{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Past Earth Network Emulator Workshop: Lab 1" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This tutorial is based on ones written by [Alan Saul](http://www.alansaul.com/), James Hensman, Neil Lawrence, and Nicolas Durrande, with additions by Richard Wilkinson. In it, we will run through some of the basic features of GPy. We will focus on three aspects of GPs: the kernel/covariance function, how to generate random sample paths, and how to do GP regression.\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We assume that GPy is already installed on your machine. You can get instructions on how to install GPy from the [SheffieldML github page](https://github.com/SheffieldML/GPy). The online documentation for GPy is available from [this page](http://gpy.readthedocs.org/en/latest/).\n", "\n", "To start off, we must first tell the Jupyer notebook that we want the plots to appear inline and import the libraries we will need:" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": false }, "outputs": [], "source": [ "%matplotlib inline\n", "import numpy as np\n", "from matplotlib import pyplot as plt\n", "import GPy" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 1. The Covariance Function" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The covariance function is the single most important aspect of a GP. We can use any function we like as long as it is positive semi-definite. We usually build a suitable covariance function by combining a small number of well-known covariance functions. However, it is possible to add your own kernels to GPy without too much trouble. A good source of information on covariance functions is available in the [kernel cookbook](http://www.cs.toronto.edu/~duvenaud/cookbook/index.html)\n", "\n", "Let's start by defining an exponentiated quadratic covariance function (also known as squared exponential or rbf - radial basis function - or Gaussian) in one dimension:" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": false }, "outputs": [], "source": [ "d = 1 # input dimension\n", "var = 1. # variance\n", "theta = 0.2 # lengthscale\n", "k = GPy.kern.RBF(d, variance=var, lengthscale=theta)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "A summary of the kernel can be obtained using the command print k. " ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " \u001b[1mrbf. \u001b[0;0m | value | constraints | priors\n", " \u001b[1mvariance \u001b[0;0m | 1.0 | +ve | \n", " \u001b[1mlengthscale\u001b[0;0m | 0.2 | +ve | \n" ] } ], "source": [ "print(k)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "It is also possible to plot the kernel as a function of one of its inputs (whilst fixing the other) with k.plot(). \n", "\n", "*Note*: if you need help with a command in ipython notebook, then you can get it at any time by typing a question mark after the command, e.g. k.plot?" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" }, { "name": "stderr", "output_type": "stream", "text": [ " /Users/pmzrdw/anaconda/lib/python3.5/site-packages/matplotlib/figure.py:1742: UserWarning:This figure includes Axes that are not compatible with tight_layout, so its results might be incorrect.\n" ] }, { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "k.plot()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Setting Covariance Function Parameters" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The value of the covariance function parameters can be accessed and modified using k['.*var'] where the string in brackets is a regular expression matching the parameter name as it appears in print k. You can also access each parameter directly:" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " \u001b[1mindex\u001b[0;0m | rbf.lengthscale | constraints | priors\n", " \u001b[1m[0] \u001b[0;0m | 0.20000000 | +ve | \n" ] }, { "data": { "text/html": [ "\n", "\n", "\n", "\n", " \n", " \n", " \n", "\n", "" ], "text/plain": [ "\u001b[1mrbf.lengthscale\u001b[0;0m:\n", "Param([ 0.2])" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "print(k.lengthscale)\n", "k['.*lengthscale']" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's use this to get an insight into the effect of the parameters on the shape of the covariance function, by setting the lengthscale of the covariance function to different values, and plotting the resulting covariance using the k.plot() method." ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" }, { "name": "stderr", "output_type": "stream", "text": [ " /Users/pmzrdw/anaconda/lib/python3.5/site-packages/matplotlib/figure.py:1742: UserWarning:This figure includes Axes that are not compatible with tight_layout, so its results might be incorrect.\n" ] }, { "data": { "image/png": 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ucV7rScD7gNcdb+pQUm3L9jVq6BGnhdleTgYnqRGUexfc+cCbgL8AvhQRDwHb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\nndcFwI69h7nvsb05VyQ1N4O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D0x1deO5jXXiMiARI+4pTTsiYNmagz9VIu9hBmFv2naSltY283By/yxLJCnEF\nJ+fcw6kuRESCpbahmd1HqgGYOKI/RQV5PlcksWaMH8ThqnpvEOaBU0wfqxVBkZ4Qb3N4QpfSmFnf\nrpUjIkGxcc8JXGRzXtt0wTNrwtmes9gtVRFJrXibw0+Z2eAEnveQmY3rSkEiEgyx85tmqTE8cGbH\nBKe1Ck4iPSaR5vCPmFldnPfXmr5ImtMVdcE2blgJvQvyqG9sYd2u4zjnMNO4CJFUizc47Qc+msDz\nHgVaEi9HRIKgLRxmY+RqrcH9CikbkMg0EukJOaEQM8eX8uqmI5ysaeTg8TpGDlaXhEiqxdscPibF\ndYhIgOw6VE1DUyvgrTZpJSOYZk8YzKubjgCwdmelgpNID+jSkSsiktnWxWzTzdA2XWCpQVyk5yk4\nichfie1vmqUr6gJr+piB5ESOwVFwEukZCk4i8lfWR34I5+flMGlkf5+rkc4U5OcydbR3LOjeozWc\nrm30uSKRzKfgJCIdHDvVwOGqegCmjRmoidQBNzN2u26Xjl8RSTUFJxHpYN2OyujHcyaqvynoZk84\nO2JvvQ78FUm5pAYnMxtlZvr1VCSNrdl5NjjNnpjI3FvxQ+xw0rUx/9+JSGoke8VpL7DZzN6R5OcV\nkR6ydoe3ahEyY8Y4rTgF3YDiAkZFxhBs2XeSppY2nysSyWzJDk7XAPcAtyX5eUWkB9TUN7Hr8GkA\nJo3sT59CHQKQDtrHErS0htmyt8rnakQyW1KDk3PuRefcz5xzCk4iacg7usP7eLb6m9JGbJ+Tzq0T\nSa24g5OZTYvjPrd3rxwR8VP7Nh3AnAnqb0oXHa+sU3ASSaVEVpxWm9mn7DxnL5hZmZk9CXw/eaWJ\nSE9bE3NF3SytOKWN0WV96dcnH/BmcIXDzueKRDJXIsHpduAzwF/MbHz7jZFVps1AP2BOcssTkZ7S\n2NzKln0nARhV1peBxYU+VyTxMjNmR1adahqa2R3pUxOR5Is7ODnnfg1cBJwA1kVWn54Afgh8FbjK\nObczNWWKSKpt2lNFa1sYgDkaQ5B25kwqi35csUNjCURSJaHmcOdcpXPu7cATwDeBa4FLnHP3Oee0\nNiySxmK36WarvyntzI0Ju2u2KziJpEpCwcnM+pvZL4G34Y0dqASWmtncVBQnIj1nbWxwUn9T2pk4\nsh+9C7zxERU7KtHvsiKpkchVdW/B62UaD5Q75/4dmAm8BLxqZl82s9zUlCkiqdTaFmbDbu+cs0H9\nChle2sdPDvEfAAAgAElEQVTniiRROaFQtM/pZE0j+47V+lyRSGZKZMXp18B3gYXOua0Azrl659zf\nA28B3g+s6mohZnaXme0xszNmtsLM5sf5uMvMrMXMKrr62iLZbvuBUzQ0tQLeNt15Lp6VNDBnUsx2\nnfqcRFIikeA03zn3Nedc+NwvOOf+DMwAVnelCDO7DbgXuBvvyrx1wDIzK32Dx5UADwPPdOV1RcSj\nbbrMMDe2QXz7MR8rEclciVxVt/4Nvl7jnPtwF+tYAvzAOfdIZDXrTqAB+NAbPO5B4FFgRRdfV0SA\nNTHTpnVFXfqaMqo/Bb28c9YrtqvPSSQV4gpOZrYg3ic0syIzm57A/fOAcuDZ9tsiV+g9Ayy8wOPu\nAMYCX4z3tUTkr4XDLnoVVt+iXowbVuJzRdJVebk50YOZK081cLiq3ueKRDJPvCtOPzezZWb2LjPr\nfb47mNk0M/sasAsvCMWrFMgBzl1XPgYM6eS1JgJfA953vq1DEYnf7sOnqa5vArzVppxQss/+lp40\nd5LGEoikUrzfIacBfwC+Apw2s01m9mcz+52ZvWxmJ4AKvBWg65xzj6SoXswshLc9d7dzblf7zal6\nPZFMtzrmh2v55LIL3FPSQexWq/qcRJIvrvEBzrkW4DvAd8xsHnA5MBooxGvkvh943jl3sgs1nADa\ngHO/Y5cBR89z/77APGC2mX0vclsIMDNrxgtuL3ShDpGstHrb2R+u5ZPV35TuLhpXSl5uiJbWsK6s\nE0mBhOcuOedW0Y2xA+d5vhYzWw0sAp4ELwFFPv/OeR5Sg3f0S6y7gGuAW4G9F3q9JUuWUFLSsYdj\n8eLFLF68uCvli6S1cNhFVyWKi3oxcXh/nyuS7srPy+GisQNZs+M4B4/XUXmqgcH9i/wuS8Q3S5cu\nZenSpR1uq66u7vLzJRyczGyxc25pJ1/7lnPu012o4z7goUiAeh3vKrsi4KHI834dGOac+0CkcXzz\nOa9bCTQ657a80Qvdf//9zJ2rQeciALsOn6a6vhnwtnhCIe16Z4I5EwezZod3peSaHZVcf/EYfwsS\n8dH5FkcqKiooL0+kHfusrnSBft/Mbjz3RjO7H7i9K0U45x4HPgV8CViDN5H8eudc+zXSQ4CRXXlu\nEelch226KepvyhSx85y0XSeSXF0JTu/DO5/u8vYbzOy7wLvxtsu6xDn3gHNujHOu0Dm3MLIl2P61\nO5xz117gsV90zmkZSSRBHRrDJyk4ZYoZ40rJiaweqkFcJLkSDk7OuT8AHweeNLNyM3sAeAdwTftR\nLCISfN78prP9TROG9/O5IkmWooI8po0ZCMCeIzWcOH3G54pEMkeXBrY4534J/CewHHgrcJVzbnsy\nCxOR1Irtb5o7Sf1NmWZezGiJVdvOd4GyiHRFXM3hZnZfJ186jje/6ePth4I65z6ZnNJEJJVWxfQ3\nzdX8powzb8oQfvbUJsD7//qGS8b6XJFIZoj3qro5ndy+EyiO+boORhJJExUxwWmeglPGmTm+lF65\nIZpbw6zcqj4nkWSJdwBml5u+RSR4vPlNXmN4Se9ejB+m/qZMU9Arl5njB7Fq2zEOn6jj0Ik6hpf2\n8bsskbSnQ6lEstDOQ6epaYjMb5pUpv6mDDUvZsTEqq3qcxJJBgUnkSy0OuYS9fJJOmYlU82bcvac\ndG3XiSSHgpNIFlq1NfZ8OvU3ZarpowdSlO91ZKzaehTv4AUR6Q4FJ5Es09oWZnXk8vT+ffPV35TB\ncnNDzJnorShW1TSy50iNzxWJpD8FJ5Ess2lvFfWNrQBcPHWI+psyXOx2nfqcRLpPwUkky7y++Uj0\n44unDPWxEukJ82MaxFduU5+TSHcpOIlkmde3nF11uHjqkAvcUzLBxBH9KS7qBXizu9rCYZ8rEklv\nCk4iWaS+sYUNu08AMKqsL0MG9va5Ikm1UMiiFwDUNDSz/cApnysSSW8KTiJZpGL7MdrC3pVVl0zV\nNl22mD81ts9J23Ui3aHgJJJFXtusbbpsND9m5MTrahAX6RYFJ5Es0t7fFDLT+XRZZPSQYgb3KwRg\nzfZKmlrafK5IJH0pOIlkicpTDew5Ug3A9LED6RNpGJbMZ2ZcMs3bmm1qaWPtjkqfKxJJXwpOIlli\n5VZt02WzBdPP9rS9uunIBe4pIhei4CSSJV6Lnd+k4JR1Lp46FIvMOl2x6bC/xYikMQUnkSzgnIv2\nNxXm5zJjXKnPFUlP69cnn2mjBwKw63A1lacafK5IJD0pOIlkgV2Hq6mqaQSgfNJg8nJzfK5I/BC7\nXbdC23UiXaLgJJIFYo9Zma/5TVlrYWyf02Zt14l0hYKTSBaIbQa+ZJr6m7LV9LGl9CnMA+D1zUd1\n/IpIFyg4iWS4M02trN7uTYseMqCIcUNLfK5I/JKbE2L+FC841zQ0s2XvSZ8rEkk/Ck4iGW7l1qO0\ntHorC5fNGI61X1olWWnhRcOiH7+6WX1OIolScBLJcK9sPNvLcmnMD03JTgunxTaIq89JJFEKTiIZ\nzDnH8g2HAMjLPbtNI9lryMDejBlSDMDG3VXU1Df5XJFIelFwEslgu49Uc/SkN6+nfFIZhfm5Plck\nQdA+liDsHCu3HvO5GpH0ouAkksFe2RCzTTdD23TiWTAt9vgVbdeJJELBSSSDLY8JTpepv0kiyieV\nkZ/nDUFdvuEw4bDzuSKR9KHgJJKh6hqaWbuzEoCRg/syqqzY54okKAryc5k/pQyAE9Vn2LpfYwlE\n4qXgJJKhXt9ylLbISoKuppNzXTFrRPTjv6w76GMlIulFwUkkQy2PGUNwmfqb5BxXzBwe/fil9Yd8\nrEQkvSg4iWSg2DEE+Xk5zJ1U5nNFEjSD+hUxdfQAALYfOMXRk/U+VySSHhScRDLQ9gOnqKppBGD+\nlLONwCKxYrfrXtaqk0hcFJxEMlDs1sulM4Zf4J6Sza6M2a5Tn5NIfBScRDLQC2sORD++QsFJOjFp\nZH8G9y8CYNW2YzQ0tvhckUjwKTiJZJjDJ+rYduAUAFNHD2DIwN4+VyRBZWbRJvGW1jCvbTnqc0Ui\nwafgJJJhXlh7dsvl6tkjfaxE0kGHq+u0XSfyhhScRDJM7Dbd1XMUnOTC5k0ZEj3D8OUNh2gLh32u\nSCTYFJxEMsip2kbW7TwOwKiyvowdqmnhcmH5eTlcEjm77lRtE5v2VPlckUiwKTiJZJC/rDtI2HnT\nwq+eMxIz87kiSQdX6Oo6kbgpOIlkkNhtumvU3yRxumLmcEKRkP1cxQGc06G/Ip1RcBLJEPWNLdGr\nogb1K2TamIE+VyTpon/fAuZOHgzAgcpath885XNFIsGl4CSSIV7ZeJiWVq+x96rZIwiFtE0n8Vs0\nd1T042dX7fexEpFgU3ASyRAdrqbTNp0k6Jq5I6Pbdc+u3q/tOpFOKDiJZIDmlrboob7FRb0o16G+\nkqCBxYXMmeht1+2vrGXHwdM+VyQSTApOIhlg5daj1De2AnD5zOHk5uo/bUnconkx23Wr9/lYiUhw\n6burSAZ4euXZH3LXaOildNE1c0bSPsHiGW3XiZyXgpNImmtsbo32N/UpzOPSi4b5XJGkq9KSmO26\nY7XsPKTtOpFzKTiJpLmX1x+iocnbprt27ih65eX4XJGks0XlZ7frnlmtq+tEzqXgJJLmlsVs0103\nf7SPlUgmuHbOqOh23bOrtF0nci4FJ5E0VtvQHL2abkBxAfOm6Go66Z7SfoXMnjAIgH3Hatil7TqR\nDhScRNLY82sORIdevnneaHJC+k9aum9R+dmVy9gVTREJUHAys7vMbI+ZnTGzFWY2/wL3fbuZPW1m\nlWZWbWavmNl1PVmvSBA8/fre6MfXXzzGtzoksywqHxUdhvnUij2Ew9quE2kXiOBkZrcB9wJ3A3OA\ndcAyMyvt5CFXAk8DNwJzgeeB35nZrB4oVyQQTlSfYeXWYwAMK+3DRWN1Np0kR2lJIQumDwXg2KkG\nKrYf87kikeAIRHAClgA/cM494pzbCtwJNAAfOt+dnXNLnHPfds6tds7tcs79B7ADeGvPlSzir2dX\n7yccady9fv5ozHQ2nSTPzQvHRj/+/at7fKxEJFh8D05mlgeUA8+23+a8yzieARbG+RwG9AVOpqJG\nkSBaFrtNd8kY3+qQzHTlrBH0LsgD4LmK/ZyJjLwQyXa+ByegFMgBzl0LPgYMifM5Pg30Bh5PYl0i\ngXXoRB0bdp8AYMLwfowf1s/niiTTFPTK5U2RI1jONLXyfMwh0iLZLAjBqVvM7L3A54B3OedO+F2P\nSE/43fJd0Y/VFC6p8paF46If/+HV3T5WIhIcuX4XAJwA2oBzB9CUAUcv9EAzew/wQ+Cdzrnn43mx\nJUuWUFJS0uG2xYsXs3jx4rgLFvFTWzgcDU45IevQiyKSTLMmDGJ4aR8Onahj5dajHDvVQFn/Ir/L\nEknI0qVLWbp0aYfbqquru/x8vgcn51yLma0GFgFPQrRnaRHwnc4eZ2aLgR8Dtznn/hTv691///3M\nnTu3e0WL+GjFpiNUnj4DwGUzhjOon36QSWqYecH8h7/bgHPwp9f28IEbpvtdlkhCzrc4UlFRQXl5\neZeeLyhbdfcBHzWz95vZFOBBoAh4CMDMvm5mD7ffObI99zDwL8BKMyuL/Cnu+dJFetZvXz67Tfc3\nl4/3sRLJBjcuOLui+YdXd+sIFsl6gQhOzrnHgU8BXwLWADOB651zxyN3GQKMjHnIR/Eayr8HHI75\n8189VbOIH6pqzvDSuoOAN2vn0ouG+VyRZLoRg/pGj2DZc6SGzft08bJkN9+36to55x4AHujka3ec\n8/k1PVKUSMD88dU9tEWmOL/l0nHk5gTidx/JcDcvHMfand7vsf/3lx1MH6Nhq5K99F1XJE045/jt\nyzujn99ymbbppGdcN380vQu837P/9Npeahuafa5IxD8KTiJpYu3O4+w/VgvAvMlljBzc1+eKJFsU\nFeRxc2Q0QVNLG7/XaALJYgpOImniiZjVJjWFS0+79apJ0Y//94XtahKXrKXgJJIGahuaeWbVfgCK\ni3pxzdxRPlck2WbcsBLKJ3nj9vYfq40eMC2SbRScRNLAk8t30dTSBniXh+fn5fhckWSjd149Mfrx\n/76w3cdKRPyj4CQScG3hML96/uwPqXdeNfEC9xZJnatnj2RgcQEAf1l3kGOnGnyuSKTnKTiJBNzy\nDYc5dKIOgAXThjJmaMkbPEIkNXJzQ7z9Si+4t4Udv31p5xs8QiTzKDiJBNzjz22LfnzbtZN9rEQE\n3nbFBHJCBngznVpbwz5XJNKzFJxEAmznodO8tsU763rEoD6aFC6+K+tfxJWzRgBQVdPIM6v3+VyR\nSM9ScBIJsEf/vCX68buvnUwo8pu+iJ9iVz5/8fQWjSaQrKLgJBJQlaca+NNrewFvBMHfaFK4BMTc\nSYOZOnoAANsOnNJoAskqCk4iAfXYc9tobfP6R269aiJFBXk+VyTiMTNuv25q9POfP73Zx2pEepaC\nk0gA1TU08+sXdwCQlxvi3deoKVyC5dq5oxg2sDcAKzYdYduBkz5XJNIzFJxEAujx57dT39gCwE0L\nxlLar9DnikQ6ys0J8b43n111euiPm3ysRqTnKDiJBExDYwu/fGYrACEzPnDDdJ8rEjm/Wy4fz4C+\n3kDMZyv2s+dItc8ViaSegpNIwPzmLzuprm8C4LqLRzNycF+fKxI5v4JeudFeJ+fgoae06iSZT8FJ\nJEDONLVGG23N4I4bL/K5IpELu/WqiZT07gXAstf3sv9Yjc8ViaSWgpNIgDz+/DZO1jQCcO2cUYwb\npuNVJNiKCvJ475u8Vae2sOOHv1vvc0UiqaXgJBIQdQ3NPPKns6tNf3fLTJ8rEonPbYsm069PPgBP\nr9zHzoOnfK5IJHUUnEQC4tFntlLT0Ax4V9JptUnSRe+CPD54o3cRg3Pw4BNadZLMpeAkEgAnqs/w\ny8jxKjkh4yNvmeFzRSKJufWqiQyKjM14cd1B1u2s9LkikdRQcBIJgB88uZ6GplYA3n7lBEYM0pV0\nkl4KeuV2CPz3P15BOKwz7CTzKDiJ+GznwVM8+fIuAHoX5PLRt6i3SdLTLZeNZ+xQb4t5094q/rxq\nn88ViSSfgpOIj5xz/NevKghHTpf/4I0XMaC4wOeqRLomNyfEP71zTvTz//ebNTRGVlJFMoWCk4iP\nnq84wGtbjgIwZEARi980xeeKRLrn0ouGsWDaUACOnmzgoT9pKKZkFgUnEZ+caWrlvsdXRz9f8u5y\n8vNyfKxIpPvMjE/eVk5OyAD4+bLNHKis9bkqkeRRcBLxyU/+sIFjpxoAWDB9KNfMGelzRSLJMXZo\nSfQA4ObWMN/+n1U4p0ZxyQwKTiI+2HbgJL942hs/kJcb4tPvmYeZ+VyVSPJ8+OaLGBwZT/DKxsM8\nvVKN4pIZFJxEelhrW5ivPPwabZFLtT94w3RGlRX7XJVIchUV5PHpxfOjn3/7f1ZxqrbRx4pEkkPB\nSaSH/eLpLWzdfxKA8cNKuOOm6T5XJJIaV88ZyZvKRwFwuq6Jby1d5XNFIt2n4CTSg7YdOMkPnvSO\nowiZ8bkPLCAvVw3hkrk+tXgexUW9APjzqn0se32vvwWJdJOCk0gPaWxu5XM/foXWtjAAt183lelj\nS32uSiS1BhYX8unF86Kf3/Po6xw9We9jRSLdo+Ak0kO+++s17DlSDcCkkf352C2aEC7Z4YZLxnL9\nxaMBqDvTwt0/PfsLhEi6UXAS6QFPr9zL489vByA/L4cvf/gyemlmk2SRzyyeT1n/IgAqtlfyw8iW\ntUi6UXASSbG9R2v46iOvRT//5G3ljBtW4mNFIj2vuHc+X/3oZdHBmD97ahPLNxzyuSqRxCk4iaRQ\nbUMzn/reizREzuu68ZIxvP2KCT5XJeKPWRMGc9c7Zkc//88fL2fv0RofKxJJnIKTSIq0toX59x+9\nzL5j3g+GccNK+Oztl2jQpWS12988lasjU/LrzrTwL997gZr6Jp+rEomfgpNICjjnuO+x1azYdASA\nkt753HvXVRTm5/pcmYi/zIwv3LGQCcP7AbD/WC3/+uBLNLe0+VyZSHwUnERS4Gd/3MSvXvCawXNC\nxjfuvIIRg/r6XJVIMPQuyOPeu66iX598AFZtO8bdP3uFcFjn2UnwKTiJJNmvX9zO959YF/388x9Y\nQPnkMh8rEgmeYaV9uO8TV5Mfubr0mVX7+ebSlToMWAJPwUkkiX770k7ueXRl9PN/vHUONy0c52NF\nIsE1Y1wp93zsiuiVdr9+cQf3PrZa4UkCTcFJJEl+/eJ2vvaLs2MH3n/DNG6/bqqPFYkE3+Uzh3P3\nHQtpv2bisee28a2lq7RtJ4Gl4CTSTc45fvbHjdzz6Eraf1F+35un8om3z9YVdCJxuPGSsXz+A2fD\n069e2M7nf/oKra2aLi7Bo0t8RLqhtTXMt/5nJb/5y87obe+/fhqfeIdCk0gi3nLpOMzgyw+voC3s\nWPb6Xk7VNnLPx66gb+SQYJEg0IqTSBdV1zfxz999vkNo+od3zOYfbp2j0CTSBTcvHMc37rySXrne\nj6bXtxzlQ/cs05BMCRQFJ5Eu2LS3ir/9ylO8tuUoAHm5Ib54x0Lef8N0nysTSW9XzR7BA59cFB1V\nsPdoDe//6lP87pVdahqXQFBwEklAa2uYn/xhAx/5xtMcqaoHoH/ffB5YskhXz4kkyawJg/nZZ6+P\nnul4pqmVLz20gs//9BXqG1t8rk6ynYKTSJx2HDzFB7/+Jx58Yj2tbV7T6szxpfz8P29i9sTBPlcn\nkllGDOrLQ5+9gb+5fHz0tj+9tpfbv/xHXo+s9Ir4Qc3hIm/gTFMrjyzbzM/+uJG2yCXSOSHjb6+f\nxsfeOpPcXP3+IZIKhfm5/Of7F3DxlCF87RevUd/YysHjddx1/7O8ad4o/vld5ZT1L/K7TMkyCk4i\nnWhtDfPE8p386HcbqKppjN4+flgJd9+xkKmjB/pYnUj2uO7iMUwbO5DP/+QVNuw+AXiTxpdvOMyH\nbrqI266drHMgpcfoX5rIOVpbwzxbsZ8f/m49+4/VRm/PCRkfvHE6H7rpInpFjokQkZ4xYlBffvyZ\n6/j9K7v57m/WcLquiTNNrXzv/9by6J+38N43T+FdV0+mT2Ge36VKhlNwEomorm/ity/t5PHnt1N5\nqqHD166dO5K/f9tsxgwp9qk6EQmFjFsuH8/Vc0bw4BPr+fWLOwg7x+m6Jh74v3X8fNkW3nXNJN52\n+XiGDuzjd7mSoSxbLu80s7nA6tWrVzN37ly/y5GAaG0Ls3LrUZa9vo9nVu2jqaWtw9fnTBzMP9w6\nhxnjSn2qUEQ6s+vwaX72x038eeU+wjE/y8zgkqlD+ZvLx3PlrBFaIZa/UlFRQXl5OUC5c64ikcdq\nxUmyTlNLG2t3VPLi2oM8u3o/J2sbO3zdDK6YOYL3LJrMvMllGmYpElDjh/XjKx+5jI++dQYPP7WJ\nP67YQ1vY4Rys2HyEFZuP0Lsgj8tnDuP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BexUq5Xzv99JLL9G5c2df44mUmeR96cxbc6rhZb/ODRxOJOKbetXj6dOpHrOX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\nxo2jYsWKp50bMWIEI0aMKE5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TiXhPhZOIH1hr+c9nZxc1feR6NbsUOcMYwy9uOnuTxNtfbyArJ9/BRCLeU+Ek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\nPi7K4UQiIqUvJMSQMLRl4bYaYpZNKpz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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "k = GPy.kern.RBF(d) # By default, the parameters are set to 1.\n", "theta = np.asarray([0.2,0.5,1.,2.,4.])\n", "for t in theta:\n", " k.lengthscale=t\n", " k.plot()\n", "plt.legend(theta)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Exercise 1" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "a) What is the effect of the lengthscale parameter on the covariance function?" ] }, { "cell_type": "raw", "metadata": {}, "source": [ "# Exercise 1 a) answer" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "b) Now change the code above to investigate the effect of changing the variance parameter." ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# Exercise 1 b) answer\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Covariance Functions in GPy" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Many different covariance functions are already implemented in GPy. Instead of rbf, try constructing and plotting the following covariance functions: exponential, Matern32, Matern52, Brownian, linear, bias,\n", "rbfcos, periodic_Matern32, etc. Some of these covariance functions, such as rbfcos, are not\n", "parametrized by a variance and a lengthscale. Furthermore, not all kernels are stationary (i.e., they canâ€™t all be written as $k ( x, y) = k ( x âˆ’ y)$, see for example the Brownian\n", "covariance function). For plotting so it may be interesting to change the value of the fixed input:" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "(-0.1, 5.1)" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" }, { "name": "stderr", "output_type": "stream", "text": [ " /Users/pmzrdw/anaconda/lib/python3.5/site-packages/matplotlib/figure.py:1742: UserWarning:This figure includes Axes that are not compatible with tight_layout, so its results might be incorrect.\n" ] }, { "data": { "image/png": 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pg0cLnHnzxrGaOCZRNyS1Z1kOQEjx54xThjHmPyVNt9baM18wxrSQ9KrKl+oo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\nSXw4EgAQigKiOElKlvS5JFv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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "kb = GPy.kern.Brownian(input_dim=1)\n", "inputs = np.array([2., 4.])\n", "for x in inputs:\n", " kb.plot(x,plot_limits=[0,5])\n", "plt.legend(inputs)\n", "plt.ylim(-0.1,5.1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Exercise 2\n", "\n", "Plot some other covariance functions. As we will see, it is very hard to intuit from the shape of these what the resulting GP sample paths will look like. \n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Computing the covariance/Gram matrix given the input data, $\\mathbf{X}$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let $\\mathbf{X}$ be a $n$ Ã— $d$ numpy array. Given a kernel $k$, the covariance matrix associated to\n", "$\\mathbf{X}$ is obtained with C = k.K(X,X) . The positive semi-definiteness of $k$ ensures that C\n", "is a positive semi-definite (psd) matrix regardless of the initial points $\\mathbf{X}$. This can be\n", "checked numerically by looking at the eigenvalues (they should all be positive if C is positive definite):" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "k = GPy.kern.Matern52(input_dim=2)\n", "X = np.random.rand(50,2) # 50*2 matrix of iid standard Gaussians\n", "C = k.K(X,X)\n", "eigvals = np.linalg.eigvals(C) # Computes the eigenvalues of a matrix\n", "plt.bar(np.arange(len(eigvals)), eigvals)\n", "plt.title('Eigenvalues of the Matern 5/2 Covariance')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 2. Prior Simulation" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Gaussian processes can be used as infinite dimensional models of function. They are defined by a covariance *function* and a mean *function*. \n", "\n", "When we compute the covariance matrix using kern.K(X, X) we are computing a covariance *matrix* between the values of the function, $f$, that correspond to the input locations in the matrix X. If we want to have a look at the type of functions that arise from a particular Gaussian process, we can never generate all possible values, but we can generate random samples from a Gaussian *distribution* based on a covariance matrix associated with a particular matrix of input locations X. If these locations are chosen appropriately then they give us a good idea of the underlying function. For example, for a one dimensional function, if we choose X to be uniformly spaced across part of the real line, and the spacing is small enough, we'll get an idea of the underlying function. We will now use this trick to draw sample paths from a Gaussian process. " ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "collapsed": false }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ " /Users/pmzrdw/anaconda/lib/python3.5/site-packages/ipykernel/__main__.py:10: RuntimeWarning:covariance is not positive-semidefinite.\n" ] }, { "data": { "image/png": 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VUe71EqLRMLJlhc+pUVGcFBFBxMFm5ULIyk5VVTJ9e0ODzJrV1CS3jY0yV4ff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\n/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8YT8XikfN2Nbp9sTVIpjyIiXCkt7WvS6XKJ44gmTGB9+blztTvWf8oUKubqVRxydMRP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o9HrZ5XazzemgtL2GbV3N7HS0U+Vox+d3gYoixRzNpNgE5iakcuK4iZw4Lo+EYXKRGEv8/m6q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\nCxAEzjrIOoNyDR2yFgW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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "k = GPy.kern.RBF(input_dim=1,lengthscale=0.2)\n", "\n", "X = np.linspace(0.,1.,500) # define X to be 500 points evenly spaced over [0,1]\n", "X = X[:,None] # reshape X to make it n*p \n", "\n", "mu = np.zeros((500)) # vector of the means --- we could use a mean function, but here it is just zero.\n", "C = k.K(X,X) # compute the covariance matrix associated with inputs X\n", "\n", "# Generate 20 separate samples paths from a Gaussian with mean mu and covariance C\n", "Z = np.random.multivariate_normal(mu,C,20)\n", "\n", "plt.figure() # open a new plotting window\n", "for i in range(20):\n", " plt.plot(X[:],Z[i,:])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Our choice of X means that the points are close enough together to look like functions. We can see the structure of the covariance matrix we are plotting from if we visualize C." ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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yVqss683pQlZAJ6NTyJt3IastZ8jqOcYcohmqWRl3+z/EHWtWXB88+OrfjIkg\nqxtWUISs7hLRH/QhK3RfCoMhq/XSJ4Ks6/r7TwFZV1Se+2SQVZaldz/Yg4fjA4GwZ69p4KUyZD2l\nZmXcq5j7/UOsfX0gnbdelzpklWW5jgJkhWpoXQRkhXagqgxZAVaHO7jbo9SArNWuq/IkkNVtnzVk\nbfPSswc/pWZl3LdseMQDLwxLBlllX2XICrchmi5NEaIpGAFZDw1MAlm1Mjr5IKtcZxLI6mufLWSN\nmSbptuFpb5yUUIassZqVcb/m6nAbXTRuo6/TQdauefA4ddYQLemErO6lBMeXlpUGZJUGXhuyqmV0\nioSsWhmdfJBVLaNTH8jqa/eFZWQ5KkTjM5qyXhuyDpkHn5VCszLuNizju6VOBlll2eeJBW6tYyCr\nLM8dsgI6GZ2Wnn7OZxwzD34MZA2tkwyyDnnYmPTcbYimsf45hGhkHZ56Am2IPjlEM1SzMu6PuYec\nCmk9+KSQ1V5ACSCrDH3YS8JdIvrDOMhq5Rr4rkshBrIW9o7FFztOAFmXG2CbBrLuWUwLWV0v3W0v\nAv16efA4HdrCIWMMvNx+hqyn1KyMexVzv++NuSeDrLKsDFkfBXadCrLKH4i+HnwXZGVHYw58ashq\nsD+e+pC1Op310TrJIKstXwRkXQb6yhPS9OC74u9y27G6DAM/K+P+iA0PG0BVXsCJIGu1oeZS9h0B\nWeVmXJ9qbpAV0MnoFAtZ622ngKyyfhLIKss23OLWwUwg65AQja8NT3vjpFr6uhri/c/fwM/KuBdc\nsWNV31Iv6lvqohGiUYesXfPgR0BWGaJZipcbknEvLatzgqwyRAOkh6zi+9KGrEMeNjYKssqy/Uzc\nurawjCz3DtH4fqrHQNYxBv7cdO7H165ZGXc7FdIHzZJB1qqz3cmtFCCrDNH4NjMnyCrLk0BWWX/4\nbHUga7VOeB68OmSV5ZCXLvtlyOo5xgxZXc3KuN9wxUMeBOKlYYMvwze3sfn6Fl2EaJab2+cYRxv3\n2IxO1tjhD9H4rvMbhj9szNbFrGcNfJdsiEb29fl9BcQ9bMz3GfuM+0bURc6Dj83oFJoto5LRaSny\nx/cJy8i6Phmd3LugDZ7tamZ0suozD96tg2MDOjRE49uWq6EhGvcYzl+zMu7XrA63yot6Noyd3WBD\nNDZkI0M0wCF8Y0M0OzgK0bB9XBmhUIhmTEYnWxcI0djdyRAN+C8lRBuir3vJxMoNybiXppXrl/WZ\nBw/EZXSw9byNAAAgAElEQVSCxufU+Nx7zIOPzegkHxymntFpu4aN8YdlUmV0ckMznSGa0GwZKzcg\n6PPE+8yDD9W1GXhtpdz2+WhWxn3HmoeBB4clg6xwOw6UISswy4xO1oNPktEpFrJC74eNxULWqr2o\ndzEBZK2Pu7F06zJkFfv3tUtlyAozM+577jU8d7uUHrs6ZJUOizJk1cro5P4InAKyds2DB3Qha8c8\n+DGQVSujUzRkdW/Burx0t5/Pg3e/jE4PHo4PBM4fsk7thc/HwM/KuG9bHhyWDLKCP8SnAVkhWUan\nqSGrWkanWMgqy8qQtWoPz4NXh6yy3BaH14KsDVt47h68e8IZssZqdsa968Fh2pC1cx78GMhab3Mq\nyDrEwHfJF6Lx+X0F6EJWuSNlyFqtHp4Hrw5ZPcfdKLt1YyGrWohGHkCsgcfT5tbB8YiNCdGAf9Te\nTcg6K+P++ABK7cV3exudCrKqZXTyQdaOefB2d1qQdYiB970PhWTs+0K85GWzRBGyds2Dtztc9oes\nWhmdIBKyyvLsISs0R1vb6PMdSKyB19bU4Z30mpVx3+43rITn3hVu0YCsahmdfJBVthfC8629rTlB\nVqvJIKssy89TAbLK8iSQFfo/bMz10uWyC7LOdh58V5vbLnX3IOusjPvj/T3Hc5deVxrIqpbRyQdZ\nXYNWpIWsofdtioWsrpJDVqWMTj7IqpXRCSIh65IMWXsZeKk+Bj6VztPAz8q4bx9uWOwesFjuqZyi\nW28pFWRlgU5GJ5/3Ve3oqC4VZJXrzR6yyrIyZK02U9TLCSBrfWzANJD17B42hqdN1uGpJ9CG6DPE\ng2+L3bfp/Az8rIx7cX3Fw089YL3ZwQZWi1tDngqyHvqmgKxyOxmyAj0gqywrQ9Zqk+F58OqQVSuj\nU0z45iznwYfWy5B1jGZl3Nmt2BcLdts1i+Wea9YsF3tSQla1jE4+yNoxDx50ISvEYa6Q2iCr3M8k\nkFUpo5MPsmpldIqGrJoZnbrCN4NDNLGQ1db3MfBSvgOJDdFkSc3LuF8bHn/qAY83Ox7CwYOXIRpt\nyApKGZ18kFWWAyAtQ1b8kBXawzJLTz/nMw5B1mqV4zu8VJC1cx58YGx462Iga37YmOhrj9WneYdo\nZmbcgcLAds1+uT948PZWNwVkVcvoBMeQ1Q0rJIastj/oQ1bovhRUIatSRicfZNXK6BQLWdUyOskP\n1tev8JTdL6PTg5dfii/YJuszZD2l5mXcd8CngI3hMbcePJAMssLtj4Y6ZJVluU6GrFV52QJZZVkZ\nsoJORqdYyApKGZ18XrrbbzYZnfC0yTo89QTaEH3ujgc/L+N+jRh0BooNN9AI0WhDVllWh6yy78wh\na5eBL1CGrKCT0cnG+fGHaKaArGoZndy6EGSdxcPGQutlyBqreRn3Hc0BuuEoRKMNWdUyOvkga9c8\neJw6a4iWDIKs7qVlpQFZpYGfBLJ2zYOHwZBVK6NTLGRVy+gExwNg6ekXCsvIclSIxmc0ZX2GrKfU\nvIz7NXVYpn5fe/AyRKMNWUPrqEBWWfZ5WL7tFMLzrQ1aLGQ9t4eNjYKs0D4PfgRk7ZoHrw1ZAZ2M\nTiFv3oWstpwhq+cYLydEMy/jvicwKNNBVrtOEshqL6CJIKu7RPSHcZDVyjXwXZfCYMhqvfQEkHW5\nAbbTQdYVlec+GWSVZendD/bgcTq0hUO0DbxUhqxS8zLuD2kadpl+LRFkDa2jAllleQLICtXQSgFZ\n5Q9EXw9+EGSFdqA6ArIa7I/nNJC12nVVngSyuu2zhqxtXvpYD74r/i63HavpDPy8jLs3LCPL+pC1\na51RkLXaUHMp+ypDVrgN0XTp7CHroQF9yFpveyrIKteZBLL62mcLWWOmSbpteNobJ9XS19UQ7/+q\nu4uC5mXc7e1z2zMzlCHrkIeNRUPWrnnwypDVvZTg+NKyOnfIqpbRyQdZxU6ngKxqGZ36QFZfuy8s\nI8u9QzS+n2ptyDpkHvzd0LyMu50K6Q3L1Mvag9eCrLJeHbJWne1ObpUIssry3CEroJPRaenpJ+sP\nn206yBpaJxlk1cro1Fj/HEI0sg5PPYE2RJ9QiMYeq09DQzRpze+8jPuO9oGJaBMhmn1RXzAiRLNq\nxNwXjSXEz4OPzei03ByipvHG3XcBy7pFs06GaIqCQ5ze9zGNmQdv62LWswa+SzZEI/seYu7AI9Hv\nKEQzJqOTdBAi58HHZnTqnpF1HKIZldEpJiwjy2MzOh3tQzOjk9Wlz4NPp3kZdztbBrH0hWXkQKxv\nad0QzXU931iGW+w85LEPG/NldGL7uDJCoRBN7MPGfBmdbJ0I0UAdvugxD17K/a10L5lYuSEZ99K0\ncv0yGaKxxxEK0QDDMzrZz73HPPjYjE5yTvtahG/cWTVqGZ3cWVi+sIwvROML5fjCMm5opjNEE5ot\nY+UGBH2eeIp58CmN8PkY+HkZdzcsI48+EWRtti+j1omGrPJ4J4CscjPyY5ojZAV0Mjr5ICu0zoPX\nhqyyfhLIKsuuly6Xs4CsQ0I0vjZa2qVSQVZ9zcu4+zx3694lgqxaGZ28kFU6LBNAVhmSkQ6b68G7\nl5bVOUHWQ/8UkLVjHrw2ZFXL6ATHZR9kbfPS3X4+D16Wozx4aA52Kw3IOsbAd+k8jPRQzcu4u/Pc\nfZ6KMmSF9pj7KMgqj1uOoUSQlY558HOCrLKsDllleQLIWq0TngevDlllOeSly359IGvDFp67B++e\n8DlAVj3Ny7jbp0K2GfdW49cfssqyNmTtnAevDFnP7WFjXbIhGtnX5/cVoAtZ5Y4mgKyyfhLIKstu\n3VjIqhaikQeQIesQzcu4QzgsI+sUIeuQh41BHGRVy+gUCVm1MjpJNDbGwPvex0JWNxqwlOclzvlo\nbMRA1q558HaHSx3IqpbRKRayhkIw9jNZBvr5wjJuaKYzRJMh61Sal3G/5ij+eZDPm1eArKCT0ckH\nWdUyOkVCVmCWGZ2sB58ko1NXWEZ+L4kga9Ve1LuYALLWx91YunVDIets58F3tbntUucJWedl3K2H\n5XpkIW9eAbJqZXTyQVa1jE6RkFUro5P7I+DztmM0BrLKkIw93kP/sZB1wMPGxkDWIQ8bgxGQ1XWO\nurx0t5/Pg3e/jE4PHo4PBM4LsvYx8OeneRl3+ScmNzbYFocfAVmrzdi4uS5kZYFORief9+W7hiBn\ndLJqg6yyPAFkrdp9XCcRZJXlkOdu+4QGR5vjtHSWDVt47h68e8LzhazzMu6+ee7u7afvSm81fu2Q\nFdrDLWMg66HvVJC13uYlQFa1jE6+z1iWJ4Cs1erhefDqkNVz3I2yW9cHsrrrJIesXQYeT5tbB8cj\n1m3D0w7+UXsekHVext03z90N0dhlmxfSA7JqZXSCY8iqltEpFrJ2zIO3uxsCWSEOc4XUF7LK94V4\nyeGwZCBkHfKwMbvDZX/IqpXRCSIhqyyngKyyHBWiGQNZoTna2kaf70BiQzTaSm9652Xc3WfLyLBL\n2z26rOsJWWWIRhuyVqekkNEpFrLK9kJ4vrVBmxNktUoCWaE9LLP09HM+4z6QVZYngazQ/2Fjrmcu\nl/lhY55jjIGsi5a28ZqXcYewl+56ZKF+PSGrVkYnH2RVy+gEcZDVNWiFHmS1/WEayOpKFbIexgKT\nQFatjE4QCVmXHHvwrnPU5aW7/QpP2f0yOj14+aX4gm0ZsvbRvIx711TIBJAVUMnoFPr3q0pGp1jI\nWu3oqC5D1lq+z3ECyFptpqiXE0DW+tgAfcgqfwxdJypD1kk1L+MuwzJy8EDTkCtCVq2MTqEHRqlk\ndIqFrHI7GbICAcgKOhmd6oPvgqzVJsPz4NUhq1ZGJ1+/WTxsLLTeKSGrvu716WyM+R5jzHuMMU8b\nY54yxvyEMeZPePq9wRjzu8aYh8aYf2GM+QKnfW2Measx5g+MMZ80xrzdGPOZUQfhhlx8r7Y2+dp2\nlLdr9sWCXb283q