsBltWPSWUbFjjiVjBGNB/DE/\ngVggs2j5Y36xmEW89EX6xAIX8WQWvZ5QD92hbnxRHwWmAootxbgsLkosJZRaSzNWbivPWH5e/ogO\ntggkEmz3+djk9fKm18tuv5+pJhNXOJ1c6XRyhcOBLayQ8CTIG5/b8p2jTujVf/5nfPOvZJv+CjbV\nF7NjB+zaJXyfCxYIr8W8eTBnjviDvZh/96NHj/Iv//IvtLa28sgjj3DttdcO6ucYEnbtgs9+Voj8\n//4vLF483DO6ZILBgS5C6Y5Cra3CzZLuNNTRIdL1000p0lZVNWAlJe/8iTCaiNLia6HJ20SLr2XA\n/C20+dto9bXiDrnJz8unzFZGmbWMEmsJJRZhxZbijFi5zC4KzYWY9ebB+UWNIRKpBD2hHrqCXRnr\nCHTQEeigPdBOe6A98/uPJWNU2CsYZx9HlaOK8Y7xVDmqmOCcwATnBKocVUO6MHZEo2zx+djs9bLZ\n6+VoMMh8q5VVTierHA5qHQ4cWfW5QidCHL7lMCUfLWH8V3Nb9mT0Cf33vgdvvAFbtojn65UrSS2v\npbliOdv7prFnn4aDB0VCaSQCM2eK6r8zZgxkBlZVnf+HrqoqL774Ivfffz8zZszg+9//PtOmTRvU\nzzPopGvlfOUrsGaNqHk/wvIJkknRWq2zU4h0euzoGGgLl7ZYbKCLUHZXoYoKYenX72Y3HklEON13\nmkZPoxj7GjnjPcPpvtOc6TuDJ+Kh3FZOpb2SKkcVFfYKISq2cYyzj6PcVk6JpQS9dpQ/EY5iArEA\nLb4Wmr3NNPuaafI2ccZ7hjN9Z2jsa6TN30aJpYTqgmomOScxuWAyNYU11BTUUFNYc0kLb0pVORoM\nstXnY4vXyxavl95EguV2O6scDlY6HCyy2ch7ix1Gzys91N1Vx8RvTqT80+Xveh5vxegT+uxuvEeO\nCMHfvBl27BDVmhYvFrZoEd0TFnHYW8nRYwpHj4rU8OPHRZPg9CFa2u+afnQvKYnyzDM/4nvf+y53\n3HEHX//613GN9sQkn0/47H/5S1EK+f77RefjQSCREK6R7u4Bc7vPt85O0TOzp0c8jZWWDjRLLisT\n1+mWcGlzOi8tZSAQC3Cy9yQnek5wsvckpzynMmNXsItKeyWT8icx0Tkxswsc7xzPeMd4Sq2laDUy\nomk0k0glaPY2c8pzilO94t/+RO8JTvSeoMHTQLGlmGlF05hWOI0ZrhkZKzSfX9HNn0iw0+9nq9fL\nVp+P7T4fRXo9K+x2avt369PNZjRv8x9WTak0f7+ZlkdbmPGHGThXOgfls49eob8QbreIL9+9W9iu\nXWJBmD9f+HPmz4c5cwhVTOFUkz4THtfQcPaBXDQKpaXdxGIP0d39DAsX/gvXX/+vVFZaKCo6u8mw\n3T6KXOANDfDlL4tF8dvfho985LxHG1UVnevTzYzTo9crok36+sSYbb29wnp6RIu4/PyB30/6d1VU\nJB7A0k2aS0qEFRXltut9Sk3R5G3imPsY9T311HXXUd9Tz/Ge4/SGe5lcMFns5ApqmFwwmer8aqoL\nqqm0V0ohv4xJppKc8Z6hrruOY+5jHOs+xlH3UY64j2DWm5lcNBObfTJR8yRa9RU0aUpYYM9nhcPB\nCrud5Q4HJe/wUTLuiVP38TpinTFm/nEmeZWD11ZrbAn9uaiqeObft0/YwYPCmppEYPPMmQM2fbrY\n3uv1BIMDvt/9+0/ym9/8BydOvMHMmQ/gdH6Knh4D3d1C5IJBsdN0OAbGdCd5m02E2pnNwkwmYXl5\nosu8Xi/cDHq9aGKs1YpRoxGWvRlQVWGplLBkUuyeEwnRUDgeF66NWEwsVGmLRETcdyQiBDwUgsqm\nLXxo/5cwxAL8sPx7rNO8F39AIRAQEZpGo1jA7HbxedKWny8+o9MprgsKBsa0OZ1Ds/AlU0kaPA0c\ncR/J/EEedR/leM9x8vPyxc6saBpTC6cytWgqUwunUumoHLMRHJLcEU2l2Ov3Z1wwW7pOkAg0UJ5o\nwRA6jaevjk5fE9OKprGgbAELyhawqHwRc0vmYtQZL+oe/r1+jnzgCIU3F1L9cDWasB82b8a/bh29\n5eWM/9KXcvqZxrbQvxWhEBw9Klw/aaurE+o+adJADno6ZbG6mj2dnTzw9a9TV1fHN77xDT760Y+i\n1WqJx4Xgp3e9Xq8Qy7SFQmIxCAaF2KaFNy3KaYHOFu5sQc8W++wFQKcbWBz0+oFFw2AQQp0esxeX\n7AXHalEZv+8FJj/xFVIlZQS+8h0MVy7Has3tDvtSUVWV9kA7BzsPcqjzEIe6DnG46zB13XWUWEuY\n6ZrJTNdMZrhmMN01nWlF07AbZStGycXTGYtlXDBbvV72BwJMM5tZ4XCwvN8VU2U0nhXRE46HOdh5\nkL3te9nTvofdbbs53nOcmcUzWVK+hGUVy1heuZzq/OrzwlZbHm2h6duN1Hykl+LUeti8mVPHj/Oj\nwkKe7O7my/fcw5cefTSnn/HyFPq3IhIZKD6StnQee3+WzCaHg681N9OVSPAft9/OHR/6ENpJk4Rf\nYtT4cLJIJET8/UMPCffWt74Fc+cOy1TiyTh13XXs79jP/o79HOg8wIHOAwDMKZnD7OLZzC6ezazi\nWcwsnonVYB2WeUpGL+lD0y3nHJous9up7Rf1xTYb1nfRrS4UD7GvfR87WnewvWU721q2EUlEqC1f\nxkqqWHrSiPnnM8GtMsP2CMaV1bzmcvHjujq219dz992fYurU+3G5XNx8c24/txT6iyUYFPntjY2o\np07x+qZNfGPjRroCAR7Q6/lQNIouHcs3btzZYSDl5QMniiO1vX0kIurdf+97UFsLDz4Is2cP2u3C\n8TAHOg+wt30ve9v3sq9jH8fcxxjvHM+80nnMLZkrrHQuZdayER0fLRm5hJNJdvn9mRDHbf2HprVZ\nh6bTLuLQ9OJvGBbu4T17YM8eWo5sY0v8FOumTuINZ4yOonYWuGZj8udz6MVDlCRK+Mw/fQ6t9sM8\n8ogRvR7+8z/h+utzM500I0roFUV5ArgR6FJV9TyVGVahvwCqqrJhwwa++c1v0nTmDF+++24+vngx\nRrd7wMmfjhFsbRWhJmbzQIhJ2tKnlOkxfeKbnz/0TwnBoCiS9oMfwBVXwAMPiKSESyAcD7O/Y3/m\nEXdP+x5O9Z5iums680vnZ/ycc0rmyNhyySXRG49nRH2z18uBQIBZFktG1Fe+i0PTC5IuRZo+9ztw\nQJwDNjSIGO5Fi2DhQhJTF3DyV1Z6N3npua+HX+36Fa8ce4UJqycQK0/SHGxDaVlJeeQ9fOn913HP\nLTPRaHK/qRlpQr8KCABPjgahz2bLli3853/+JwcOHOC+++7j05/+NI5zK1ipqnABtbcL0U/HGHZ2\nDsQddnUNxCX6fKQcRcQc44lbK0lYSogbC0noC0jqbCS1VlIaMylNHimtEVVjRNXoUQ0G6I8gUXRK\nxjR5moxprVphNi06hw5dvg59vh5dgQ59gR4lHBQ7/P/+b5F6/MAD4j/v25BIJTjSdYSdrTvZ2bqT\nXW27ON5znOmu6SwqW8TC8oUsLFvIrOJZF31wJZG8Fe3RKG96vbzZ18ebXi9nIhGWZcWuL7HbsVxa\nvRQh6MeOCcs+1wOxCUrb/PkiYcco/l/3vNzD5k9tZsO4DbzU/RJmi5l/+qd/YvXqj/HUU05++UtY\neV0PS2/fwBnt33j11KvEkjG+tupr3Lv43hz8dgYYUUIPoCjKBOCl0Sb0afbv388PfvADXn75ZT75\nyU/yuc99jsq/U0I44UsQPhEmfCpMuCFMpDFCtDlKtEVY0p9An69Bb0+hNyXQGaLodGG0aghtMog2\n7kcT96NMS4myAAAgAElEQVQJ+1EiAZSQH8IhUFP9J69WVKOZVJ4V1WAhpbeQ1JlJKmaSqolkKo9E\n3EAioiMR1hL3KyQCoLNrMBQbMJaoFAf/QlH9EyTLJhP+4H1o1rwH4/g89KV6WoIt7GjdwY6WHexs\n28m+9n1UOapYPG4xi8sXs2TcEuaUzCFPN0JdVpJRRVMkkqkN86bXS088ziqHg1X9JQTmW63o3s1T\ncG/v2XWljx8XxQKPHxfRCdOnC8uO1HuLnox9Z/r4+Yd/zp/2/Yl6XT13fOQOPvGJu0kkFvHoowrr\n1okW0PfdJ3J40qiqysnek8SSMWYWz7yE39L5SKEfJM6cOcMjjzzCk08+yXXXXcd9n7uPWdZZBPYH\nCOwPEDwcJHg0SMKTwDTZhKlaWN7EPIxVRowVRozjjOgL9Sjv5lEuGhVB79nhQD7fQGC83z/wOn3d\nHyqU8gVJ+FLE/HriERMxQylRnQuFDmzxHXiN8H9zivjJkm6SOpU57snMD0xkYWoCSywTKKmwYJqg\nR19sFvGlabNaB67NZllSWfK2tEQibOjrY2NfHxv6+vAnk1zpcLDa6eQKp5NZFsvb+9fTT9LnVrJL\nlyNtaBAhbula0tXVA11famqEK/VtSCaTvL7+dX7xrV/w8paXmT9+Pp9+8NOsed+t/PnPJn78YzGF\nz38ePvEJEbo8lEihHySiHVG8b3ppfaOVp9Y+xW/P/JYiYxEfm/cxbr3pVgrmF2CebiZvfN67E/JB\nRlVVTvedZlvTFrae3sTW5q3U951ijnUSnzzp4H1/ayK/J4y69DqC5bWEu01EOhXCbgNhj4lwnxVF\nk8Rs6sas78SsbcWsnsGcOEVepBFNOCAecbOF/+9dZ49v9bVzzWCQ3bdGGV2xGBv6+njd42FDXx+9\n8TirnU5WO51clZ/PDLN54GBeVcUGJe0Gza6XkV0MqblZ7MrTRY/S1evStaYnTRJJIO/w/4qqquzc\nuZPf/e53/O6p3+EMO1lTsIbP/OwzaCZP5ec/FwFtixeLVhHvfe/wBeaNOqF/8MEHM69Xr17N6tWr\nL/meuSDuieNZ78GzzkPfG33EO+M4Vjqwr7BjX2rHPN/Mq5te5Uc/+hEHDx7kk5/8JPfccw8TJkwY\n7qkDosrg3va9bG3eytbmrWxp3oKCworKFSyvWM7yyuUsKFtwtgtm507hw08/i37uc2I3hPgjiHfF\nCdWHhNX127EQsfYYphoTlml5WCZrsUwES1WSPGcYJRIeSDzITkJIZ3td6HU4PHCd/fVU6q0XA5Pp\n/OsLjede5+UNXGebXFTeFYFEgjf7+ljndrPe46EpHmeVonBNJMLVHg+z3G406bTrnp6BmhpdXWLU\n6weCGsrKBmpoZBdDqqzM2RZaVVX27NnDs88+y+9//3sMOgPXOq5leeNyVnzrKnYWlPGLXyocPCh2\n7vfck/mTGFI2btzIxo0bM68feuih0SX0I2VHr6oqwSNBev7cQ89feggeCeJY6SD/2nycq51Y51hR\ntBf+vdbV1fGzn/2M3/zmNyxevJhPf/rT3HjjjUNaIrk33MvW5q1sbtrM1uat7G3fS01hDSsqVlBb\nVcuKyhWMd4y/uLDG5mb48Y9FLZ2lS0XVzL+zfUmGkoSOhQgeDQoX1iFhib4EllkWLHMtWOdasc61\nYpljQWd95zHNgMhGC4fPXgyyX6cXhvT30tfZP3vudTrN+NzX8fjAIpCXd74ZjQPjhSw70y3b0tlw\nF7J01lx29pxGI8bsa0UZyLRLWzbptOvsTL10+nXa0tl82anY8bhwEWanY0ciYsz+vWUtvolQiN1O\nJ69VVfG3mhr2VVWxuK6Oaw4e5D0nTrCwtxedzSYiztJWWDhg6Yi0tA1SzaZsUqkU27dv5/nnn+fZ\nZ59Fr9fzj7f+I6tiq7A+aSVwfRWv2St4+lkts2fDpz4F739/5kz2olHVFMHgUQCs1lk5/Qwjakev\nKMozwJVAIdAFfF1V1f/L+v6wCr2qqvj3+HH/3o37T27UpErRLUUU3lSIY5UDbd478zmHw2H++Mc/\n8vjjj3PixAnuvPNO7r777pxXzVRVlca+RjY3bWZL0xY2N2+m2dvMknFLqK2sZWXVSpZWLL30jNJQ\nCH73OyH6Xq/oenXXXRfdLCDuiRM8FCRwMEDwQFCcZRwJYqwwYp1nxbrAim2+DesCKwbXCKvDnkwO\npD6nF4LsGhTnCmG2ZQtldh2LbEHNrnORLbhpEU5fZwt0tminRTz770dVB0Q/vRikF4RzFw29fqBG\nR/Zik71QZS9kWU9Bp+12XsvP51WLhQ16PZUaDdcajVxrt7PK5cLscIy47ueRSITXX3+dP//5z7z4\n4osUFRVx6623ctutt1F8oJjDX2/hTWc5ryiltLq13HWXaOE8efLF3yOZDOH378Lr3YLXuwWfbyt6\nfREVFfczbtz/l9PPM6KE/m1vMExCHzoRouPXHXQ904WiUXDd7qL4A8VY5lhylshTX1/PE088wZNP\nPklVVRV33nknd9xxB4WF51fOezsSqQQHOw+yuWlzxgBWVq1kZdVKaitrmVs6F53mXe6U3w5VFYXT\nfvpT0QDl+uvFM+zq1e/YSZlKpAjVhcQh9r4Agb0B/Pv86Ow6bAuF6NsW2bAttGEoHllicbkSTiZ5\no6+PV3p7eaW3l95Eguvy83lvQQHvyc+n7J1udYeI9vZ21q5dy1//+lfWr1/P3Llzufnmm7n11lup\nnlRN+7Pd/O6LvbwSLmZ72Ml7r1f4xCfguuvE+vf3UFWVSKQBn287Pt92vN5thELHsFrnYLevwOFY\ngd1ei9FYOiifTQr9W5AMJul8ppOO/+sgfDJMyUdKKPloCdb51kHN0kwkEqxbt44nn3yStWvXsnr1\naj784Q9z8803Y36Lx9RQPMSOlh1C1Js3s71lOxX2Cmora1lVtYqVVSuZ4JwwPNmlHg889RT84hci\nqucTnxC7/Kqqd/2WqqoSaYjg3+PHv9uPf4+fwN4AWptWiP4iG7bFQvz1BSOocM8Y5lQ4zNqeHl7u\n7WWT18t8q5U1BQWsKShgntWau8zTHJJIJNixYwevvPIKa9eupaGhgeuuu44bb7yRG264gaKiIlJJ\nlVe/5+FX/y/O37wFTK6BT3xex+23K3+3U2cs1o3fvwu/fyc+3w58vp1otSbs9mXY7cuw2ZZisy1C\nqx2asGMp9OcQPBqk7bE2Op/uxLHSQdmnyii4vgCNfuiPy30+H88//zy//e1v2blzJzfccAMf/OAH\nmb9yPnu69ghXTPMWDncdZk7JnLN27BeqoT2sqCrs3Sv8+L//vUguufNO4cy0XnrNGlVVCZ8KE9gT\nwL/bj2+Xj8DeAPpiPbZFNuyL7diW2LAtsKG1yLDOSyWWSrHJ6+WvPT38tacHXzLJ9QUF3NC/a3eO\npMp4WTQ0NLBu3TrWrVvH+vXrmTBhAmvWrGHNmjWsWLEic052aF+KJ74e5NlX9Wi08KHbUnzyQRM1\nNedrZTzeRyCwF79/N37/Hvz+XcTjvdhsC7HZFmO3L8VuX4rRmPuGIheLFHqESHjWeWj+72YCBwKU\nfaqM8n8qJ69q+JN8VFXlRO8J1h5eyx+2/4H9vfsJa8OUJcpYPXE1d151J1dWX4lJbxruqV48kQi8\n9JLofrVpE9x0E3z4w3DttTktnakmVUL1Ify7hPD7d/kJHg5immQSO/4lYgGwzLagMYzCgnRDjDsW\nY21vL3/p6WFdby9TzWZuLCzkxsJC5o/QXXtnZycbNmxg/fr1rF+/nlAoxLXXXpuxsqyOa/X18Myv\nk/zuiSQet8qaSi93fcnI6s/YM2UJYjE3gcA+AoF9+P178fv3EI93YrHMxW5fjM22CKt1IWbzFJQR\nVBL7shb6VCKF+/dumr7bBApU3F9ByYdK0BiH7x8omoiyt30vW5q3CGvaQp4uj9oq4YapraylMFnI\nX176C3/605/YsWMHV111Fe973/u48cYbKSkpGba5vyu6uuCPf4SnnxYZie9/P9x+u6izMwgJValY\niuChYEb4/Tv9hBvCWGZbxK6/fwEwTzGPyPyGoURVVepCIV7s6eGl7m4OBYO8Jz+fmwsLub6wMDc1\nY3JMe3s7mzZtyoQXtrW1ceWVV3L11Vdz9dVXM2vWrLNcmEePwnPPwR+eStLZkuKKhJtbVsd4338V\nYJjuJhA4QCCwv1/c95NI+LFa52GzzcdqXYjNtgCzeSqKMrKfEi9LoU/FU3Q+2cmZ/zqDsdzI+K+N\nJ/+64ekg3xXsYlvzNhG/3rKVfe37qCmsobayVlhVLVWOt/Zn9/b28vLLL/Piiy/y6quvMn36dG64\n4QZuvPFG5s2bh2Y0lU5ubIQ//EFYayvceivcdhtceeWgFslPBBIE9gbw7ewX/11+4j1xbAuz/P2L\nbSK5bQTuWnNJUlXZ7vPx5+5uXujuJpRM8r6iIt5XWMhqp/Mte54OB6qqUl9fz5YtW9iyZQubNm2i\nt7eX2traTI7N3Llz0WbNWVVF7bHnn4fn/qjS15XiSnMHtUV7WHXvYQxLzxBOHiEYPIhO58RqnYvV\nOi9jeXkTR9RO/WK5rIReTap0PtPJ6QdPkzcxjwlfn4DzisHp0XghEqkEhzoPsa1lm7DmbfSEe1g6\nbikrKldQW1nLknFLsBlt7+r9o9EomzZtYu3ataxdu5a+vj6uu+46rrvuOq699trRtds/eVJstZ57\nTqSo33QT3HKLCHGwWAb99rHumDjo7Rd+/24/alzNHPZaF4poH+M446gX/2gqxXqPhxe6u3mxu5sS\ng4Fbioq4paiIBdbBDT54J/h8Pnbt2sW2bdvYvn0727dvx2azUVtbS21tLatWrWLGjBnnbW4SCdFW\n+oUXkjz/fBISYa6YvoPl055jxjV/RXF6sNim94v6XCyWOVitc9DrC4bpk+aey0LoVVWl5689NPx7\nAzq7jonfmUj+6r9zZJ4DVFWl2dfMztad7GjZwY7WHext38t453iWjVvGsoplrKhcwXTX9EFrb9fQ\n0MBrr73Ga6+9xuuvv05lZSXXXHMN11xzDatWrcLpHLpF7pJoaoI//1nYzp1ih3/TTXDjjaLu/xAR\nbYsK0U9H++z2g4LY+S/sF//5NoxVI1/8A4kEL/f28qfubl7u6WG21cqt/eJebRr+855IJMKBAwfY\nvXs3u3btYufOnTQ1NTF//nyWL1/OsmXLWLZsGeXl5x9wplIJOjsbWLu2l7/8xcyGDRMpKznD8hXP\nsXLqFibnJXEUz8G1aAnOioWYTNUj3vVyqYx5oQ8cCHDyCyeJtcaY9PAkCm8qHJQ/wq5gF3va9rCr\nbZew1l2oqCwZt4Sl45aydNxSFo9bjDNveMQ1kUiwZ88e1q9fz+uvv86OHTuoqanhyiuvZNWqVdTW\n1o6OHb/HA6+8An/9qxjHjYM1a4TV1g5p4o2qqkRboiK8c09AjPsCpGIprPP7k7vmWbHOt2KaYkKj\nG95Hfm8iwUvd3TzX3c16j4fldju3uVzcUlQ0rP52v9/PwYMH2bdvH3v37mXfvn3U19czdepUFi5c\nyJIlS1iyZAkzZ848K3s8lYoRDp8kGDxKKHSUY8d6WL++jI0bF3Ps2FLmzTrGqsknWOJvpyxUTEnt\nYoo/UIF11uXXmWzMCn28J07DVxvofqGbCQ9OoOyespyESKqqSpu/jf0d+0V3pI697Gnbgz/mZ2GZ\nqLW+ZNwSFo9bTKW9csTu7GKxGLt37+aNN95g8+bNbN26FZfLxYoVK1i2bBnLly9n1qxZZ/k3RxzJ\npEjMevVVIfp1dbBqFbznPSKCZ8aMYak/E22PiuSu/kqlgX0Bom1RzNPNA6UdZluwzLZgKBpcgfXE\n4/y5u5tn3W7e9HpZ7XRym8vF+woLyR/iEMhUKkVjYyMHDx7k0KFDHDp0iP3799Pa2srMmTNZsGAB\nCxYsYP78+cyZM4e8/m5siUSAUKiu345lzOdroa7u/ezadStbtqzA12dl9cxeVqgRZhx0UzjVQOFN\nhbje78I8wzxi/xaHgjEn9GpKpf2Jdhq/1kjx7cVM+OYE9M539x86HA9z1H1UNKbuOsTBzoPs79iP\nRtEwr3QeC8sWMr9MdEg6twnwaCOVSnH48OGz/J8tLS3MmzePxYsXs2jRIhYuXEhNTc3IPeDt7oYN\nG0SRtXXrROmB1avhqqvEOGXKsBUeSwQSorzD/kCmtk/gYACtWYtllgXzTDOWmRYsMyyYp5svKdGr\nLx7nhe5u/uh2s8nr5Zr8fD7gcnFTYSH2d9EL9Z2STCY5c+YMR48e5dixYxw5coQjR45w9OhRCgsL\nmT17NnPmzGH27NnMmzePKVOmoNVqicXaCIXqs0RdWDzejck0BbN5Gh7PMrZvX8nGjTVsetPO5JI4\ntU4fC92dTAr0UXhtPvnX5lNwQwHG0pGZgTscjCmhDx4NUn9PPaSg5ic12OZf3KGmN+KlrruO+p56\njrmPcbT7KEe6jtDia2FK4RRml4im1HNL5jKvdB6l1tJRLeoXS19fH3v27GHXrl3s2rWLffv24Xa7\nmTt37lk2c+ZMrDlIeso5jY1C+DdsgDfeEPVjrrgCVq4Ubp65cwc1muftSLt+gof7i7sdCRI6Jip8\naswazNPMwqaaMdWYME8xkzcx74JPpr5Egj93d/MHt5s3+/q4yunk9uJibiosxDZI4t7T08OJEyc4\nfvw4J06coL6+nrq6Ok6ePInL5WL69OnMmDGDGTNmMHPmTGbMmIHVaiAcPtEv6PWEw2lhr0ejMWE2\nT8NsnorZPB2zeRowjR07qnjlLwqvrlXp6YHlhX4WBd0sSPYw8UorjiscOK90Yp1nvexDYt+KMSH0\nqXiKpu810fpoKxMemkD5Z8rP+gdPpBK0+9s53Xeaxr5GGj2NNPQ1cKLnBCd7TxKKh5haNJVpRdOY\nWjiVma6ZzHDNYHLBZPTakZnhN1x4PB727dvHgQMHOHjwIAcOHKCuro6SkhJmzZrF9OnTMzZt2rSR\ndeB75gy8+aYIwdiyRbxetAiWLRO2dKkoczvMqKpKtDVKuD48UN75RIjwiTDRlijGcUZM1SZ0k4w0\nlqTYZA+z3hakeoqDm6cW875iV0527olEgpaWFhobG2loaMjYyZMnOXnyJKlUiilTpjBlyhRqamqY\nOnUqU6dOpaamBr3e2y/i9WeJeizWQV7eRMzmqZhMU/uFXYi7Xp9PPJRk18sxXnkhyetbtOxtMjBV\nH2RRsocraiIsvkKLc7kd+zI7phrTZbHhygWjUuhTaopgLEhfpI+2g23s/8Z+gqVB9Hfp6TP20RHo\noD3QTnugnRZfC52BTlwWF+Md45mYP5GJTmE1hTXUFNRcNjv0wSKZTNLQ0MChQ4c4duwYdXV1HDt2\njPr6ekwmEzU1NdTU1FBdXZ2xiRMn4nK5hvf37vHA9u3Cz582i0WI/+LFsHChKNVQXDx8czyHSCTB\n+gOdvLm/i6Y6H/N6Dczq0VPUppJojpHwJUR3sv4OZYZyA8ZyI4YSA/oSvRiLRG9gX8hHS0sLzc3N\ntLS00NTURFNTE2fOnOHMmTO0t7dTUlLChAkTqK6uZtKkSUyaNInJkydTXV2Nw2EgHD7eL+jHs3bo\nJ9DpbP1CPiUj6ibTFPSRSuIdKaLtUWKtMSJnIjQcSfDmQQNbmszsDtmx65OsqAhx1cI4V79XQ+ky\n8WQz3IfZo5lRJ/Smb5uIJCKY9WZsCRumbhNF5UWUTyin2FKMy+yi1FpKma2MMmsZFfYKym3lcmc+\nDKiqSkdHR+bR/tSpUxk7ffo0kUiECRMmUFVVRVVVFZWVlVRUVDBu3DjGjRtHeXk5Dodj6BYDVRUx\n+7t2we7dojbP3r2iFs+8ecLVM3euaAQ9efLblyzMESlVZZPXy287O3nO7Wa6xcKHiov5R5eL4nOi\nZaK+KG2H22g90krbqTbaTrfR3tpOh7uDTk8nXYEu3FE37qQbLVpK9CUUG4sps5ZRbi+n3FlORVEF\nFa4Kyl3lGK06UvY2EpYG4uZG4qZG4sZTxIynSGn96CMT0YcnogtOROediKZnPJru8ai9ZhLeBElf\nkrgnTrw7TqIngcaiIeyycCAvnz1RJ9u7rQQSGq5YkODa9ypcf7uOCZOkoOeaUSf0gWgApUOh/s56\nSMK0J6dhmjj8cb+Sd47P5+P06dM0NzfT1NSU2Vm2trbS0tJCe3s78Xic0tJSSktLKS4uzlhRURFF\nRUUUFhZSUFBAQUEB+fn5OBwODLkMFUyL/4EDA3bokGhXN3UqzJolonumTxfjxIk58fvH43G2tLby\ndGMjL545gzUUYoVGwyxVRfH76e3tpaenh56eHrq7u3G73bjdbvr6+igoKKC4uJjS0lJKSkooKSmh\nvLycsrIyysrKGDduHGVlZZhVM3FPnERfgojHTThURzh2nEjqJDHtSWKGUySMzWhiRegDE9H5J6L1\nTkSXvg6XotFrUfQKil5Ba9KiMWvQmDTobDq0di06h46QTsfOU0be3KNjwxsKDQ3imOTqq0Vw1KxZ\nw9di73Jh1Am9+0U39Z+qp+K+Cqq+XPWWXZwkY4NgMEh7eztdXV10dnbS1dVFV1dXRuC6u7vxeDz0\n9vbi8Xjwer3odDqcTic2mw273Y7NZsNqtWKxWLBYLJjNZkwmEyaTiby8PIxGIwaDAaPRiF6vz5hW\nq0Wr1aLRaNBoNCiKkv6DQRsOY21qwnLmDJamJmxNTdhaWjB5PPiLiugrLsZTVERPQQFdDgedVitd\nej3hWIxwOEwoFCIYDJ5lfr8fr9+P1+cjHo+jMZuxO52U5udTVliI0+kkPz8/s7AVFBRQVFSEy+Wi\nsLCQ4uJiCgoK3jIkNpVKEIk0ZEW2iDEcrieVivUfgqZ95+nrGrTad7aRCgbFEUj6HPzwYViyRAj7\nVVeJ6xFa3HLMMqKEXlGUNcAjgBb4haqq3zvn++rWqq3M+O0MHLWOS7qXZGyiqiqhUAiv14vP58Pv\n9+P3+wkEAgSDQUKhEKFQKCO2kUiEWCxGNBolGo0Sj8czlkwmSaVSmVFVVVRVzQg+gEajySwIWq0W\ns0ZDeShERTBIeTBIaSBAsddLkdeLORzGl59P0OUiXFJCtLycZEUF4cpKNuXn85zJxAmtlvePH89d\nVVWsdDrfldsqkfCfF6IYCtURiTRgMJT2R7RkH4ZOxWB49+dUwSBs2wYbNwrbv18cbaSjWpcvF82m\nJMPHiBF6ReQg1wPvAVqBXcCHVFU9lvUzaqw7hr5Qbgcko5BwWIR8nj5NoqGB08eO4T5xAn1LC9Vd\nXdj9fjRlZSgVFaK0Q7rB9bhxA42vy8vBahXN1+NuQqFjBIMDSUSh0DHi8V5MphoslukZUTebp7+r\n3fmFCATEjv2NN4SwHzggjjCyhX0IyhFJ3gEjSeiXAw+qqrqm//W/A6iq+t2snxkxzcElkneKqqrs\n8vv5TWcnv+vqYprZzMdKSviAyyWyVKNRUbWzuRlaWqC1FbW1lVRLA2prI7R3oOnyoiopYvkQL1BI\nFTlQi11oSivRlVajL5+Ovnw6iqtYNNIuLLzk7bTHI4T9zTeFuB85IgKSrrhiQNiHoEe35BLIpdBf\nagjCOKA563ULsPQS31MiGXaaIxGe6uzkyc5OEqrKnSUl7FywgInnCHBM8RHMbyJoOEyw9DChGUcI\nBo8AGiyWmVgsV2A2TcOiTsLiLyCvJ4HidoPbDZ2d0NYNB7aB+0XxtZ4ekS2s1QrBLyyEgoIBy8+/\noHUnnGw9ls/rexxs3Kzj1CmRYnDllfDww+I6b/h78kiGiUsVerlVl4wZgskkz7ndPNnRwb5AgA+4\nXDwxdSrL7HZSqRDB4CHa+w4RCBwiGDxMMHgYVY1iNs/EYpmFxTKT4uIPYrHMwmC4hDh+VRVO9N5e\nIfw9PWKL3v9a7e7Bv/ckngYPobY+kr19WOMertL2cVPCi2oyoylwonQ64TUn7HSCs98cDjHm5w98\nLfu1wzEozWMkw8ulCn0rUJn1uhKxqz+Lb3zjG5nrdHMBiWQkkFJV3uzr49ednbzQ3U2tzcb/V5Rg\nebmbWOh1As0H2Rk8SDTajMk0Fat1NhbLbAoK3ovFMhujcVzucwYUReQBWK1QVUUyCQcPiuTgTfvF\nqCgi3HHVx4U7piod7phKCYe8xwNer7D0dV+fuG5vh2PHBr7u8Qjr6xPN4K3WgaeH9JNE+smisFC4\nl9LmcgmTDv5LJt1hazC4VB+9DnEYew3QBuzkAoex0kcvGWk0hsM82X6G1zt2UMMprjW1MCF1gljo\nEFqt5byGFibTFDSaoQkoCAZFwu+WLULUt28XZ7srV/aL+yqYMGGQar0lk+DzDTxBpK2nR4zd3QPu\npe5u4W7q6hKrTHExlJSIsbRUHEaXlYnD6PQBdXGxDMC/SEbMYWz/ZK5nILzyl6qq/tc535dCLxl2\nkskgbu8etnZu5kzvDpzxY1QqzRiMEymyL8Rmm4fFIsTdYHAN6dza2oSop+3oUZHIu2qVEPYVK8Tm\necSiquIpoqtLnDt0dkJHh3hyaG8XH7CtTRxae71C+KuqhE2YMGDV1VBZKV1H/YwooX/bG0ihlwwx\nyWSYQGA/fv9u/P7ddHp3koic5jTjCRlnUV2whGUlV+C0zc1J6OI7m5tIRtq6dUDYfT4h5itWCGFf\ntGgMx7BHIiI6qblZFKg7cwZOnxYhrKdOiSeEqipRnjpt06aJDOYRVL9oKJBCL5H0k0olCIWO4vPt\nxO/fic+3k3D4ODrTNM4o03gtMp523XSuLVvBR0orKTUObb1zr1e4YbZuFbZjh/BmrFghqi6vWCGq\nMkhvRj+RiBD9Eyegvl5YXZ2ID9XpYOZM8bgze7aoYTR79phdFaXQSy5botEOfL5t+Hw78Pm2Ewjs\nwWAox25fSp5lIXtSU/hlXyE7AzE+WFzM3aWlLLLZhqTIWioFx4+LjNNt24Swnzkj4tfTO/Zly0a4\nG/a+uP8AABoUSURBVGakoqrCHXTkiDiZPnhQpPPW14tidQsWiDoNS5eKhWAY2yzmilEn9F/8ospn\nPyvccBLJxZJKJQgGD+H1bsHn24rPt41EwovdvqzflmK1LuZgRMcTHR38vquLhTYbnygt5R+KijAN\nsq/X6xV9z7dtG6ic7HAIMV++XAj7nDmyRsygEo0K8d+9W/xj7NwpXEALFohHpvQJ9kjqsXCRjDqh\nv/9+lV/9SoSB3XsvXHONfFSVnE8yGcTn24HXuwmvdzM+3w6MxnE4HCux21dgty/HbJ6Comhwx2I8\n1dnJ/3V0EEwm+XhpKXeVllI1SFlByaTQk7Sgb98udusLFghRX75cCPwI6IEi8fvFP9LmzcJ27BC+\n/quuEuJzxRWjIhx01Am9qqoEAvDUU/DYY6J8yKc/DXfdJR9jL2cSCR9e72b6+t7A632TQOAgVus8\nHI6VOBy1OBy16PWFAz+fSvFyby//19HB6x4PtxQV8YnSUq5wOtHk2DXT2jrQ12TnTtizRwSLLF0q\nbPlyUapX7tZHAbGY6FewYQP87W/iH3PxYlizBm66SZSrHoFNjEal0KdRVfGo+9OfwosvwnXXwac+\nJRZaGVU1tkkk/P3CvoG+vo2EQsew2RbjdF6Jw3EldvvSC0bB1AWD/F9HB092djIxL49PlJZye3Fx\nzppme73iyX/XrgFhj0YHRH3pUuH+zc/Pye0kw43fLyq7vfwy/OUv4pD35pvh/e8Xbp4RIkSjWuiz\n6euDZ56BX/5SnLN85CNw553iYF0y+kmlYvh82/F4/obH8/+3d+fxcZXnocd/j2TZlmyts0gCyViA\nLWPjGG/ESSAIYsCGgO0axxC2AOmnTdritmlTArQVzeUmN3ShuW0akku5QADHYLAxcAlLosSXUPC+\n4wXLxoukmdE62jzSzNs/3iNbGGFrpJHmjHi+n8/56OicM2ceHel9dOY97/I2ra3byMmZS17eleTl\nXUlOzqWkpfXdCqalu5tVgQBP1NZysLOT2wsLubuoiCmD/Mjd3m6f4fVMSLVhg23tN3OmvcnrSepD\n1iFJuYsxtr3r2rXw4ov2j2HxYrj5ZjtQUBKT/ohJ9L3t2gVPP22rd7xeuOUWWL5cH+CmEjuu/B4a\nG9+koeENmpvXk5VVTn7+fPLyvkJu7pfO2G7dONPv/WdNDWtCIa7Mz+eeoiIWFBQwagAPdTo6bOOM\nTZvssnGjbbU3dapN6j3TzE6dOmwzDCq3q66GF16wd6A1NTYJ3XGHvRMY5v/8IzLR94hGYf16e51X\nr7Ytp266CZYutTO+KXfp7m6msfEtGhpep6HhdSCNgoJryc+/hvz8q8jIKDjrOY50dvJUXR1P1NQw\nNi2Nu4uLua2w8BNzq55JW5sdY71nythNm2xSLy+3zRvnzLHL9OkwzE3pVarauxeefRaeegqys+Gu\nu+C22+zYPsNgRCf63rq67POT1athzRr7MOzGG2112qxZ2nInGexd+27q61+lvv41Wls3k5v7JQoK\nFpCffy1ZWeX9arPeGY2ytr6eJ2pq2BAO8zW/n7uKipjbjzbvgYCtfulZNm+2HS2nTrV/Fz3L9Ok6\nNK9KgFjMDuz/xBP2weLChbY1yZe/PKR3+Z+ZRN9bNGo7oKxbZ691S4t9aL5woZ2sOAWbyaaMWCxC\nU9Nvqa9fR339KxgTxeP5Kh7PdeTlXUl6ev9msDDGsLm1lSdqalgZCDDTafO+5FPavHd12Q5I27ef\nmuN761bbefKSS04ts2bZXvLaAkYNucZGe4f/2GO2/n7FCvtwcQh6534mE/3p9u+3D81ff91W9Vx8\nMcyfb1vvzJund3KD1d3dQkPD/yMUWkNDw+tkZpbj9d6Ix3MD48ZdHFdP00AkwjNOm/fWXm3ez3N+\nSbEYfPSRfU6zcyfs2GG/7ttnhz3p3eN9xgy7TR+UqqQyBt5+Gx591DbT+sEP4J57EvoWmuhP09lp\n7/bfeste+97Tpl12mU38uTov+Vl1ddUTCq0lGHyR5ubfkZt7GV7vYjyeGxgzpji+c8VivNbQwBM1\nNVQ1NXGj18udviLOa85j7wfC7t18bMnJsa2tpk+3y7RpdtHp7pTr7d9vqxhmz07oaTXRn0U4bBP/\nb39rRwfctMk+yJ03z7aymDtXO7v0iESChEIvEQy+QEvLe+TnX43PtxSP53pGjcqJ+3w7Wlv5yZ4A\nv9wcxhPIZXLIQ8axcRzcl8aBA3YAwilTbB+VqVPt12nTtI26UqfTRB+nri5bv/vee7bd9IYNthXV\nRRfZVlM9g+BNmzZsD9STqquriVDoJQKBlbS0/BcFBQvw+Zbh8SwkPf3s7dRjMTu8+MGD9jru2Bel\natcJ9hyI0fHRWEabNC6cZPjclHTKy23v8/Jyu6RAz3OlXEETfQK0tdm64C1b7AO+XbvsMnq0vePs\nSUwXXmjnQzj//NSuRohGO6ivf5VA4BkaG39Nfv5X8PuX4/F89RPJPRy2QwAcPWrrzo8csV97hg8/\ncgTy8w15pd20+dsI+JqZOXkUyy/JZvmsbIr8onXoSg2SKxK9iCwDKoEpwFxjzOZPOc6Vib4vxtg7\n1d7DYH/4oV0OHbL1/D0T45SWnpodrbj41Axq+fnuafZpTIzm5vUcP/40hw+/RTT6ZUSW0d19FfX1\n405OCFRbe2pCoOPHbQunkhL7s/X8rKWltvNau7eVt0fXsaq5lkmZmdxZVMTX/H5ytceRUgnllkQ/\nBYgBjwHfGQmJ/kxiMZsMDx8+dZfbMztaTc2pWdRaW0/Nqezx2H8OPcv48fZTwbhxtjXW2LG2886Y\nMbZnZnq6XUROtSqJRk8tXV12fKZIxD6A7uiwS3u7fd+2NvtMqKmpg1CogcbGLsLhPNracsjKAq83\n7eSczj3Te/p8p6b2LCqyfRVycz/eqqXOaTXzZG0tTd3d3FFUxB2FhUxK5Y84SrmcKxJ9r2B+w2cg\n0fdXJGKb2tbX26WlxQ6a1dxsE3HP0tFhk/WJE3aJRqG7237tuVzGnEr+6em2Wmn0aPsQeexY+88i\nM9P+48jKihCLvU8k8joZGXsoKfkiZWXXUVp6EXl58T947ohGebm+nqdqa/l9SwuLPB7uLCriiiEY\nKVIp9UmJTPT6eTvBRo+2d8qFhcPzfuHwVmpqfk4gsJKcnHkUF9+Dx/N3pKXFP8NOzBjeaW7mqbo6\nVgeDzM7O5s7CQlZNm8Y4l4zop5SK3xkTvYi8CfQ1lcL9xph1/X2TysrKk+sVFRVUVFT096WqD9Fo\nO4HALzl+/DEikRqKi+9hzpytjB1bOqDz7Wtv5+m6On5RV8e4tDTuKCpi+5w5lGivM6WGTVVVFVVV\nVUNybq26SSHt7Qc4fvwn1NY+RW7uFzjnnD+moGABIvHfbQciEX4ZCPCLujo+OnGCW/x+bi8s5JLx\n44dlflWl1Jm5sepGM8MQMSZGQ8OvOHbsx4TDmygqupvZszeSmTkx7nO1RaOsDYV4pq6Od5qbucHr\n5aGJE5mfnz+gYYCVUqlhMK1ulgA/BrxAM7DFGLOwj+P0jn4AotE2amv/L0eP/m/S0zM599x78ftv\nIT09vuqU7liMtxobeSYQYF0oxBdyc7nV72ex18t4bRKplGu5qtXNWd9AE31cTpw4zrFj/0ZNzc/J\nzb2ckpI/Jzf38riqU4wxvNfSwjOBAKsCAcrGjuXrhYUs9/spjGOMd6VU8rix6kYNUlvbHo4ceYRQ\n6CX8/luZOfNdsrIujOscu9raeLaujucCAcakpfF1v5/fz5rFBUMwhKpSKnXoHX2StbS8x+HDP6Cl\n5V3OPfdPOPfcPyEjw9Pv1x/s6GBlIMBzgQBN3d3c7Pdzq9/PDH2oqlRK06qbFGeMoampisOHH6aj\nYz+lpX9NcfHd/Z7A49iJE6wKBFgZCFDd2clNPh+3+P18KTdXOzMpNUJook9RxhgaG9/i0KGH6OoK\nMGHC9ygsvI20tLN3W62LRFgdDLIyEGBnWxuLvV5u9vu5Ki9PW8woNQJpok8xpxJ8Jd3dDZx33t/i\n9y8/a/v3YCTCi6EQqwIBNoXDXO/xsNzv59qCAsZocldqRNNEn0Kamn5HdfWDRCIBJk78u7Mm+FAk\nwkuhEM8Hg7zX0sKCggKW+/0sLCjoc15VpdTIpIk+BYTDmzh48H46OvYzcWIlfv/XSUvru5FT0Enu\nLzjJ/dqCApb5fFzn8egYM0p9Rmmid7H29v1UVz9Ic/N6zjvvbyku/mafdfC1J06cTO4bw2EWOMl9\noSZ3pRSa6F0pEgly6NBDBAIrKS39S0pKVnxi5qajnZ28GAqxOhhkW2sr13k83OTzsaCggCxN7kqp\nXrTDlItEox0cPfqvHDnyjxQW3sqll37A6NHek/s/7OjgxWCQ1cEg+zs6uMHj4a9KS7k6P5+xmtyV\nUsNA7+gHyBhDMPg8H374XbKzZ3H++f+LrKxJGGPY2dbGS6EQLwaD1EYiLPZ6+QOfjyvz8sjQ1jJK\nqX7QqpskC4e3cODACrq7W7jwwkfJzbuC/2ppYU0oxEuhEN3GsMTrZYnXyxdzc0nXTkxKqThpok+S\nrq4GqqsfJBhcTel5leweu5Q19Y2sra/Hm5FxMrnrmO5KqcHSRD/MjIlRU/M4B6sfpGX8V1mVfg9r\nm2JMzcpiidfLIq9XJ8pWSiWUJvphVN2wgT37vkVjVxc/MisoyZvDYq+XGzweisaMSXZ4SqkRSlvd\nDCFjDLvb21kX+IjI8YeZ0fUq27L/nIvK/oj1Hi85OlmHUirFDCpricgjwFeBCPAhcJcxpjkRgQ2n\n7liM37e0sDYUYm0oRHn0Xb4d+2cys7/A56fsYdHYvuZHV0qp1DCoqhsRuRp42xgTE5EfAhhj7jvt\nGFdW3bRFo7zR0MDaUIhXGxooGTOGm/KEivYfkd7+PpMn/5SCgmuTHaZS6jPKNVU3xpg3e337HrB0\ncOEMrZoTJ3ilvp61oRC/a25mXk4ON3o8PFRWRmbLKxw48Gf4/TdTNm3nJ3q1KqVUqkpkhfPdwHMJ\nPN+gGWPY095+skpmb0cHCwoKuK2wkGemTiV31CgikSD7999Bbet2pk1bTW7uF5MdtlJKJdRZE72I\nvAn0VUl9vzFmnXPMA0DEGPNsX+eorKw8uV5RUUFFRcVAYu2XqDH8vrmZNaEQL9fXcyIW40aPh++X\nlXFFXh6je/VMDYXWsm/fH1NYeBtTpjxJerrOraqUSo6qqiqqqqqG5NyDbl4pIt8A/hD4ijGms4/9\nQ15H3x6N8mZjI2tCIV6pr6dkzBgWeTws+pTOS93dzezfv4Lm5vVMmfIkeXmXDWl8SikVL9e0oxeR\nBcA/AVcYY0KfcsyQJPr6ri5eqa9nTSjErxsbmZOdzSKn89J5Y8d+6uuamtbzwQd3kJ9/LRdc8I+M\nGjU+4bEppdRguSnR7wdGAw3OpneNMd8+7ZiEJfqPOjtPjiezORxmfn4+i71ervd4KMg487yrsVgX\nhw49RG3t40ye/DO83hsSEpNSSg0F1yT6fr3BIBP9nl4jQR7q7OQGZzyZq/Pz+z21XkdHNbt330JG\nRj7l5U8wZoy2i1dKuduITvTGGLa2trI6GGR1KES4u5slPh9/4PVyeW4uo+Ic5jcQWMX+/X/KhAnf\no6RkBSI6TLBSyv1GXKI3xrAxHOaFYJAXgkEAlvp8LPX5mJudTdoARoKMRjs5cGAFTU2/ZurUlWRn\nzx5Q/EoplQyu6TA1GMYYNoTDPB8M8nwgwJi0NJb5fKyeNo0Zgxzmt739ALt3LyMzs5zZszcxalRO\nAiNXSqnUMqx39D3VMisDAVYFg4wW4Wt+P8t8PqaPG5eQMdyDwdXs2/ctJk6s5JxzvqXjwiulUlLK\nVd3saW3luUCAlYEAXcZws9/Pcr+fzyUouQPEYt1UV99PILCKadOeJydnbkLOq5RSyZByib74nXdY\n7vdzi9/P3OzshN9lRyJBdu9ejsgoLrro2Y9Nzq2UUqko5RJ9dyw2ZPOmhsOb2blzCYWFt1JW9n1E\n+tfkUiml3CzlHsYOVZKvq3uOAwfuZdKk/8Dvv2lI3kMppVJdSk6XZEyUgwcfIBhcxYwZbzN+/OeS\nHZJSSrlWyiX67u5W9uy5le7uZmbNel/r45VS6ixSqptoZ+cRtmy5jIwMHzNmvKFJXiml+iFlEn1L\ny0Y2b55HUdHtlJf/nLS00ckOSSmlUkJKVN2EQuvYu/ceyst/jte7KNnhKKVUSnF9oj927N85fPhh\npk9/hZycS5MdjlJKpRzXJnpjDAcP3kcotJaZM98hM7Ms2SEppVRKcmWij8W62Lv3m3R07GPWrHfI\nyPAkOySllEpZA070IvJ94EbAAPXAN4wxRwYbUDTaxq5dyxBJZ8aMt0lPzxrsKZVS6jNtwEMgiEi2\nMSbsrP8ZMMMY880+juv3xCNdXQ3s2HE9WVkXMXnyz0hLc+UHDqWUGnKJHAJhwM0re5K8YzzQ5+Tg\n/XXiRC1bt1aQk/Mlyssf1ySvlFIJMqhsKiIPA7cD7cC8gZ6no+MQ27bNp7j4LiZMuF/HkFdKqQQ6\nY6IXkTeBvmbSvt8Ys84Y8wDwgIjcB/wLcFdf56msrDy5XlFRQUVFxcnv29v3sW3bfEpLv0tJyZ/G\n/QMopdRIUFVVRVVV1ZCcOyHDFIvIBOA1Y8zFfez71Dr6trZdbNt2DWVl/4Pi4j7/Ryil1GeSK+ro\nRWRSr28XAVvieX04vJVt2+ZzwQWPaJJXSqkhNJg6+h+ISDkQBT4EvtXfF4bDm9m+/TomT/53fL6l\ngwhBKaXU2Qzr5ODQO8n/FJ9v8ZC+t1JKpaqUm2Gqh03yC5k8+TFN8kopNUyGbZji1tZteievlFJJ\nMCyJvq1tN9u3L2DSpH/D51syHG+plFLKMSyJftu2azj//Ed0Am+llEqCYXkYe+zYzzjnnD8c0vdR\nSqmRJJEPY4e91Y1SSqmzc0WHKaWUUqlBE71SSo1wmuiVUmqE00SvlFIjnCZ6pZQa4TTRK6XUCKeJ\nXimlRjhN9EopNcJpoldKqRFu0IleRL4jIjERKUhEQEoppRJrUIleREqBq4HDiQkneYZqUt5E0zgT\nKxXiTIUYQeN0s8He0f8z8N1EBJJsqfLL1zgTKxXiTIUYQeN0s8FMDr4IOGqM2Z7AeJRSSiXYGacS\nFJE3gaI+dj0AfA+4pvfhCYxLKaVUggxomGIRuRh4G2h3NpUAx4BLjTGB047VMYqVUmoAXDUevYhU\nA7ONMQ2DD0kppVQiJaodvd61K6WUSw35DFNKKaWSK+47ehH5TxGpE5EdvbZdKiLvi8gWEdkgInOd\n7WNF5DkR2S4iu0Xkvl6vmS0iO0Rkv4j8a2J+nLPGOUNE3nXieVlEsnvt+54Tywcick2v7a6JU0Su\nFpGNzvaNInKlG+PstX+CiLSKyHfcGqeIfM7Zt9PZP9ptcSarHIlIqYj8RkR2OdfnXmd7gYi8KSL7\nROQNEcnr9ZphL0fxxpmscjSQ6+nsH3w5MsbEtQCXAzOBHb22VQHXOusLgd84698AnnPWM4FqYILz\n/fvYh7cArwEL4o1lAHFuAC531u8C/sFZnwpsBTKAicABTn3acVOclwBFzvo0bPNW3BZnr/0vAL8E\nvuPGOLGtzrYB053v84E0F8aZlHKEbXF3ibM+HtgLXAT8CPius/1vgB8660kpRwOIMynlKN44E1mO\n4r6jN8asBxpP21wD5DrredgWOD3bx4lIOjAOiAAtIlIMZBtj3neOewpYHG8sA4hzkrMd4C1gqbO+\nCFuQuowxh7B/oJ93W5zGmK3GmFpn+24gU0Qy3BYngIgsBg46cfZsc1uc1wDbjTE7nNc2GmNiLowz\nKeXIGFNrjNnqrLcCe4BzgRuBJ53Dnuz1nkkpR/HGmaxyNIDrmbBylKiHsfcB/yQiHwGPAPcDGGN+\nBbRg/1APAY8YY5qwP9zRXq8/5mwbarvEdvQCWAaUOuvnnBbPUSee07cnO87elgKbjDFduOx6ish4\nbI/pytOOd1WcwGTAiMjrIrJJRP7ajXG6oRyJyETsJ5D3gEJjTJ2zqw4odNaTXo76GWdvSSlH/Ykz\nkeUoUYn+ceBeY8wE4C+c7xGR27AfNYuBMuCvRKQsQe85EHcD3xaRjdiPTpEkxnImZ4xTRKYBPwT+\nKAmx9fZpcVYC/2KMaccdHek+Lc5RwGXA152vS0TkKpLXiqzPOJNdjpyEsxpYYYwJ995nbN2BK1p0\nxBtnsspRHHFWkqBydMaesXG41Bgz31l/Afg/zvoXgZeMMVEgKCLvALOB/4/tZNWjp8PVkDLG7AWu\nBRCRycD1zq5jfPyuuQT7H/OYy+JEREqAF4HbjTHVzma3xHmds+tSYKmI/AhblRcTkQ4nbjfE2XM9\njwC/M07/DxF5DZgF/MIlcfZcz6SVIxHJwCalp40xa5zNdSJSZIypdaoRejpJJq0cxRln0spRnHEm\nrBwl6o7+gIhc4axfBexz1j9wvkdExgHzgA+c+rEWEfm8iAhwO7CGISYiPudrGvAg8B/OrpeBm0Vk\ntHOnNAl4321xOk/jXwX+xhjzbs/xxpgal8T5UyeeLxtjyowxZcCjwMPGmJ+47XoCvwKmi0imiIwC\nrgB2uSjOnzq7klKOnHM+Duw2xjzaa9fLwJ3O+p293jMp5SjeOJNVjuKNM6HlaABPjp8DjmM/Vh7B\ntg6Yg61r2gq8C8x0jh2DvTvaAezi40+NZzvbDwA/jjeOAcR5N3Av9kn3XuB/nnb8/U4sH+C0IHJb\nnNjC3wps6bV43Rbnaa/7e+Av3Xg9neNvBXY6Mf3QjXEmqxxhq7NiTrnu+XtbABRgHxbvA94A8pJZ\njuKNM1nlaCDXM1HlSDtMKaXUCKdTCSql1AiniV4ppUY4TfRKKTXCaaJXSqkRThO9UkqNcJrolVJq\nhNNEr5RSI5wmeqWUGuH+G3MdcAZHQPgmAAAAAElFTkSuQmCC\n", "text": [ "" ] } ], "prompt_number": 16 }, { "cell_type": "markdown", "metadata": {}, "source": [ "The samples appear very similar to those which we obtained indirectly. That is no surprise because they are effectively drawn from the same mutivariate normal density. However, when sampling $\\mathbf{f}$ directly we created the covariance for $\\mathbf{f}$. We can visualise the form of this covaraince in an image in python with a colorbar to show scale." ] }, { "cell_type": "code", "collapsed": false, "input": [ "fig, ax = plt.subplots(figsize=(8,8))\n", "im = ax.imshow(K, interpolation='none')\n", "fig.colorbar(im)" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 17, "text": [ "" ] }, { "metadata": {}, "output_type": "display_data", "png": "iVBORw0KGgoAAAANSUhEUgAAAcIAAAHMCAYAAABGEqg1AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n", "text": [ "" ] } ], "prompt_number": 17 }, { "cell_type": "markdown", "metadata": {}, "source": [ "This image is the covariance expressed between different points on the function. In regression we normally also add independent Gaussian noise to obtain our observations $\\mathbf{y}$,\n", "$$\n", "\\mathbf{y} = \\mathbf{f} + \\boldsymbol{\\epsilon}\n", "$$\n", "where the noise is sampled from an independent Gaussian distribution with variance $\\sigma^2$,\n", "$$\n", "\\epsilon \\sim \\mathcal{N}(\\mathbf{0}, \\sigma^2 \\mathbf{I}).