8PoNQur1mxY324Vb5mdYBf+0P76vC+uc6SHSuuWdfbrCCr7btbrLne3KPcUBmb\nNc04yYYDF8BCVgn6lp7y0tnOorm8ql/LRW2UOL4Dt8P6KvBeyjW2ITDrk3spuO8LUXfjvPcNhxvb\nbw83Rf3acQvq92KlnVO3dfrtnfdb8ZLbqF9mC6vtYxaF/XarEM2Cog7PVaOnCu9Vo0L+k7UaWdeN\nkE01cnaHPgsx8hrLGrIulnvY7G7HjhxHvnLbi8g2X1kuG7IG3h0lvjp39C2degJtrnwHIuv6jNjz\nUt+fyi8D/h7wr+p1/w7w08aYLyzL8hGAMeZ1wHcBrwI+Avxt4F11H+uWvBl4OfD1wNPAW4Efr7cf\nli8sE/LSlSCrVkYnH2QNrZMMssqybzuFuBxqgxYLWefwsLFoyArt8+CVIWu1yvEdXirI2jkPPjA2\nvHWhaydDVs8xThui6fUplmX5NfK9MeavA78PvAj4xbr6NcAby7L8qbrPq4CngFcAbzPGPBv4ZuCV\nZVn+fN3n1cAHjDEvKcvyPcEDsJ6S/Oxk2fXa3bZQv9Y/ZJhkkNWuMxlkdcMKipDVXSL6gz5khePL\nzNVgyGpjxxNB1nX9/U8FWffFIh1kleWC5kBx13Gv0YP6QFZZr23gpeYHWYf8REo9FyiBPwIwxnw+\n8DzgZ22HsiyfNsb8KvBS4G3Ai+v9yj4fNMZ8tO7Tbtx9/1Bt89LHQlaATRrIGlonGWSVZbmOAmSF\nanhfBGSFdqCqDFnh9omkU0BWgN12nQayuu2zhqxtXrqGB59Wg427McZQhVd+sSzL36yrn0dl7J9y\nuj9VtwE8AVyXZfl0Sx+/7J9NQmGZFJD1UNaHrF3rqENW2VcZssJtiKZLU4RoCkZA1kMDk0BWrYxO\nsZBVLaOTWzf0YWMyVNPY7qkha8w0SbcNT3vjpDxtaTRm6z8I/CngzyodS7d2r4Wb51QY+JNU3/1z\nnoTlk1W7vO92B1hb+EbWKTxsLPafrEMeNjbqn6xd8+Bx6qwhWtL5T1b3UoLjS8sqdInFKHYevC8M\nJIeG6yMkyegU+U9WrYxOsf9kVcvohFPnhmhkuy8sI8tRIRqf0ZT1Y+bBS/U18DF6H/B+p27r66im\nQcbdGPP3ga8Bvqwsy98TTR+j+jaeoOm9P8HtmX0MWBljnu1470/UbS07/gHYvLAq219/edVCu5c+\nBLLKcu3Ba0FWWT8JZJVlnycWuLWOgayyPHfICuhkdFp6+jmfccw8eG3ICuhkdPJ9+UMeNiY9d3n9\nnsSDTwVZXwK80Kn7HeAH+p9WpHpNhYSDYf/LwJ8vy/Kjsq0syw9TGeiXif7PBr4U+KW66r1Un4Ls\n83zgc4Ff7jyALu/bLbuvtjb5ap0maY6mScrpkXLpTpOU0yLtVEjbp7nO7TRJO71STpOsIKszTVJO\ncdyI10LU+aZNLsVy7albVJDVnSbpTjpbOu/d5ZKmgfVNbusr+5XeiLKtv/EsZV93ONhpkkVRTZOk\noDkV0tbtnLqt08+dJimnShbOdnaw3FfTJNf7XQOcutMk7dRHOU1STotcHOqKo2mScp1VXb9a7A7T\nJO/Napqk28GORik52txRSqBNLt3t+9Q2YmOnXaZTr70ZY34QeBL4OuAZY8wTddMnyrK0v7dvBr7X\nGPMhqqmQb6T6iXoHHADrDwNvMsZ8nCrA8hbg3a0zZaC6SAy3v/TuL34KyCrLypAV/LHRZJBVlpUh\n66PArlNBVnkj3teD74Ks7Gg8aCw1ZDXYGUrTQNZq11VZHbLa8kVA1mWgrzwhLciqr76f1LdRAdP/\n26l/NfCjAGVZfr8x5gHwQ1SzaX4BeLmY4w7wWqph/naqofxO4DujjsC9/XPjnm5YZixkhd4PG4uF\nrM32doOvAlmrDTWXsu8IyCo3I3c9R8gK6GR0ioWs9bangqxyHXXIKsvW+XLrYCaQdUiIxteGpz29\neu2lLMuoME5Zlq8HXt/SvgO+u34Nl72i5ZJA2b0Pd/u1hXYSQVatjE7RkLVrHvwIyCrDI/IuXF5K\ncHxpWZ0TZD30nwqyiu9rCsg66GFjcFz2QVbXUSo8dXJw+PqFruuD5vawsdNo2iDQaJW3RekByF/6\nUFhmKGR1++KUaw9+CGSF9nnw6pC16mx3cisFyCpDNL7NzAmyyvIkkFXWHz7bdJA1tI4KZJXlkJcu\n+91pyLogpWZm3PdUBl5kl5EDxB0Isk4OFDi+kkPhG1luNX7tGZ1WDYMeNw/eZ/B9GZ3W9hZdhGiW\nG/EpxRp33wUs6xbNuj7z4G8Y/rAxWxeznjXwXbIhGtnX5/cVcDwPPjajk8+4Swchch58bEan7nDf\ncYgm+mFjvoxOMWEZWRd62FgoLBNy3EYbeHkALvjsMw/erYNjI94VokmnmRl3O89hScPAI6pDIRrf\nfXcR6BcK0YA/LCMHYiCj03U93zhFRqcdHIVo2D6ujFAoROObBy/DMrZslzJEY+sCIRq7OxmisR9h\naH6B+1vpXjKxckMy7qVp5fplfebBA3EZnaDxOTU+9x7z4GMzOsk57WsRvnEfXdA1Dx6Iy+jkc5xC\nIRj7mSwD/XxhGfd67gzR+OLa7rdud2D7uJ54n3nwobo2Az+dZmbc9zRvezxE33rhWpDVbbdSgKyg\nk9EpGrLK41WGrMAsMzpZDz5JRqdYyAqt8+C1IausV4es9XE3lm5dhqwDjrW/ZmbcrTwG3qrLg5dl\nn2fuemRuu61TgKxDHjY2CrLKc1SGrFoZndwfgVNAVhmScW/2kkBW6cVPAFnVMjpBuOzz3H1eutvP\n58G7X0anBw/HBwJ3DbLOzLjLUW8V8OC1IKuv3e2LU649+C7IWm0mPA9eHbLK45bnpwFZaZ8H79vM\nuUJWtYxOsZBVlieArNU64XnwoyCrLIc8d9snNDj6QNaGOTh3D9494bTmd2bGXYZlpBwPXg6QsZCV\nlna7L5zyoV87ZIX2cIs2ZO2cBz8GstbbnAqyDjHwXfKFaHx+XwG6kFXuaALIKuvVIavnuBtlt24s\nZFUL0cgDiDXweNrcOjgesdPE4Gdm3K3n7hs9A0I0vvtuN3wRCsvIuoGQdcjDxsZA1kEPG4uFrB3z\n4O3utCDrEAPvex8Kydj3BcdDxR6TGmTtmgdvd7jUgaxDHjYGkZBVlmcPWaE52tpGn+9Augx8Ws3Q\nuLdd0oEQjfXCh0DWIQ8bO/JE/JBVhmimgKxqGZ18kFW2F8LzrX/k5gRZrSaDrLIsP89EkLVqL+pd\nKENWaJ8HH+Oly2UXZJ3tPHjI89y9cmNYbp0iZHXX8Xnutq4nZNXK6BQLWdUyOvkgq2vQirSQNfS+\nTbGQ1VVyyGrLE0FW6bGrQ9Ylxx686xx1eeluP58H734ZnR48HB8IXDJknZlxD8XcXQU8+CGQ1ZYT\nQFZAJaNTLGRlgU5GJ5/3Ve3oqC4VZJXrzR6yyvIEkLVq93EdBchaHxswDWT1sbWGkZ+DB59GMzPu\n0n3pkuPBywHSB7JC05ArQlatjE6xkPXQNwVkldvJkBXoAVlleQLIWq0engc/CrJqZXSKCd+c5Tz4\n0Ho+yJpWMzPu1nP34TDf6BkQonHvu90B6IZoCPSLgKxaGZ1iIataRicfZO2YBw+6kBV05sGH3od8\nrCSQtWsevDJkHfKwsWjIqpnRqSt8MzhEEwtZbX0fAy/lOxB3xKTTzIx7H8/dKhCisV54F2S1ZblU\ngqxaGZ1iISsoZXTyQVZZ9m2nEJ5vbdAyZBXltrDM0tPP+Yz7QFZZ1oasnfPgA2PDWxcDWbvmwTe2\nf44hmnSamXG38t3aJISsOEt3HZ/nbutaY4VmUsi6rD3/JJDVDSskhqy2P+hDVvDfB0qpQtbD3RyT\nQFbrDKSArPtiMS1kXTr9ennw8kvx2Q1Zn8LAp9XMjHvBcBAR8OC7IGublz4WsgIaGZ1iISvc/mio\nQ1ZZlutkyFqVly2QVZYngKzVZop6qQtZQSmjk89Ld/u5P4auEzULyJpOMzPu0O8SdOV48HJQhCAr\nTrvclK8fgX6+AXwoTwNZZVkdssq+M4esXaOrQBmygk5Gp/oD64Ks1SbD8+DHQNZBDxtrM+62HIKs\nXfPgZaimsd1zgKxpNTPjLr959xJMCFll2ReCaQvfyLqe8+C1IataRicfZO2aB49TZw3RkkGQ1b20\nrDQgqxxdk0DWrnnwoApZtTI6+SCrWkYnOB4AS0+/UFhGlqNCNKF/j2rMg5fyHkgSzcy4y9kySh68\na3jdi2rIw8ZCHj6ir1uuPfiUkDW0jgpklWWfh+XbTiE839qgxULWc3vY2CjICu3z4JUha7XK8R2e\nBmQFdDI6hbz50ASFWULWHJbxyL0EoelXyX7QPM2ekLXNm3e9dLct1G8r+k4IWe06SSCrvYAmgqzu\nEtEfxkFWK9fA++4DpQZDVutQTARZ1/X3nwKyrqg898kgqyxL736wB4/ToS0iMNbAp9XMjLscuXB7\neQ9VwIN3Y3UxAxFPP9nu8+ZleQLIGlpHBbLK8gSQFarLJAVklT8QfT34QZAV2oGqMmSF27SP2pC1\n2nVVngSyuu2zgqwLUmpmxh2O/1+oGKKB5qCImQcfCsHEQFbo/bCxMZC1a51RkLXaUHMp+ypDVjiv\nefAFIyDroYFJIKtWRicfZJXrTAJZfe2zgaxpNTPjbgdQrIE/c8ga8i5sWRmyDnnYWDRk7ZoHrwxZ\n3UsJji8tq3OHrGoZnSIhq1ZGJx9kVcvo1Aey+tp9YRlZ7h2i8f1Ua0HWNJqZcYfjyyyBBx8K0YTC\nMkMhq9sXp1x78FqQVdarQ9aqs93JrRJBVlmeO2SFjnnwypC1ax78GMgaWicZZO2aB+9znKTnLq/f\nyT34tOZ3ZsZdfsuuHzVDyCrLE0BWm8QjCWSV3vkEkFWGPuzl4i4R/eF8IWth71jc8ZAIsi43wDYN\nZN2zmBayul66214E+kV58BC+F4TxkDWtZmbcoduPSgBZpeeuCVlludObHw9ZwR9zV4GsiHOcALI+\nonmdWs0RsrKjMQc+NWQ12B9Pfchanc76aJ1kkNWWk0DWK6Ckv2INfPbchVzfbeIQjfSeQmGZPpDV\nbbdKBFmb7e0Gvzdklcc7AWSVm3F9qrlBVuiYB68NWettp4Cssn4SyCrL1vly6+BMIWtazcy4Sw01\n8GcEWUOhnESQVSujkxeyynOcALLKn/mleLk3vO6lZXVOkFWGaID0kFV8V9qQVS2jExyXfZDVdY7c\nEI3s5wvLyHJriMbnxfh+qvtA1jwV0pEbQT2BB68FWX3tbl+ccu3BD4Gs0D4PfhRklcctzy8RZJUh\nGt9m5gRZZXkSyCrrD5+tDmSt1gnPg