\n", "$$\n", "we can use properties of Gaussian variables, i.e. the fact that sum of two Gaussian variables is also Gaussian, and that it's covariance is given by the sum of the two covariances, whilst the mean is given by the sum of the means, to write down the marginal likelihood,\n", "$$\n", "\\mathbf{y} \\sim \\mathcal{N}(\\mathbf{0}, \\alpha \\boldsymbol{\\Phi}\\boldsymbol{\\Phi}^\\top + \\sigma^2\\mathbf{I}).\n", "$$\n", "Sampling directly from this density gives us the noise corrupted functions," ] }, { "cell_type": "code", "collapsed": false, "input": [ "K = alpha*np.dot(Phi_pred, Phi_pred.T) + sigma2*np.eye(x_pred.size)\n", "for i in xrange(10):\n", " y_sample = np.random.multivariate_normal(mean=np.zeros(x_pred.size), cov=K)\n", " plt.plot(x_pred.flatten(), y_sample.flatten())" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": "iVBORw0KGgoAAAANSUhEUgAAAXoAAAEACAYAAAC9Gb03AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nrkJggg==\n", "text": [ "" ] } ], "prompt_number": 18 }, { "cell_type": "markdown", "metadata": {}, "source": [ "where the effect of our noise term is to roughen the sampled functions, we can also increase the variance of the noise to see a different effect," ] }, { "cell_type": "code", "collapsed": false, "input": [ "sigma2 = 1.\n", "K = alpha*np.dot(Phi_pred, Phi_pred.T) + sigma2*np.eye(x_pred.size)\n", "for i in xrange(10):\n", " y_sample = np.random.multivariate_normal(mean=np.zeros(x_pred.size), cov=K)\n", " plt.plot(x_pred.flatten(), y_sample.flatten())" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": "iVBORw0KGgoAAAANSUhEUgAAAXoAAAEACAYAAAC9Gb03AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nGs04Rwu9RqPRjHO00Gs0Gs045/8Bs0G0WMypIzEAAAAASUVORK5CYII=\n", "text": [ "" ] } ], "prompt_number": 19 }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Function Space Reflection\n", "\n", "How do you include the noise term when sampling in the weight space point of view?\n", "\n", "## Gaussian Process\n", "\n", "In our [session on Bayesian regression](./bayesian approach to regression.ipynb) we sampled from the prior over parameters. Through the properties of multivariate Gaussian densities this prior over parameters implies a particular density for our data observations, $\\mathbf{y}$. In this session we sampled directly from this distribution for our data, avoiding the intermediate weight-space representation. This is the approach taken by *Gaussian processes*. In a Gaussian process you specify the *covariance function* directly, rather than *implicitly* through a basis matrix and a prior over parameters. Gaussian processes have the advantage that they can be *nonparametric*, which in simple terms means that they can have *infinite* basis functions. In the lectures we introduced the *exponentiated quadratic* covariance, also known as the RBF or the Gaussian or the squared exponential covariance function. This covariance function is specified by\n", "$$\n", "k(\\mathbf{x}, \\mathbf{x}^\\prime) = \\alpha \\exp\\left( -\\frac{\\left\\Vert \\mathbf{x}-\\mathbf{x}^\\prime\\right\\Vert^2}{2\\ell^2}\\right).\n", "$$\n", "where $\\left\\Vert\\mathbf{x} - \\mathbf{x}^\\prime\\right\\Vert^2$ is the squared distance between the two input vectors \n", "$$\n", "\\left\\Vert\\mathbf{x} - \\mathbf{x}^\\prime\\right\\Vert^2 = (\\mathbf{x} - \\mathbf{x}^\\prime)^\\top (\\mathbf{x} - \\mathbf{x}^\\prime) \n", "$$\n", "Let's build a covariance matrix based on this function. First we define the form of the covariance function," ] }, { "cell_type": "code", "collapsed": false, "input": [ "def exponentiated_quadratic(x, x_prime, variance, lengthscale):\n", " squared_distance = ((x-x_prime)**2).sum()\n", " return variance*np.exp((-0.5*squared_distance)/lengthscale**2)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 20 }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can use this to compute *directly* the covariance for $\\mathbf{f}$ at the points given by `x_pred`. Let's define a new function `K()` which does this," ] }, { "cell_type": "code", "collapsed": false, "input": [ "def compute_kernel(X, X2, kernel, **kwargs):\n", " K = np.zeros((X.shape[0], X2.shape[0]))\n", " for i in np.arange(X.shape[0]):\n", " for j in np.arange(X2.shape[0]):\n", " K[i, j] = kernel(X[i, :], X2[j, :], **kwargs)\n", " \n", " return K" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 21 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now we can image the resulting covariance," ] }, { "cell_type": "code", "collapsed": false, "input": [ "K = compute_kernel(x_pred, x_pred, exponentiated_quadratic, variance=1., lengthscale=10.)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 22 }, { "cell_type": "markdown", "metadata": {}, "source": [ "To visualise the covariance between the points we can use the `imshow` function in matplotlib." ] }, { "cell_type": "code", "collapsed": false, "input": [ "fig, ax = plt.subplots(figsize=(8,8))\n", "im = ax.imshow(K, interpolation='none')\n", "fig.colorbar(im)" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 23, "text": [ "" ] }, { "metadata": {}, "output_type": "display_data", "png": "iVBORw0KGgoAAAANSUhEUgAAAcIAAAHWCAYAAADkX4nIAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nhAAAAABJRU5ErkJggg==\n", "text": [ "" ] } ], "prompt_number": 23 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Finally, we can sample functions from the marginal likelihood." ] }, { "cell_type": "code", "collapsed": false, "input": [ "for i in xrange(10):\n", " y_sample = np.random.multivariate_normal(mean=np.zeros(x_pred.size), cov=K)\n", " plt.plot(x_pred.flatten(), y_sample.flatten())" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": "iVBORw0KGgoAAAANSUhEUgAAAXkAAAEACAYAAABWLgY0AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n/w+tDSt7ZtfSrwAAAABJRU5ErkJggg==\n", "text": [ "" ] } ], "prompt_number": 24 }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Exercise: Moving Parameters\n", "\n", "Have a play with the parameters for this covariance function (the lengthscale and the variance) and see what effects the parameters have on the types of functions you observe." ] }, { "cell_type": "code", "collapsed": false, "input": [], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 101 }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Gaussian Process\n", "\n", "The Gaussian process perspective takes the marginal likelihood of the data to be a joint Gaussian density with a covariance given by $\\mathbf{K}$. So the model likelihood is of the form,\n", "$$\n", "p(\\mathbf{y}|\\mathbf{X}) = \\frac{1}{(2\\pi)^{\\frac{n}{2}}|\\mathbf{K}|^{\\frac{1}{2}}} \\exp\\left(-\\frac{1}{2}\\mathbf{y}^\\top \\left(\\mathbf{K}+\\sigma^2 \\mathbf{I}\\right)^{-1}\\mathbf{y}\\right)\n", "$$\n", "where the input data, $\\mathbf{X}$, influences the density through the covariance matrix, $\\mathbf{K}$ whose elements are computed through the covariance function, $k(\\mathbf{x}, \\mathbf{x}^\\prime)$.\n", "\n", "This means that the negative log likelihood (the objective function) is given by,\n", "$$\n", "E(\\boldsymbol{\\theta}) = \\frac{1}{2} \\log |\\mathbf{K}| + \\frac{1}{2} \\mathbf{y}^\\top \\left(\\mathbf{K} + \\sigma^2\\mathbf{I}\\right)^{-1}\\mathbf{y}\n", "$$\n", "where the *parameters* of the model are also embedded in the covariance function, they include the parameters of the kernel (such as lengthscale and variance), and the noise variance, $\\sigma^2$.\n", "\n", "Let's create a class in python for storing these variables." ] }, { "cell_type": "code", "collapsed": false, "input": [ "class GP():\n", " def __init__(self, X, y, sigma2, kernel, **kwargs):\n", " self.K = compute_kernel(X, X, kernel, **kwargs)\n", " self.X = X\n", " self.y = y\n", " self.sigma2 = sigma2\n", " self.kernel = kernel\n", " self.kernel_args = kwargs\n", " self.update_inverse()\n", " \n", " def update_inverse(self):\n", " # Preompute the inverse covariance and some quantities of interest\n", " ## NOTE: This is not the correct *numerical* way to compute this! It is for ease of use.\n", " self.Kinv = np.linalg.inv(self.K+self.sigma2*np.eye(self.K.shape[0]))\n", " # the log determinant of the covariance matrix.\n", " self.logdetK = np.linalg.det(self.K+self.sigma2*np.eye(self.K.shape[0]))\n", " # The matrix inner product of the inverse covariance\n", " self.Kinvy = np.dot(self.Kinv, self.y)\n", " self.yKinvy = (self.y*self.Kinvy).sum()\n", "\n", " \n", " def log_likelihood(self):\n", " # use the pre-computes to return the likelihood\n", " return -0.5*(self.K.shape[0]*np.log(2*np.pi) + self.logdetK + self.yKinvy)\n", " \n", " def objective(self):\n", " # use the pre-computes to return the objective function \n", " return -self.log_likelihood()" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 26 }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Making Predictions\n", "\n", "We now have a probability density that represents functions. How do we make predictions with this density? The density is known as a process because it is *consistent*. By consistency, here, we mean that the model makes predictions for $\\mathbf{f}$ that are unaffected by future values of $\\mathbf{f}^*$ that are currently unobserved (such as test points). If we think of $\\mathbf{f}^*$ as test points, we can still write down a joint probability density over the training observations, $\\mathbf{f}$ and the test observations, $\\mathbf{f}^*$. This joint probability density will be Gaussian, with a covariance matrix given by our covariance function, $k(\\mathbf{x}_i, \\mathbf{x}_j)$. \n", "$$\n", "\\begin{bmatrix}\\mathbf{f} \\\\ \\mathbf{f}^*\\end{bmatrix} \\sim \\mathcal{N}\\left(\\mathbf{0}, \\begin{bmatrix} \\mathbf{K} & \\mathbf{K}_\\ast \\\\ \\mathbf{K}_\\ast^\\top & \\mathbf{K}_{\\ast,\\ast}\\end{bmatrix}\\right)\n", "$$\n", "where here $\\mathbf{K}$ is the covariance computed between all the training points, $\\mathbf{K}_\\ast$ is the covariance matrix computed between the training points and the test points and $\\mathbf{K}_{\\ast,\\ast}$ is the covariance matrix computed betwen all the tests points and themselves. To be clear, let's compute these now for our example, using `x` and `y` for the training data (although `y` doesn't enter the covariance) and `x_pred` as the test locations." ] }, { "cell_type": "code", "collapsed": false, "input": [ "# set covariance function parameters\n", "variance = 16.0\n", "lengthscale = 32\n", "# set noise variance\n", "sigma2 = 0.05\n", "\n", "K = compute_kernel(x, x, exponentiated_quadratic, variance=variance, lengthscale=lengthscale)\n", "K_star = compute_kernel(x, x_pred, exponentiated_quadratic, variance=variance, lengthscale=lengthscale)\n", "K_starstar = compute_kernel(x_pred, x_pred, exponentiated_quadratic, variance=variance, lengthscale=lengthscale)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 27 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now we use this structure to visualise the covariance between test data and training data. This structure is how information is passed between trest and training data. Unlike the maximum likelihood formalisms we've been considering so far, the structure expresses *correlation* between our different data points. However, we now have a *joint density* between some variables of interest. In particular we have the joint density over $p(\\mathbf{f}, \\mathbf{f}^*)$. The joint density is *Gaussian* and *zero mean*. It is specified entirely by the *covariance matrix*, $\\mathbf{K}$. That covariance matrix is, in turn, defined by a covariance function. Now we will visualise the form of that covariance in the form of the matrix,\n", "$$\n", "\\begin{bmatrix} \\mathbf{K} & \\mathbf{K}_\\ast \\\\ \\mathbf{K}_\\ast^\\top & \\mathbf{K}_{\\ast,\\ast}\\end{bmatrix}\n", "$$" ] }, { "cell_type": "code", "collapsed": false, "input": [ "fig, ax = plt.subplots(figsize=(8,8))\n", "im = ax.imshow(np.vstack([np.hstack([K, K_star]), np.hstack([K_star.T, K_starstar])]), interpolation='none')\n", "# Add lines for separating training and test data\n", "ax.axvline(x.shape[0]-1, color='w')\n", "ax.axhline(x.shape[0]-1, color='w')\n", "fig.colorbar(im)" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 28, "text": [ "" ] }, { "metadata": {}, "output_type": "display_data", "png": "iVBORw0KGgoAAAANSUhEUgAAAcQAAAHWCAYAAADpQfmPAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nhBACgBZEIYQQAoAWRCGEEAIA8P8DbPxAZZG6AZUAAAAASUVORK5CYII=\n", "text": [ "" ] } ], "prompt_number": 28 }, { "cell_type": "markdown", "metadata": {}, "source": [ "There are four blocks to this color plot. The upper left block is the covariance of the training data with itself, $\\mathbf{K}$. We see some structure here due to the missing data from the first and second world wars. Alongside this covariance (to the right and below) we see the cross covariance between the training and the test data ($\\mathbf{K}_*$ and $\\mathbf{K}_*^\\top$). This is giving us the covariation between our training and our test data. Finally the lower right block The banded structure we now observe is because some of the training points are near to some of the test points. This is how we obtain 'communication' between our training data and our test data. If there is no structure in $\\mathbf{K}_*$ then our belief about the test data simply matches our prior.\n", "\n", "## Conditional Density\n", "\n", "Just as in naive Bayes, we first defined the joint density (although there it was over both the labels and the inputs, $p(\\mathbf{y}, \\mathbf{X})$ and now we need to define *conditional* distributions that answer particular questions of interest. In particular we might be interested in finding out the values of the function for the prediction function at the test data given those at the training data, $p(\\mathbf{f}_*|\\mathbf{f})$. Or if we include noise in the training observations then we are interested in the conditional density for the prediction function at the test locations given the training observations, $p(\\mathbf{f}^*|\\mathbf{y})$. \n", "\n", "As ever all the various questions we could ask about this density can be answered using the *sum rule* and the *product rule*. For the multivariate normal density the mathematics involved is that of *linear algebra*, with a particular emphasis on the *partitioned inverse* or [*block matrix inverse*](http://en.wikipedia.org/wiki/Invertible_matrix#Blockwise_inversion), but they are beyond the scope of this course, so you don't need to worry about remembering them or rederiving them. We are simply writing them here because it is this *conditional* density that is necessary for making predictions.\n", "\n", "The conditional density is also a multivariate normal,\n", "$$\n", "\\mathbf{f}^* | \\mathbf{y} \\sim \\mathcal{N}(\\boldsymbol{\\mu}_f,\\mathbf{C}_f)\n", "$$\n", "with a mean given by\n", "$$\n", "\\boldsymbol{\\mu}_f = \\mathbf{K}_*^\\top \\left[\\mathbf{K} + \\sigma^2 \\mathbf{I}\\right]^{-1} \\mathbf{y}\n", "$$\n", "and a covariance given by \n", "$$\n", "\\mathbf{C}_f = \\mathbf{K}_{*,*} - \\mathbf{K}_*^\\top \\left[\\mathbf{K} + \\sigma^2 \\mathbf{I}\\right]^{-1} \\mathbf{K}_\\ast.\n", "$$\n", "Let's compute what those posterior predictions are for the olympic marathon data." ] }, { "cell_type": "code", "collapsed": false, "input": [ "def posterior_f(self, X_test):\n", " K_starstar = compute_kernel(X_test, X_test, self.kernel, **self.kernel_args)\n", " K_star = compute_kernel(self.X, X_test, self.kernel, **self.kernel_args)\n", " A = np.dot(self.Kinv, K_star)\n", " mu_f = np.dot(A.T, y)\n", " C_f = K_starstar - np.dot(A.T, K_star)\n", " return mu_f, C_f\n", "\n", "# attach the new method to class GP():\n", "GP.posterior_f = posterior_f" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 32 }, { "cell_type": "code", "collapsed": false, "input": [ "model = GP(x, y, sigma2, exponentiated_quadratic, \n", " variance=variance, lengthscale=lengthscale)\n", "mu_f, C_f = model.posterior_f(x_pred)\n" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 34 }, { "cell_type": "markdown", "metadata": {}, "source": [ "where for convenience we've defined\n", "\n", "$$\\mathbf{A} = \\left[\\mathbf{K} + \\sigma^2\\mathbf{I}\\right]^{-1}\\mathbf{K}_*.$$ \n", "\n", "We can visualize the covariance of the *conditional*," ] }, { "cell_type": "code", "collapsed": false, "input": [ "fig, ax = plt.subplots(figsize=(8,8))\n", "im = ax.imshow(C_f, interpolation='none')\n", "fig.colorbar(im)" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 35, "text": [ "" ] }, { "metadata": {}, "output_type": "display_data", "png": "iVBORw0KGgoAAAANSUhEUgAAAcgAAAHMCAYAAABRMDj8AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n/wHTT20xe4Vr7gAAAABJRU5ErkJggg==\n", "text": [ "" ] } ], "prompt_number": 35 }, { "cell_type": "markdown", "metadata": {}, "source": [ "and we can plot the mean of the conditional" ] }, { "cell_type": "code", "collapsed": false, "input": [ "plt.plot(x, y, 'rx')\n", "plt.plot(x_pred, mu_f, 'b-')" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 36, "text": [ "[]" ] }, { "metadata": {}, "output_type": "display_data", "png": "iVBORw0KGgoAAAANSUhEUgAAAXwAAAEACAYAAACwB81wAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAALEgAACxIB0t1+/AAAIABJREFUeJzt3XmYFNXVx/HvYV9ExyCbioq7uIWgoKBh1IiIBrck+LrH\nLLwuUeMuLiAR0agx+sYFE6OCUYnigiJBILRRjFERBEUMIqCggIojIuvAef+4NdIMM0P3TE9XL7/P\n88wzXVW3q8801OnqU7fuNXdHREQKX4O4AxARkexQwhcRKRJK+CIiRUIJX0SkSCjhi4gUCSV8EZEi\n0SiVRmY2H1gOrAfWuXu3SttLgeeAj6JVo939psyFKSIidZVSwgccKHX3ZTW0ednd+2UgJhERqQfp\nlHSsjttFRCRGqSZ8Byaa2Vtm9qtqtvcws3fM7EUz65y5EEVEJBNSLen0dPfPzKwNMMHMZrv7K0nb\n3wY6uvtKMzsWeBbYM9PBiohI7Vm6Y+mY2SBghbvfUUObeUDX5Jq/mWnQHhGRWnD3jJTMt1jSMbMW\nZtYqetwS6A3MrNSmnZlZ9Lgb4YNkswu87p7zP4MGDYo9BsWpGBWn4qz4yaRUSjrtgGeifN4I+Ju7\nv2RmA6IkPhz4CXCemZUDK4FTMxqliIjU2RYTvrvPA75fxfrhSY/vAe7JbGgiIpJJutO2ktLS0rhD\nSInizJx8iBEUZ6blS5yZlPZF21q/kJln67VERAqFmeHZumgrIiKFQQlfRKRIKOGLiBQJJXwRkSKh\nhC8iUiSU8EVEioQSvohIkVDCFxEpEkr4qRg7FsrKNl1XVhbWi4jkCSX8VPTsCddeuzHpl5WF5Z49\n441LRCQNGlohVRVJ/oor4LbbYOhQKCmJOyoRKXCZHFpBCT8d8+dDp04wbx7sskvc0YhIEdBYOnEo\nKwtn9vPmhd+Va/oiIjlOCT8VFeWcoUPDmf3QoZvW9EVE8oBKOqkYOzZcoE2u2ZeVwZQpcNxx8cUl\nIgVPNXwRkSKhGr6IiKRNCV9EpEgo4YuIFAklfBGRIqGELyJSJFJK+GY238xmmNk0M3ujmjZ3m9kc\nM3vHzLpkNkwREamrRim2c6DU3ZdVtdHM+gK7u/seZtYduA84JEMxiohIBqRT0qmpH2g/4BEAd/8P\nUGJm7eoSmIiIZFaqCd+BiWb2lpn9qortOwCfJC0vBHasa3AiIpI5qZZ0err7Z2bWBphgZrPd/ZVK\nbSp/A9jsttrBgwd/97i0tJTS0tI0QhURKXyJRIJEIlEv+057aAUzGwSscPc7ktbdDyTc/YloeTbQ\ny92XJLXR0AoiImnK6tAKZtbCzFpFj1sCvYGZlZqNAc6K2hwClCUnexERiV8qJZ12wDNmVtH+b+7+\nkpkNAHD34e7+opn1NbMPgW+Bn9dbxCIiUisaLVNEJIdptEwREUmbEr6ISJFQwhcRKRJK+CIiRUIJ\nX0SkSCjhi4gUCSV8EZEioYQvIlIklPBFRIqEEr6ISJFQwhcRKRJK+CIiRUIJX0SkSCjhi4gUCSV8\nEZEioYQvIlIklPBFRIpEKlMc5q1162D2bJg5E8xg223DT+fO0KpV3NGJiGRXwSX8tWvhiSfgvvtg\nxgzYaSc44ICQ8L/6Cr78Ev77X+jZE/r1g1NOgbZt445aRKT+FcyctmvXwp/+BHfeCXvtBZdeCr16\nQcuWm7ddvhzGj4fnnoNx42DAALjySigpqbfwRERqJZNz2hZEwp87F049Fdq0gZtugh/8IPXnfvwx\nDBkSkv8118All0ADXdkQkRyhhJ/k73+HCy+E666D3/wmlG5qY/Zs+PWvoUkTGDECtt8+s3GKiNRG\nJhN+Xp/L3nQTDBwYyjIXXVT7ZA+w997wz3/CD38YviG88ELm4hQRyQUpneGbWUPgLWChu/+40rZS\n4Dngo2jVaHe/qYp9ZPQM/9Zb4aGHIJGA9u0ztlsAXn01lIiuuAIuvjiz+xYRSUcmz/BT7aVzMTAL\nqK4z48vu3i8TAaXizjvhz3+Gl1/OfLIHOOwwmDIF+vSBTz+FYcNU1xeR/LfFNGZmOwJ9gb8A1X3K\nZOTTJxUPPQR33x3KLzvsUH+vs/PO4Uz/lVfgnHOgvLz+XktEJBtSOW+9E7gC2FDNdgd6mNk7Zvai\nmXXOWHSVTJsWuk+OGxf616dk7FgoK9t0XVlZWL8FrVvDxImwdGlI+uvXpx2yiEjOqLGkY2bHA0vd\nfVpUq6/K20BHd19pZscCzwJ7VtVw8ODB3z0uLS2ltLS6XW7u66/hpz8Nfe333jvlp4U7rK69FoYO\nDR3ty8o2LlcYOza0S+6IX1YGU6bQ4rjjeOYZ6NsXzjsPhg+v28VhEZGaJBIJEolEvey7xou2ZnYz\ncCZQDjQDtiZclD2rhufMA7q6+7JK62t90dY93BHboQPcc08tdlCR5K+4Am67bWPyr7y9qg+FqN03\n30Dv3tC9e7iGoKQvItkQSz98M+sFXF5FL512hG8BbmbdgL+7+y5VPL/WCf/uu2HkyFBTb9q0VruA\n+fOhUyeYNw922Sy8LX8oRE2OPDJ8+Fx7bS3jEBFJQxy9dCp4FMAAAHcfDvwEOM/MyoGVwKmZCKzC\n/PnhTtjXX69Dsi8rC0l83rxqkzklJSHZV3woVDHOQklJ6J9/6KGw++7Qv38t4xERiUFO32nrDscf\nH7pJXnNNLV84hXLNJu1qOMOvMGMG/OhH8Oyz0KNHLeMSEUlB0Qyt8NRTMGhQ6J3TpEktX7iGC7Ic\nd9zG5VQ+FJKMGwfnnhvKTLvtVsvYRES2oCgS/tdfh3HrR40KZ/j1KpUPhSr86U+h186//w1bbVXP\nMYpIUSqKhP+b38CaNfDAA/UYVB25h7P8lSvDGPzquSMimVbwCf+DD8JZ/QcfwPe+V8+B1dHq1XD4\n4eEC7uWXxx2NiBSagk/4P/tZGLHy6qvrOagM+fjj0D9/5MhwMVdEJFMKOuG/9RaccALMmQMtWmQh\nsAyZPBlOOw2mTtVY+iKSOQU9Hv7AgXD99fmV7AGOOAIuuCAMq6yB1kQkF+VUwp80CT76CH7xi7gj\nqZ2BA8MH1fXXxx2JiMjmcibhu4eE+bvfQePGcUdTOw0ahDr+o4+mNBiniEhW5UzCnzgRVqzI/+EK\n2rSBxx8P31IWLow7GhGRjXIm4d96axjrvhBmljrssHAfwemnawx9EckdOZFep04Nfe7/53/ijiRz\nrr4aGjUKE62LiOSCnOiW2b9/6Md+6aVZCSVrPvss3E/wxBPQq1fc0YhIPiqofvhz54ZkP28etKpu\nivQ89o9/wK9+BdOnhykTRUTSUVD98G+/HQYMKIBkX83cuX3Wj6V//zDmTpY+W0VEqhRrwl+6NJQ7\nLroozigypGLu3IqkXzHEcs+e3HwzLFoE994bb4giUtxiLekMGxaGUPjrX7MSQv2rYRKVOXPCZCmT\nJsEBB8Qcp4jkjYKo4a9fHyYOGT0aunbNSgjZUcPcuSNHhg+5N9+Eli1jiU5E8kxB1PDHjYN27Qos\n2VeeO7dSTf/MM8Pfe8klMcUnIkUttoR/771w/vlxvXo9SJ4WcZddwu/kmn7k3nshkQgzeYmIZFMs\nJZ25c+GQQ8I48s2bZ+Xl618a0yROnQrHHguvvw677prlOEUkr+R9Df/KK2HDhtAls1j98Y/w2GNh\nEvRaT9AuIgUvrxP+6tWw007w2muw++5Zeemc5A79+sFeexX3B5+I1CzrF23NrKGZTTOz56vZfreZ\nzTGzd8ysS037Gj0aunQp7mQPYcLzhx+GJ5+EMWPijkZEikGqF20vBmYBm30dMLO+wO7uvgfwa+C+\nmnb00EP5O8FJprVuHW48+9WvYMGCuKMRkUK3xYRvZjsCfYG/AFV9regHPALg7v8BSsysXVX7WrAA\npk0LpQwJDj003KfVvz+sXRt3NCJSyFI5w78TuALYUM32HYBPkpYXAjtW1XDkyJDYmjVLK8aCd9ll\n0LZtSPwiIvWlUU0bzex4YKm7TzOz0pqaVlqu8krwH/4wmFNOgcGDobS0lNLSmnZZPMzgkUfgoINC\nd9VCmhdARNKTSCRIJBL1su8ae+mY2c3AmUA50AzYGhjt7mcltbkfSLj7E9HybKCXuy+ptC/v3Nl5\n992Q4GRz77wDP/oR/POfsP/+cUcjIrkga7103H2gu3d0907AqcA/k5N9ZAxwVhTYIUBZ5WRf4Zxz\nlOxrcuCBcOedcPLJm4+0LCJSV+kOreAAZjbAzAYAuPuLwEdm9iEwHKh2wIQzzqhtmAWgmvHyGTt2\nk1VnnAF9+oTfmg9XRDIp9hmvikbyWDslJZsvJ1m3Dnr3hm7dwuTuIlK88vpO26JWw3j5lX35ZZj6\n8YYb4KzKRTQRKRpK+PmshvHyK5s1C0pL4bnnQn99ESk+BTEeflHawnj5lXXuHIZfOOWUMMKoiEhd\nKOFnS4rj5VfWty8MGhQu5C5duoXXSPHCsIgUJyX8bJkyZdOafUlJWJ4yZYtPHTAATj0Vjj8evv22\nhoY1TKQuIqIafp5wh3PPDWf5zzxTwxj6aVwYFpHcp4u2RWrdulDPb9IkjLLZqLqBMdK4MCwiuU0X\nbYtU48Zh/PwVK0JXzSpvzErzwrCIFA8l/DzTtGko6SxZEuYV2CTp1/LCsIgUB5V08tS334aLuO3a\nwYgRUU0/jYnURSQ/qIYvAKxaFXrvrF0bpo5s0SLuiEQk01TDFwCaNw+Jvm1bOPpoWLYs7ohEJJcp\n4ee5Ro3CPME9eoSxd95/P+6IRCRXKeEXgAYNQoeca6+FXr0K4MZa3TEsUi+U8AvIOeeEgdZ+/WsY\nMgTKy+OOqJZ0x7BIvdBF2wK0aBGcfTasXg2PPpqn917pjmERQBdtZQt22AFeeglOOgkOPjiMuOlO\nfpVKSkpCsu/UKfxWshepMyX8AtWgAVx2WUj8//d/YVz9d7c9PH9KJbpjWCTjlPALXJcu8MYb0L8/\nHHHC1vzW7+DzS4eF8XaqmmIxF74F6I5hkXqhhF8EGjaE88+H996DtdaMvZ6+mas6jeKLX1y1eakk\nFy6Y1mEoaRGpni7a5pNMDJ1QVsYnF93GzRuuYtRTDfnJqY047+KmdOmyaRtdMBXJDbpoW6zqevYd\nte949xXc9+jWzHqnnJ3ef4kTfryBQw4Jtf5Fi9AFU5ECpTP8fFOXs+9qviGU/+s1xjfsy5NPwpgx\nsPfu5Rxr4zji8oPoNmkYTW4ZsvE5GqBNJKuyOniamTUDXgaaAk2A59z9mkptSoHngI+iVaPd/aZK\nbZTwM6UeJzhZu7SMyb94lAm7/JLEv5vxwQdOl1Zz6dKvI10OacoBnb5hj0cH0eq2G0LST77Aqm8C\nIhmX9dEyzayFu680s0bAq8Dl7v5q0vZS4FJ371fDPpTwM6G+6+uVzuDLyuCtxAqmjfmEaav34d13\nYe5cp5V/w26dm9Dx63fZ4Zj92GHXZrRvH4ZrbtcuDOjWunW4YCwitRfb8Mhm1oJwtn+2u89KWl8K\nXObuP67huUr4dVX5bDqms+sNG+CzNz5h7qGns+iu0Sxc04aFC8OkLBU/S5eG8LbZJiT/ig+C9u3D\njWE77AAdO8Kuu8L224f7BkRkc3Gc4TcA3gZ2A+5z9ysrbe8FPA0sBBYRvgHMqtRGCb+ucqV+nuK3\njPXr4csvQ/JfujR8ECxeHC4Mf/opLFgQqlLLloXKVOfOsO++sN9+0LUr7LYbWEb+m4vkrzjP8LcB\nxgNXu3siaX0rYH1U9jkWuMvd96z0XB80aNB3y6WlpZSWltYtesm+eviWsWoVzJ0b7hOYNQtmzoS3\n3gpz9x58MBx+OBxxRHjcpEmG/x6RHJNIJEgkEt8t33jjjfHNeGVm1wOr3P32GtrMA7q6+7KkdTrD\nLwRZ/JaxeHG4S/jll2HyZPjwwzBExI9/HKZ37NAhN+IUqU/Z7qWzHVDu7mVm1pxwhn+ju09KatMO\nWOrubmbdgL+7+y6V9qOEL3WybBmMHx+6jv7jH7D33nDaafCzn4XrA5vIkesdInWV7YS/P/AI4Sat\nBsBId7/NzAYAuPtwM7sAOA8oB1YSeuy8Xmk/SviSMevWwcSJ8Nhj8PzzcOih8MtfQr9+0Lhx1Eh3\nDEsB0CTmIkklm5Ur4emn4c/3lfPBrHLOGdCMCy4IvYDq854FkWzQ0AoiScNMtGgBZxxfxsvfv5jE\n+LWsXg0HHginnryW1y97UkMsi0R0hi/5q4aSzfKPy/jraRO565OT2LlTQ675zQp6T7oKu1llHckv\nKumIVKiuZBOVfMq3KmHUKBg2DJo2KueGH0+n35CD1L9f8oZKOiJQ86xYxx0HJSU0agSnnw4zZsD1\ngxsx6PmDOOggeOGFaNrHusiFyWJE0qCEL/kpzVmxGjSAE0+Et98OzQYODD17Jk+uQwy5MFmMSBpU\n0pH8VMcbqzZsgFGj4Prrw3g+w4aF4RzSpq6fUs9UwxfJkHXr4MEHYcgQ6NULbropjOGTFnX9lHqk\nGr5IhjRuDP/7vzBnThi4rXt3uOgi+PzzFHdQ03UEkRyjhC8CtGwJ110H778flvfZJ1Rnvv22hiel\neR1BJG4q6YhU4cMPQ+5+9VUYNAjOPRcaNarUSAO0SRaohi+SJW++CVddFcbvv/lmOOkkjdEv2aUa\nvkhdpdiH/uCDYdIkuOsu+N3vQo1/woQM9OEXiYESvhSnNPrQm8Exx8DUqXD55XDhhXDkkaHcI5JP\nVNKR4lXLPvTl5TBiROjC2akTDB4cZuUSqQ+q4YtkSh360K9bByNHhs+JHXcMtf5jj83DGr8uPuc0\n1fBFMqGOfegbNw69dz74AAYMgGuuCcMyjxgBa9ZEjfJhvJ1Uylv58HfIlrl7Vn7CS4nkiK++cj//\n/PC7qmV39xde2HS5ot0LL1S5yw0b3MeNc+/d271tW/drr3X/eGbZll8nF1TENW9e1fGl8n5JvYhy\nZ2bycKZ2tMUXUsKXXJJKMq9Dkps92/3CC9233db9mKPW+hNH/8VXzZ6ffpJM80OnTubNCylh3ryq\nt2/pQ6Em2fw7CkwmE75q+CI1qePgaCtXwrPPwkP3ruLtKSs57qSmnHL2VvTuDc2bp/H6dZmMPZUa\nfTV/59q1sHhxuA9h6VL4as7nLLv8ZpZfcgNrW2zLmjXhInaTJtC0afibttsuTCrftm0Yl6hNG7Cv\nNal8bemirUg21XVwtCi5fXrW1TxzxWs85SczbWZjDj8cjt7+PY4+tyN7d9t648XeFJNxuq9fVbIt\n36qET95bztzrH2buEb/ko8UtmD9nLfOnfMp834mvyhrQrh1svz20KVlH6wVT+V7PfWg1YwpNjzmC\nJts0p2FDWDfzfdZ02IVV3pwvvggfDp8tLOfD/26Axk3Yay/out8aesx/jB6Djmbnx4Zp9rEUZTLh\nq6QjUpO6lDGSn1+pLPT5h2U+apT7L85c7Tu3+sK/t+1679PH/YYrV/noY4b7u6997atXJ+2npnJL\nDeWS9evdlyxxf2vych99zHC/feCXfv5+Ce9z1FrfYw/3pk3dd9xupffquc7PPdd96FD3xx5zf238\ncl/0yARfv77mv2NLyxuWfeVLl7q//LL77be7n9xnhbfjM+/Uca1fcon75Mnu69al95YWG1TSEcmC\nLJZTPrvkVt7ocQlvDJ/Gu+2OYvbcxixYEEojHdqW0/7L92jbfVdaznqTrXr3oPm2zYAwrv/6b1ex\ncvwrrPhBL75Z25QvF69j6fRP+bxZRz5b0oBWraBjR9hpu5V0mvgAu95wJp0Oas3uu4cvLs2aZe7v\nqPGbSLTdL7+CGVc/xnO7/Zbnxjdn0SI4+2z45S9hjz1Se1uLiUo6ItmQzf7pVZSN1q2DhbOWs3jI\nA3x24nl8vrIl336xim/HTGRlj6Ox5s1o0CD0+2/ZYBVbTX6erfodSevJT9L2t2fQZtdWdOgQXSvI\n1kQt1ZW/avjwnL24hAcfDN1Z99sv3M9w9NFV3M9QpPcLZK2kAzQD/gNMB2YBw6ppdzcwB3gH6FJN\nm/r5viOS72oqG6XTu6W6sk+2ulTW8e9Ys8Z9xAj3zp3dDzrI/ZlnQlfXrP8dOYZsdssEWkS/GwGv\nA4dV2t4XeDF63B14vZr91OubIpKXMpXEMvWhUVuZ+DuiONevd3/6afcDD3Tv2X2dv/GHVzZ/ndpe\nU8lDWU34vjFhtwDeBDpXWn8/0D9peTbQrorn1+d7IpKfMpGMc+HMtx7+jvIvvvIHjxjpHdqv9zPO\ncF+8OGq3pfsFCky2z/AbRCWdb4DfV7H9eaBH0vJEoGsV7er1TREpWoV0U1MVZ/DLl7tfdVW4e3nk\n/St8w3k6w6/tT8oXbc1sG2A8cLW7J5LWPw/c4u5TouWJwJXu/nal5/ugQYO+Wy4tLaW0tDSl1xaR\nIlLNhd+piW849ydf07FrOx54qDHbtyjMm7cSiQSJROK75RtvvBGPo5eOmV0PrHL325PW3Q8k3P2J\naHk20Mvdl1R6rqfzWiJShGrqTTR2LGsP7snQe0p44AF4+GE4prt66aS1r5qSsJltB5S7e5mZNSec\n4d/o7pOS2vQFLnT3vmZ2CPBHdz+kin0p4YtI9dK47yGRgDPOgLPOgiFDqphvuIBkM+HvDzxCqOM3\nAEa6+21mNgDA3YdH7f4E9AG+BX5euZwTtVHCF5HqpdnPfulSOPPMcL/Ck09C69ZZjDWLdOOViAiw\nfn2Yh+CZZ2DMGNhnn7gjyjxNgCIiAjRsCL//faj89OoF48fHHVFu0xm+iBSEV1+Fn/wE7rgDTj89\n7mgyJ5Nn+AV8qUNEislhh8GkSdCnD3zxBVx8cdwR5R4lfBEpGPvuG870e/cOSX/IkDycVL4eKeGL\nSEHZeeeQ9I8+OvTgGTZMSb+CEr6IFJw2bUJ556ijwrKSfqCELyIFqXVrJf3K1C1TRApWRdJ/8cVw\nw26x0xm+iBS01q1D//zDD4dtt4ULLog7ovgo4YtIwevQASZMCEm/pKSw+umnQwlfRIpCp07hTP+o\no8JZf58+cUeUfbrTVkSKymuvwYknhjP+Aw+MO5ot01g6IiK11KMH3HMPHH88LFwYdzTZpZKOiBSd\nn/4UFiyAvn3DTVpbbx13RNmhko6IFCX30GNnwYIwtHLDhnFHVDWVdERE6sgM7roLVq0KY+oXAyV8\nESlajRuH2bJGj4aRI+OOpv6ppCMiRe+996C0FF54Abp3jzuaTamkIyKSQfvuCw8+GCZQWbIk7mjq\nj87wRUQi110X5kyfMAEa5UgfRk1iLiJSD9avh+OOg/33h9tuizuaQCUdEZF60LAh/O1v8NRT4WJu\nodEZvohIJVOnhrF2XnsN9tgj3liyeoZvZh3NbLKZvWdm75rZRVW0KTWzr81sWvRzXSaCExGJQ9eu\ncOON8LOfwerVcUeTOVs8wzez9kB7d59uZlsBU4ET3f39pDalwKXu3q+G/egMX0Tyhjv07w/bbQf3\n3htfHFk9w3f3xe4+PXq8Angf2L6quDIRkIhILjCDP/8ZXnoJRo2KO5rMSOuirZntAnQB/lNpkwM9\nzOwdM3vRzDpnJjwRkfhssw38/e9w4YUwd27c0dRdyj1No3LOU8DF0Zl+sreBju6+0syOBZ4F9qy8\nj8GDB3/3uLS0lNLS0lqELCKSPT/4AVx7LZx2WhhZs3Hj+n29RCJBIpGol32n1EvHzBoDLwDj3P2P\nKbSfB3R192VJ61TDF5G85B7Gzz/gABg2LLuvne1eOgY8CMyqLtmbWbuoHWbWjfBBsqyqtiIi+cYM\nHnoIRoyASZPijqb2UumlcxjwL2AGoVYPMBDYCcDdh5vZBcB5QDmwktBj5/VK+9EZvojktQkT4Oc/\nh+nTQ++dbNDQCiIiMbn8cpg3L9yNa1nom6ihFUREYjJ0KMyZAw8/HHck6dMZvohImmbOhCOPhNdf\nh912q9/X0hm+iEiM9t8fBg6EM8+E8vK4o0mdEr6ISC1cfDG0aAG33hp3JKlTSUdEpJY++STcmDVh\nAnz/+/XzGirpiIjkgI4d4Y47QmlnzZq4o9kyneGLiNSBO5x8Muy1F9xyS+b3r374IiI5ZOlSOPDA\n0De/Z8/M7lslHRGRHNK2LTz+OLRvH3ckNdMZvohIDtMZvoiIpE0JX0SkSCjhi4gUCSV8EZEioYQv\nIlIklPBFRIqEEr6ISJFQwhcRKRJK+CIiRUIJX0SkSCjhi4gUCSV8EZEiscWEb2YdzWyymb1nZu+a\n2UXVtLvbzOaY2Ttm1iXzoYqISF2kcoa/Dvitu+8LHAJcYGb7JDcws77A7u6+B/Br4L6MR5oliUQi\n7hBSojgzJx9iBMWZafkSZyZtMeG7+2J3nx49XgG8D2xfqVk/4JGozX+AEjNrl+FYsyJf/hMozszJ\nhxhBcWZavsSZSWnV8M1sF6AL8J9Km3YAPklaXgjsWJfAREQks1JO+Ga2FfAUcHF0pr9Zk0rLmu1E\nRCSHpDTjlZk1Bl4Axrn7H6vYfj+QcPcnouXZQC93X5LURh8AIiK1kKkZrxptqYGZGfAgMKuqZB8Z\nA1wIPGFmhwBlyckeMhewiIjUzhbP8M3sMOBfwAw2lmkGAjsBuPvwqN2fgD7At8DP3f3teopZRERq\nIWuTmIuISLxqfaetmf3VzJaY2cykdd3M7A0zm2Zmb5rZwdH6Zmb2uJnNMLNZZnZ10nO6mtnM6Kat\nu+r256Qc54Fm9u8onjFm1ipp2zVRLLPNrHcuxmlmR5vZW9H6t8zsiFyMM2n7Tma2wswuy9U4zeyA\naNu70fYm9R1nmv/mcR5DVd58aWbfM7MJZvZfM3vJzEqSnpP14yjdOOM6jmrzfkbb634cuXutfoDD\nCV00ZyatSwDHRI+PBSZHj88BHo8eNwfmATtFy28A3aLHLwJ9ahtTGnG+CRwePf45MCR63BmYDjQG\ndgE+ZOO3oFyK8/tA++jxvsDCpOfkTJxJ258CRgGX5WKchGtZ7wD7R8vbAg3qO840Y4zzGGoPfD96\nvBXwAbAP8Hvgymj9VcAt0eNYjqNaxBnLcZRunJk8jmp9hu/urwBfVVr9GbBN9LgEWJS0vqWZNQRa\nAmuB5Wbz91B4AAADdUlEQVTWAWjl7m9E7UYAJ9Y2pjTi3CNaDzAROCV6fALhoFrn7vMJ/1G751qc\n7j7d3RdH62cBzc2sca7FCWBmJwIfRXFWrMu1OHsDM9x9ZvTcr9x9Q33HmWaMcR5DVd18uQNJN1xG\nvyteN5bjKN044zqOavF+Zuw4yvTgaVcDd5jZx8BthIu7uPt4YDnhP+184DZ3LyP8kQuTnr8oWlff\n3jOzE6LHPwU6Ro+3rxTPwiieyuvjjjPZKcBUd19Hjr2fFu7duBIYXKl9TsUJ7Am4mf3DzKaa2RUx\nxllljLlyDNmmN1+284298ZYAFXfXx34cpRhnsliOo1TizORxlOmE/yBwkbvvBPw2WsbMziB8De0A\ndAIuN7NOGX7tdJwLnG9mbxG+Uq2NMZaa1Binme0L3AIMiCG2ZNXFORi4091XsvmNeXGoLs5GwGHA\nadHvk8zsSOK5ebDKGHPhGIoSz2jCzZffJG/zUFPIiR4g6cYZ13GURpyDydBxtMV++Gnq5u4/ih4/\nBfwletwDeMbd1wOfm9kUoCvwKpsOwbAjG8tA9cbdPwCOATCzPYHjok2L2PQsekfCJ+iiHIsTM9sR\neBo4093nRatzJc6+0aZuwClm9ntCiW+Dma2K4s6FOCvez0+Af7n7smjbi8APgEezHWcN72Wsx5CF\nmy9HAyPd/dlo9RIza+/ui6PywtJofWzHUZpxxnYcpRlnxo6jTJ/hf2hmvaLHRwL/jR7PjpYxs5aE\nUTdnR/Wz5WbW3cwMOBN4lnpmZm2i3w2A69g4uucY4FQzaxKdPe0BvJFrcUZX78cCV7n7vyvau/tn\nORLn/VE8P3T3Tu7eCfgjMNTd78219xMYD+xvZs3NrBHQC3gvjjirey+J8RiK9lvVzZdjgLOjx2cn\nvW4sx1G6ccZ1HKUbZ0aPo9pcZY6uCD8OfEr4yvkJoUfBQYRa1HTg30CXqG1TwtnSTOA9Nr3K3DVa\n/yFwd23jSSPOc4GLCFfGPwBurtR+YBTLbKIeR7kWJyERrACmJf1sl2txVnreIODSXHw/o/anA+9G\nMd2SjTjT/DeP8xg6DNgQHdcV/9/6AN8jXFj+L/ASUBLncZRunHEdR7V5PzN1HOnGKxGRIqEpDkVE\nioQSvohIkVDCFxEpEkr4IiJFQglfRKRIKOGLiBQJJXwRkSKhhC8iUiT+H+rIzqsWek8zAAAAAElF\nTkSuQmCC\n", "text": [ "" ] } ], "prompt_number": 36 }, { "cell_type": "markdown", "metadata": {}, "source": [ "as well as the associated error bars. These are given (similarly to the Bayesian parametric model from the last lab) by the standard deviations of the marginal posterior densities. The marginal posterior variances are given by the diagonal elements of the posterior covariance," ] }, { "cell_type": "code", "collapsed": false, "input": [ "var_f = np.diag(C_f)[:, None]\n", "std_f = np.sqrt(var_f)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 37 }, { "cell_type": "markdown", "metadata": {}, "source": [ "They can be added to the underlying mean function to give the error bars," ] }, { "cell_type": "code", "collapsed": false, "input": [ "plt.plot(x, y, 'rx')\n", "plt.plot(x_pred, mu_f, 'b-')\n", "plt.plot(x_pred, mu_f+2*std_f, 'b--')\n", "plt.plot(x_pred, mu_f-2*std_f, 'b--')" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 38, "text": [ "[]" ] }, { "metadata": {}, "output_type": "display_data", "png": "iVBORw0KGgoAAAANSUhEUgAAAXUAAAEACAYAAABMEua6AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n", "text": [ "" ] } ], "prompt_number": 38 }, { "cell_type": "markdown", "metadata": {}, "source": [ "This gives us a prediction from the Gaussian process. Remember machine learning is \n", "$$\n", "\\text{data} + \\text{model} \\rightarrow \\text{prediction}.\n", "$$\n", "Here our data is from the olympics, and our model is a Gaussian process with two parameters. The assumptions about the world are encoded entirely into our Gaussian process covariance. The GP covariance assumes that the function is highly smooth, and that correlation falls off with distance (scaled according to the length scale, $\\ell$). The model sustains the uncertainty about the function, this means we see an increase in the size of the error bars during periods like the 1st and 2nd World Wars when no olympic marathon was held. \n", "\n", "## Exercises\n", "\n", "Now try changing the parameters of the covariance function (and the noise) to see how the predictions change.\n", "\n", "Now try sampling from this conditional density to see what your predictions look like. What happens if you sample from the conditional density in regions a long way into the future or the past? How does this compare with the results from the polynomial model?\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## The Importance of the Covariance Function\n", "\n", "The covariance function encapsulates our assumptions about the data. The equations for the distribution of the prediction function, given the training observations, are highly sensitive to the covariation between the test locations and the training locations as expressed by the matrix $\\mathbf{K}_*$. We defined a matrix $\\mathbf{A}$ which allowed us to express our conditional mean in the form,\n", "$$\n", "\\boldsymbol{\\mu}_f = \\mathbf{A}^\\top \\mathbf{y},\n", "$$\n", "where $\\mathbf{y}$ were our *training observations*. In other words our mean predictions are always a linear weighted combination of our *training data*. The weights are given by computing the covariation between the training and the test data ($\\mathbf{K}_*$) and scaling it by the inverse covariance of the training data observations, $\\left[\\mathbf{K} + \\sigma^2 \\mathbf{I}\\right]^{-1}$. This inverse is the main computational object that needs to be resolved for a Gaussian process. It has a computational burden which is $O(n^3)$ and a storage burden which is $O(n^2)$. This makes working with Gaussian processes computationally intensive for the situation where $n>10,000$. " ] }, { "cell_type": "code", "collapsed": false, "input": [ "from IPython.display import YouTubeVideo\n", "YouTubeVideo('ewJ3AxKclOg')" ], "language": "python", "metadata": {}, "outputs": [ { "html": [ "\n", " \n", " " ], "metadata": {}, "output_type": "pyout", "prompt_number": 111, "text": [ "" ] } ], "prompt_number": 111 }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Improving the Numerics\n", "\n", "In practice we shouldn't be using matrix inverse directly to solve the GP system. One more stable way is to compute the *Cholesky decomposition* of the kernel matrix. The log determinant of the covariance can also be derived from the Cholesky decomposition." ] }, { "cell_type": "code", "collapsed": false, "input": [ "def update_inverse(self):\n", " # Perform Cholesky decomposition on matrix\n", " self.R = sp.linalg.cholesky(self.K + self.sigma2*self.K.shape[0])\n", " # compute the log determinant from Cholesky decomposition\n", " self.logdetK = 2*np.log(np.diag(self.R)).sum()\n", " # compute y^\\top K^{-1}y from Cholesky factor\n", " self.Rinvy = sp.linalg.solve_triangular(self.R, self.y)\n", " self.yKinvy = (self.Rinvy**2).sum()\n", " \n", " # compute the inverse of the upper triangular Cholesky factor\n", " self.Rinv = sp.linalg.solve_triangular(self.R, np.eye(self.K.shape[0]))\n", " self.Kinv = np.dot(self.Rinv, self.Rinv.T)\n", "\n", "GP.update_inverse = update_inverse" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 39 }, { "cell_type": "code", "collapsed": false, "input": [ "for i in xrange(10):\n", " y_sample = np.random.multivariate_normal(mean=mu_f.flatten(), \n", " cov=C_f)\n", " plt.plot(x_pred.flatten(), y_sample.flatten())\n", "plt.plot(x, y, 'rx')" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 43, "text": [ "[]" ] }, { "metadata": {}, "output_type": "display_data", "png": "iVBORw0KGgoAAAANSUhEUgAAAXUAAAEACAYAAABMEua6AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nAABJRU5ErkJggg==\n", "text": [ "" ] } ], "prompt_number": 43 }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Capacity Control\n", "\n", "Gaussian processes are sometimes seen as part of a wider family of methods known as kernel methods. Kernel methods are also based around covariance functions, but in the field they are known as Mercer kernels. Mercer kernels have interpretations as inner products in potentially infinite dimensional Hilbert spaces. This interpretation arises because, if we take $\\alpha=1$, then the kernel can be expressed as\n", "$$\n", "\\mathbf{K} = \\boldsymbol{\\Phi}\\boldsymbol{\\Phi}^\\top \n", "$$\n", "which imples the elements of the kernel are given by,\n", "$$\n", "k(\\mathbf{x}, \\mathbf{x}^\\prime) = \\boldsymbol{\\phi}(\\mathbf{x})^\\top \\boldsymbol{\\phi}(\\mathbf{x}^\\prime).\n", "$$\n", "So we see that the kernel function is developed from an inner product between the basis functions. Mercer's theorem tells us that any valid *positive definite function* can be expressed as this inner product but with the caveat that the inner product could be *infinite length*. This idea has been used quite widely to *kernelize* algorithms that depend on inner products. The kernel functions are equivalent to covariance functions and they are parameterized accordingly. In the kernel modeling community it is generally accepted that kernel parameter estimation is a difficult problem and the normal solution is to cross validate to obtain parameters. This can cause difficulties when a large number of kernel parameters need to be estimated. In Gaussian process modelling kernel parameter estimation (in the simplest case proceeds) by maximum likelihood. This involves taking gradients of the likelihood with respect to the parameters of the covariance function. \n", "\n", "## Gradients of the Likelihood\n", "\n", "The easiest conceptual way to obtain the gradients is a two step process. The first step involves taking the gradient of the likelihood with respect to the covariance function, the second step involves considering the gradient of the covariance function with respect to its parameters. The relevant terms of the negative log likelihood are given by\n", "$$\n", "E(\\boldsymbol{\\theta}) = \\frac{1}{2}\\log |\\hat{\\mathbf{K}}| + \\frac{1}{2} \\mathbf{y}^\\top \\hat{\\mathbf{K}}^{-1} \\mathbf{y}\n", "$$\n", "where $\\hat{\\mathbf{K}} = \\mathbf{K} + \\sigma^2 \\mathbf{I}$ is the noise corrupted covariance matrix. The gradient with respect to that matrix can be computed as\n", "$$\n", "\\frac{\\text{d}E(\\boldsymbol{\\theta})}{\\text{d}\\hat{\\mathbf{K}}} = \\frac{1}{2}\\hat{\\mathbf{K}}^{-1} - \\frac{1}{2}\\hat{\\mathbf{K}}^{-1}\\mathbf{y}\\mathbf{y}^\\top \\hat{\\mathbf{K}}^{-1}\n", "$$\n", "The can then be combined with gradients of the covariance function with respect to any parameters, $\\frac{\\text{d}\\hat{\\mathbf{K}}}{\\text{d}\\theta}$ using the chain rule. Mathematically that is written as\n", "$$\n", "\\frac{\\text{d}E(\\boldsymbol{\\theta})}{\\text{d}\\theta} = \\text{tr}\\left(\\frac{\\text{d}E(\\boldsymbol{\\theta})}{\\text{d}\\hat{\\mathbf{K}}}\\frac{\\text{d}\\hat{\\mathbf{K}}}{\\text{d}\\theta}\\right),\n", "$$\n", "where the two gradient matrices are multiplied together. In in implementation, however, that is inefficient. It is more efficient to perform an element by element multiplication of the two matrices.\n", "\n", "### Overall Process Scale\n", "\n", "In general we won't be able to find parameters of the covariance function through fixed point equations, we will need to do graident based optimization, however there is one parameter that does have a fixed point update. Imagine the covariance $\\hat{\\mathbf{K}}$ has an overall scale such that $\\hat{\\mathbf{K}} = \\alpha \\boldsymbol{\\Sigma}$. In this case the gradient of the covariance matrix with respect to $\\alpha$ is simply $\\mathbf{C}$ and $\\hat{\\mathbf{K}}^{-1}\\mathbf{C} = \\alpha^{-1}$. This means we can write,\n", "$$\n", "\\frac{\\text{d}E(\\boldsymbol{\\theta})}{\\text{d}\\alpha} = \\frac{1}{2\\alpha}\\left(n - \\frac{\\mathbf{y}^\\top\\mathbf{C}^{-1}\\mathbf{y}}{\\alpha}\\right)\n", "$$\n", "which implies a fixed point updated is given by\n", "$$\n", "\\alpha = \\frac{\\mathbf{y}^\\top\\mathbf{C}^{-1}\\mathbf{y}}{n}.\n", "$$\n", "The availability of a fixed point update for the overall scale means that sometimes, if we have a process of the form,\n", "$$\n", "\\hat{\\mathbf{K}} = \\alpha \\mathbf{K} + \\sigma^2 \\mathbf{I}\n", "$$\n", "where $\\mathbf{K}$ might be an exponentiated quadratic, or another covariance, that represents the signal, and $\\sigma^2$ represents the contribution from the noise. Rather than representing directly in this form we might represent the model as\n", "$$\n", "\\hat{\\mathbf{K}} = \\sigma^2\\left(\\hat{\\alpha}\\mathbf{K} + \\mathbf{I})\\right)\n", "$$\n", "where $\\hat{\\alpha} = \\frac{\\alpha^2}{\\sigma^2}$ is a signal to noise ratio. Although some care will need to be taken if the actual noise is very low as numerical instabilities are likely to occur.\n", "\n", "## Capacity Control and Data Fit\n", "\n", "The objective function can be decomposed into two terms, a capacity control term, and a data fit term. \n", "$$\n", "E(\\boldsymbol{\\theta}) = \\frac{1}{2}\\log |\\hat{\\mathbf{K}}| + \\frac{1}{2} \\mathbf{y}^\\top \\hat{\\mathbf{K}}^{-1} \\mathbf{y}\n", "$$\n", "The capacity control term is the log determinant of the covariance, $\\log |\\hat{\\mathbf{K}}|$. The data fit term is the matrix inner product between the data and the inverse covariance, $\\frac{1}{2} \\mathbf{y}^\\top \\hat{\\mathbf{K}}^{-1} \\mathbf{y}$.\n", "\n", "The log determinant term has an interpretation as a log volume. The determinant of the covariance is related to Gaussian density's 'footprint'. Recall that the determinant is the product of the eigenvalues, and the eigenvalues represent a set of axes which describe the correlations of the Gaussian densities (the directions being given by the corresponding eigenvectors). The product of these eigenvalues gives the area (or volume) of the Gaussian density. Roughly speaking it represents the diversity of different functions the Gaussian process can represent. If the number is large, then the process can represent many functions. If it is small then the process can represent fewer functions. Although the terms 'many' and 'few' are badly defined here because the space is continuous and the Gaussian process represents a continuum of different functions. However, the intuition is maybe useful. \n", "\n", "The data fit term is a little like a quadratic well, trying to locate the data at the lowest point. The data fit term can be driven to zero by increasing the scale of the covariance. However, this causes the capacity term to also increase, so a penalty is paid for this. Ideally, the data fit term should be reduced by matching correlations seen in the data with a corresponding correlation in the covariance function." ] }, { "cell_type": "code", "collapsed": false, "input": [], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 112 } ], "metadata": {} } ] }