1eHrLIc8tJlvz6QtWHkU3jwaTUz4y5Hp/xDwEQGHpoDxKXt\nsk4OFDi+kmPmwbcav9sQzb6oLxgRolk1DHrcPHifwfdldFrbW/QUGZ1k3aJZ12ce/A3nmdHJ97tu\nt2X7WY+7d0Ynn3GXDkLkPPjYjE7dM7KKo/bojE5Lcc31CcvIutDDxkJhGd8fGBvbHWrg5QGEft71\nNTPjDs37qTEGvuuWamSIxnff7YYvQmEZWecLy8iBWN/SuiGa6/qhTikyOu0gXUYnu5QhGlsXCNHY\n3ckQjT2UkH/k/laONfC+976ZOe5odYeKPaZBGZ2g8Tk1Pvce8+BjMzrJB4epZ3TarmFj/GGZsQ8b\nk21uv14hmtBsGSs3IDhkhA3XzIy7HN0aBr6PAiEa64UPgaxDHjZ25InEQ1bQyejkg6xqGZ0iISsw\ny4xO1oNPktEpFrJC6zz4MZC1ai/qXUwAWevjbizduqGQNfk8+BxzD0gaeKsUkFXWD/DgZdnnxbse\nWcibV4CsWhmdfJBVLaNTJGTVyujk/ggMnQc/BrJ2zYMHdCFrxzz4MZB1yMPGYARkdZ2jLi/d7efz\n4N0vo9ODh+MDgW7ImsMyjtpmHM8MstryRJC12kx4HvwYyErXPHh5fhqQlfZ58L7NxEJWud4UkFUt\no1MsZJVlZchatYfnwatDVlkOee62T2hwtDlOS2fZMPJjPfi0mplxl5+s7x+pM4Os0DTkiSErtIdb\nxkDWQ9+pIGu9zUuArGoZnXyfcci42x0pQ9Zq9fA8eHXI6jnuRtmt6wNZ3XXUIWv23B35jLmWgfdd\nWrLeda9HQlZ3ALohGgL9BkJWrYxOcAxZ1TI6xULWjnnwdndDICvozIP3vW8L+0wGWbvmwdsdLvtD\nVq2MThAJWWU5BWSV5agQTV/Imk4zNO6Q1sD3USBEY73wLshqy3KZELLKEI02ZAWljE6xkFW2F8Lz\nrX/k5gRZrSaDrLIsP08FyCrLk0BWaJ8HH+Oly2WfefCN7Q/x4LPnLuR+U+7h++rGQlZo9+wHePBu\n2fXS3bZQv56QVSujkw+yqmV0gjjI6hq0Qg+y2v4wDWR1lRyy2nICyKqV0QkiIeuSYw/edY66vHS3\nX+Epu19GpwcPxwcCzZGVZ8s4kpeIa5RnBlmHPGzM581HQlZAJaNT6N+vKhmdYiFrtaOjugxZa7VB\nVllWhqzVZop6OQFkrY8N0Iesgx421seDz567Rz4DL+tPHKKxh9UFWXHa5aZ8/Qj08w3gQz/9jE6h\nB0apZHSKhaxyOxmyAj0gqywrQ9Zqk+F58OqQVSujk69f1zx4GappbDfWwGfPPaApDXzbPHjXvT5B\nRieIgqxaGZ18kFUto1MsZO2YBw/DIat8L7/dVJBV7mcSyNo1D34EZNXK6BQNWTUzOrn9QmEZWY4K\n0XRB1jSamXHfO+/P3IN3Da97UQ152FjIw0f0lfs+lPUyOvkga2idZJBVln3bKYTnWxu0WMg6h4eN\njYKs0B6WWXr6OZ9xCLJWqxzf4aWCrJ3z4ANjw1sXunaSQdYclnEkDTaEDXyov1wnxsDj1Mtt4DkW\nWzdhRidZ1/qHDJ2MTj7IqpbRKRayumEFRcjqLhH9QR+ywvFIc6UKWQ93c6hDVq2MTrGQVS2jk/xg\nfcFD4xQAACAASURBVO3Sux/swcsvZenU62uGxh3iDLwWZB2qgAfvxupiBiKefrLd5837ICugkdEp\nFHNXyegkz68tDi/Lch0FyArVaLhYyCrLypAVdDI6xUJWUMro5N5l+9rVIWuOuQu13ZOfeYjGHlaf\nefChEMxQyHoo60PWrnXUIavsqwxZ4bzmwRcoQ1bQyehUf2B95sFrQ9ZBDxtrM+62PPRhY9Jxa2zX\nZ+Cz595DGbI26nrOgx8DWYc8bGwUZO2aB49TZw3Rkk7IKo01YvVUkNUdeXKfch9yn3JouMOmE7J2\nzYOHwZBVK6NTLGRVy+iEU+eGaGS7Lywjy1EhmgxUPZKhFYgL0cj6E3vwoRBNKCyjCVllufbgtSCr\nrJ8Esspy2w2drCuE51sbNB9kleWLhKzQPg9+BGTtmgevDVkBnYxOvi+/ax68z3GSnru8fr0efA7L\nRCjWwIf6y3V8fpTvh0Fe/nIbeI7F1p0YsnoHpQ5ktUk8JoOs9gJKAFll6MMaa3eJ6A/jIKuVa+B9\ndkVqMGS1jkUCyLrcANvpIOuKynNPAlldL91tLwL9oj34K7dBVTM27kM8+CGQVSoBZJWee2rIKsvK\nkBX8sdFkkFWWlSHro8CuU0HWtlHZpsGQFdqB6gjIarA/ntNA1mrXVVkdstpyMsiaPXchd547HBtx\nOA672LYzDtFI7ykUlhkLWaH3w8ZiIWuzvd3gq0DWakPNpew7ArLKzchdXwxkPTSgD1nrbU8FWeU6\n6pBVlq3z5dbBSMiaTjMz7kOUIWujnAiyamV0ioasXfPgR0BWGaJZipcbkpHv3R+Bc4asahmdfJBV\n7HQKyKqW0ckHWV1HyQ3RyH6+sIwsB0M06dTLuBtjvg34duDz6qp/C7yhLMt3ij5vAL4FeC7wbuDb\ny7L8kGhfA28CvpHqknsX8B1lWf5+3FH4bkIzZPX2o6WsDFmhfR68OmStOtud3EoBssoQjW8zc4es\ngE5Gp6Wnn6w/fLbpIGtoHRXIKsshL132GwxZ06iv5/7bwOuAf09lmf468A5jzJeUZfkBY8zrgO8C\nXgV8BPjbwLuMMV9YlqW993oz8HLg64GngbcCPw58Wb9DcQ049AvR2DbXaMu6E8+DD4Vl5ECRp+j2\nI9Bu94VTPvRrz+i0ahj0uHnwPoPvy+i0trfoIkSz3IhPKda4+y5gWbdo1vWZB3/D8IeN2bqY9WIJ\njw3RuPeG1Nt4JPodhWjGZHSSDkLkPPjYjE7d4b7jEM2ojE4xYRlZF3rYWCgs43PcSvyRZiX1Mu5l\nWf5fTtX3GmO+HfjPgA8ArwHeWJblTwEYY14FPAW8AnibMebZwDcDryzL8ufrPq8GPmCMeUlZlu/p\nd/hdBt5VqM1XP8bAt91V2ONG9B2Z0QmnHArftHkhvlkSgYxO1/V84xQZnXZwFKJh+7gyQqEQjW8e\nvO9hY3YpQzS2LhCisbuTIRr7EYZGmc+tGHJH7o5Kd/6WlRylcnS6w8GW1TI62c+9xzz42IxOck77\nWoRv3Fk1ahmdfI5TKARjP5NloJ8vLONez0P9wR7q67kfZIy5B3wDlRPzS8aYzweeB/ys7VOW5dPG\nmF8FXgq8DXhxvU/Z54PGmI/WfXoadxjvwZ9xiMZ64VqQ1W23UoCsoJPRKRqyyuNVhqzALDM6WQ++\nC7ICOhmdfJAVWufBa0NWWa8OWevjbizdujGQdcXtbVUC9TbuxpgvAn6Z6hA/CfyV2kC/lOpG4yln\nlaeojD7AE8B1WZZPt/SZQH0MvLtOXwPfBlll/QAPXpZ9nrnrkbnttk4BsmpldIqGrPIclSGrVkYn\n90fgXCDroX8KyNoxD14bsqpldIJw2ee5+7x0t5/Pg5flWx8piYZ47v8OeAHwHOCvAj9qjPly1aMK\n6p9S+SZSfxp4YV1uC4e4BjvWwHfNg58RZPW1u31xyrUH3wVZq82E58GrQ1Z53PL8NCArJMvodA6Q\nVZbVIassTwBZq3XC8+BHQVZZDnnutk9ocNi2/+/H4I9+rKp/TB1v/wQp1du4l2VZAL9Vv32/MeYl\nVLH276eyTE/Q9N6fAN5flz8GrIwxz3a89yfqtg79F8B/XJd9Ec+xIRrbdiYhGntYWpCVlna7L5zy\noV87ZIX2cIs2ZO2cBz8GstbbnAqyDjHwXbIhGt/vut2W7acKWeWOJoCssl4dsnqOu1F269og6/Oe\nhOc+2byV+uT74A9fRCrdU9rGuizLD1MZ6JfZhhqgfinwS3XVe6lOS/Z5PvC5VKEeBfmGfpcv1VZf\neOrcNvne1+Ye042nvhB15fHhhEIqobL7amuTr21HebvmcbFgt12zLxZc79cHUGqX16zYsT7cKl+z\nOsCv/aF9dXgv17Ft16zrbS4bfXeLNdebe5QbKm9yTTNOsuH2r/UWskrQt3TKdim3s2gur+rXclEb\nJY7vwK2LcCXeyyWivxsPD4FZn9zReuOU5Qj0jVZ3OBxG4h5uivq14xaeyuXOU+eW5futeNkd725f\nZgur7WMWhf12qxBNFWq5HRFVeG/HQoyi9WG0XDcgazVydoc+cp3Gsoasi+UeNjtYlrdjQY4Lt9z2\nIrLNluUPYgL18tyNMd8H/HPgo8B/AHwT8BXAX6q7vJlqBs2HqKZCvhH4HeAdcACsPwy8yRjzcaqY\n/VuAd/efKeObhWI11oMPhWhk3Qwh65CHjR15In7IKkM0U0BWtYxOPsgq2wthjOsfublDVmiOZisV\nyCrL8vNMBFmr9qLehTJkhfZ58CEvPRayrkiqvmGZzwT+AfBZwCeA3wD+UlmWPwdQluX3G2MeAD9E\n9SemXwBeLua4A7yW6qt+O9UweSfwnWNOQkchA09L3VjIiqj33TQ7IRp5GHJJoOzz2peeOjx1PSGr\nVkanWMiqltHJB1ldg1akhayh920aA1mlJy+Hij0vYDhkHfCwsTGQdcjDxiASsi5p51x26TpHhadO\nDo6+Vnegeu2mLMtviejzeuD1Le074Lvrl4JCc9d9LuoQyCrX8dXNCLLacgLICqhkdIqFrCzQyejk\n876qHR3VpYKscr0pIKtaRicfZJXlCSBr1e7jOgqQtT42IA1klZ9fAk30G5JadyhEYw9rCGSVp+kz\n/r5+vgF86Kef0SkWsh76poCscjsXCFnVMjr5PmNZngCyVquH58GPgqxaGZ1C/c4sLDNTdRl4V1Ma\n+LZ58K57PfKfrO4AdEM0BPpF/JNVK6NT7D9Z1TI6+f7J2jEPHlD9JyvozIP3vW8L+4TmwdtzGfRP\n1iEPG7M7XPb/J+uQh41F/5NVM6OTr19izcy47zva75AH7xreGMgqT0+GXdru0WVdC2TVyugUC1lB\nKaOTD7LKsm87hfB8a4M2J8hqlQSyQntYZunp53zGfSCrLGtD1s558IGx4a3zQdYclnHlM9KplBqy\n4tTLbeBsWwmy4izddXyeu61rg6xKGZ1iIataRic4hqxuWCExZLX9YRrI6koVsh7u5pgEsmpldIJj\nyKqW0Ul+sLLunKZCno+6DPxcIOtQBTz4Lsja5qWPhayARkanWMgKtz8a6pBVluU6GbJW5WULZJXl\nCSBrtZmiXupCVlDK6OQLbxbkmHtYvqEodYdCNPawuiArTrvclK8fgX6+AXwoTwNZZVkdssq+GbIe\n+kVBVtDJ6FQffBdkrTYZngc/BrIOethYm3G3ZetI5bBMKnUZeFcXAlll2ReCaQvfyDqFh42Ngaxq\nGZ18kLVrHjxOnTVESwZBVvlefrupIKvcjzpk7ZoHD6qQVSujkw+yqmV0guMBsKT5Q5dAF2DcY0I0\nMNyD7wrRyPoTe/Cu4XUvqiEPGwt5+Ii+brn24FNC1tA6KpBVln2emG87hfB8a4MWC1nn8LCxaMgK\n7fPglSFrtcrxHZ4GZAV0MjqFvPkclolRl4HX3LYmZPW12W3Ase+F51hsXYQH3+bNu1662xbqtxV9\nJ4Ssdp0kkNV6YBNBVneJ6A/6kNWeOuIUXA2GrNahmAiyruvvPwVkXVF57skga2JdiHGHOA/+3CCr\n1ASQVRqvtoGIp59s93nzsjwBZA2towJZZXkCyArVaLgIyArtQFUZssJt2kdtyFrtuiongaw55t5H\nvqEodcch65CHjbWFb9xyz4eNjYGsXeuMgqzVhppL2VcZssJtiKZLU4RoCkZA1kMDk0DWIQ8bi4Ws\ncp0kkPUBSXVhxn2s+oZ3MmRtlCeErEMeNhYNWbvmwStDVmmsEaungqy+4KDczxjIqpbRKRKyamV0\n8kHWQQ8bg+NyCLJmoDpEMSEaiPPgh4RoZP2JPfhQiCYUlhkKWd2+OOXag9eCrLJeHbJWne1ObpUI\nssry3CEroJPRaenp53zGMfPgx0DW0DpqkDUD1aHq64WP2XaGrI3yBJC1SuJBGsgqvfMJIKsMfVhj\n7S4R/WEcZLVyDbzvPlAqBrIW9o7FHQ+JIOtyA2zTQNY9i7SQNXvuYxTjwd8xyCo9d03IKsud3vx4\nyAr+mLsKZEWc4wSQ9RF+w5oKsraNyjbFQFZ2NObAp4asBvvjqQ9Zq9NZH62jBlkzUJUaYuh8Q1Hq\nDkFWOdik9xQKy/SBrG67VSLI2mxvN/i9Ias83gkgq9yM/JjmCFkBnYxOsZC13nYKyCrrk0DWHJaZ\nm/oYeHedvgb+jCBrKJSTCLJqZXTyQlZ5jhNAVhmiWYqXG5KR790fgXOBrDJEA6SHrOK70oasahmd\n4LjsOk4JNEPj3uZptykmROPbrlaIRtbHhmhmBFl97W5fnHLtwQ+BrNA+D34UZJXHLc8vEWSVIRrf\nZuYEWWV5Esgq6w+frQ5krdYJz4MfDVmz5x5SKF7epq4QTdt2x4ZobNuZhGjsYXU9bMx6r9LTcK/k\noQ8bO/S7DdHsi/qCESGaVcOgx82D9xl8X0antb1FT5HRSdYtmnV95sHfMPxhY7YuZr1YwmNDNL7f\ndbm/Ao7nwcdmdPIZd+kgRM6Dj83o1D0jqzhqj87otBTXnDzWPM+9TUMM/Bh1GXhXoTZtA992V2GP\nG9F3ZEYnnLIbonHb5Z2CG5aRt+P1La0bormuH+qUIqPTDtJldLJLGaKxdYEQjd2dDNHYQwmNMp9b\nIb+SWLmj1Z2/ZSVHqRyd7lCxxzQooxM0PqfG595jHnxsRif54DD1jE7bNWzMcVgmz5bpUgoPPkPW\nYFgmBFmHPGzsyE2Nh6ygk9HJB1nVMjpFQlZglhmdrAefJKNTLGSF1nnwYyBr1V7Uu0gAWXNY5hKk\nOQ++y8C3QVZZP8CDl2WfF+96ZCFvXgGyamV08kFWtYxOkZBVK6OT+yNwCsjaNQ8e0IWsHfPgx0DW\nIQ8bgx6QNU+FjFFKyHpu8+DPFLLa8kSQtdpMeB78GMhK1zx4X4x4DGSFZBmdpoasahmdYiGrLCtD\n1qo9PA9+NGTNnnsf5RBNfzkevPSs+0BWeZo+4+/r12r82iErtIdbxkDWQ9+pIGu9zakg6xAD3yVf\niMbn+hSgC1nljpQha7V6eB78aMiaPfe+mhNkTWngfZeWrHfd65GQ1b3N9kEzX7+BkFUroxMcQ1a1\njE6xkLVjHrzdnRZkHWLgfe9DIRn7Xg4NdwipQdauefB2h8v+kFUroxMEIGv23Icoe/D9FQjRWC+8\nC7LK05Nhl7Z7dFnXE7LKEI02ZAWljE6xkFW2F8LzrX/k5gRZrSaDrLIsP08FyCrLSSDrqiSlLtS4\nz0GngKzQ7tkP8ODdsuulu22hfj0hq1ZGJx9kVcvoBHGQ1TVoRVrIGnrfpljI6io5ZB3wsLFYyKqV\n0QkCkHV9G/5JoQs27hmyTgpZtTI6RUJWQCWjU+jfryoZnWIha7Wjo7pUkFWuN3vIKsvKkLXaTFEv\n9SHrM6ub4I+ihi7YuFvlEE1/OR689KxDkBWnXW7K149AP5/VOvTTz+gUemCUSkanWMgqt5MhK9AD\nssqyMmStNhmeBz8Wsu4fbPkU6XQHjDtkyBo7D951r0+Q0QmiIKtWRicfZFXL6BQLWTvmwYMuZIXb\nETTGwIfeyxGYHLIOediY3eGyHbJqZXQKQdZ7i8ehj1hFd8S4w3APvitEQ2C7MR58V4hG1p/Yg3cN\nr3tRaWV0knUtkFUro5MPsobWSQZZZdm3nUJ4vrVBy5BVlNvCMktPP+czDkHWapXjOzwtyHq92PI0\n6XSHjPtQdRl4zW2nhqw49XIbeI7F1k2Y0UnWtUFWpYxOPsiqltEpFrK6YYXEkNX2B33ICv77QClV\nyKqU0ckHWbUyOoUg673GL72+7phxv+uQdagCHnyKjE4+b94HWUElo1Mo5q6S0ckXI/bF4WVZrpMh\na1VetkBWWVaGrKCT0Snk9T9qQBd93THjbpUha385Hrz0rDUzOvn6+azWoawPWbvWUYessu/MIWvX\n6CpQhqygk9HJxvnxh2hSQNaH2bin0jlA1jZlyNqoS5TRyQdZhzxsbBRk7ZoHj1NnDdGSQZBVvnfj\n9JoGfhLI2jUPHgZDVq2MTiHIuiAD1YQ6NWQdEqKR9Sf24EMhmlBYRhOyynLtwWtBVlk/CWSVZZ/7\n7dtOITzf2qDFQtZze9jYKMgK7fPgR0DWrnnwYyGrDPml0B037kPV1wsfs21NyOprs9uA5mV25pBV\nlkEVstokHpNBVjd5Q2LI6i4R/WEcZLVyDbzvPlBqMGS1jkUCyLrcANt0kFWGdVIoG/c7BVmlEkBW\n6bmnhqyyrAxZwR9zTwZZZXkCyArVaEgBWdtGZZsGQ1ZoB6ojIKvB/nimgaxXg+6c45WN+0EZsvZX\nIEQjvadQWGYsZAWVjE6hB4f1fdjYKMhabai5lH2VISvchmi6dPaQ9dCAPmStt50Ksm4yUJ1SU0PW\nvsqQtVFOBFm1MjpFQ9auefDKkFUaa8Tqc4SsahmdfJBV7DQFZF1mz31qTQlZtUI0sv6MPPiUkNXt\ni1OuPfghkBXa58GrQ9aqs93JrRJBVlmeO2QFdDI6LT39ZP3hs9WDrPez534KpQjRtG13bIjGtrlG\nW9adeB58KCzjZnRyjXcofCPLrcavPaPTqmHQ4+bB+wy+L6PT2t6iixDNciM+pVjjHpvRyRo7bj3a\nouAQp/d9TGPmwdu6mPViCY8N0fjQyxXwSPQ7CtGMyegkHYTIefCxGZ1C4b4cljmZzmEefNsxhNp8\n9WMMfNtdhT1uRN+RGZ1wyqHwjXs7PjCj03X9UKcUGZ12cBSiYfu4MkKhEM2YjE62ToRooA5f9JgH\nL+VzK+TXGCt3VLrzt6zkKJWjMxTZU8voZD/3HvPgYzM6yQeHrUX45l6e535KZcjaX4EQjfXCtSCr\n226lAFlBJ6NTNGSVxzsBZJWbcePrc4OsgE5GJx9khdZ58GMh6zp77lnt6mPg3XX6Gvg2yCrrB3jw\nsuzzzF2PzG23dQqQVSujUzRklec4AWSVIZmleLkevHzv/gicC2Q99E8BWTvmwY+FrKsMVE+tuc6D\nl/Wuob4AyOprd/vilGsPvguyVpsJz4NXh6zyuGPj8L4Auu9OoDiGrHTMg58TZJVldcgqywkga465\nn43mFqKxbWcSorGHpQVZaWm3+8IpH/q1Q1ZoD7doQ9bOefDKkPXcHjbWJRui8f2u223ZfqqQVe4o\nAWTNYZmz0twhq5aBD0U/fRZqQIjGd9/thi9CYRlZNxCyamV0gjjIqpbRKRKyamV0kiNpjIH3vY+F\nrL4hpAZZu+bB2x0uh0HWReMXQ1/ZuPfW3Dz4thj8jCGrUkYnH2SVIZopIKtaRqdIyArMMqOT9eCT\nZHTqCsvI70UJsm6i7luGKxv3i1TIwNNSNxayQrtnP8CDl2WfF+96ZCFvvidk1croFAtZ1TI6RUJW\nrYxO7o+Az9uO0RjIKkMy7s3eaMiqlNEpBFnzs2XOUnOFrHIdX92MIKstJ4CsgEpGp1jIygKdjE6+\nALrvTgByRierNsgqywkg6/qcPXdjzN8Cvg94c1mWf0PUvwH4FuC5wLuBby/L8kOifQ28CfhGqo/1\nXcB3lGX5+2OOZ3rlEE1/OR689Kz7QFZ5mj7j7+vXavz0MzrFQtZD36kga73NS4CsahmdfJ+xLCeA\nrJvEf2K6N3RFY8yfAb4V+HWn/nXAd9VtLwGeAd5ljFmJbm8Gvhb4euDLgc8GfnzosZxWaW+tjuUb\n+l0T1nzr3rTUuW3yva9N1tu6G47NhK0rjw8zFFIJld1XW5t8bTvK2zX7YsGuXl7v1wdQapfXrNix\nPoRqrllhM+3sD+2rw3u5jm27Zl1vswrR2L67xZrrzT3KDZXbs6YZJ9lw+/xyC1kl6Fs6ZbuU21k0\nl1f1a7mojRLN38gltwb0SryXSynX2PZxf9yR7I4qOdLc977hcBiJe7gp6teOW3gqlzunbuu07533\nW/GyO97dvswWVtvHLAr77VYhmuq57tfnGZYxxnwa8A+pvPP/wWl+DfDGsix/qu77KuAp4BXA24wx\nzwa+GXhlWZY/X/d5NfABY8xLyrJ8z6AzOamGevBdIRoC270wD16GaGIhqzw9ZciqldEpFrKCUkan\nWMgq2wthjGuDNifIapUEskJ7WGYkZN24DEpZQz33twL/rCzLn5OVxpjPB54H/KytK8vyaeBXgZfW\nVS+m+ghknw8CHxV97ojSxtyaCnnwbXV9PHi3Xm7D3fa5e/DmyIOXnrtcuh689Njte9un6fUvDx68\n9fylB19BVseDl973hqYXLz14+V5689aDdzx3FlWowvXgpVcubx6g6bn73sOxWzLEg3dHHqL+xrNE\nvHeHg+vBH3nu0vtu3M1x7M27Hr3rwQsv3nrw6/3O8eDPbCqkMeaVwJdQGWlXz6O6Yp9y6p+q2wCe\nAK5rox/qM0Pddcg6VAMhq1ZGJx9kBZWMTrGQFUAlo1MsZK12dFSXIWst3+eYALI+OKewjDHmc6ji\n5V9ZluXUwWbgnTSvQIAvAr54+kMJKkPW/hoAWXHa5aZ8/Qj0Cxm/OkQzBWSV5Ukgq9xOhqxAALKC\nTkanAn7sp+DH/jmweMx+8SlKY/j404ORZ5T6eu4vAj4DeJ8xxl6NC+DLjTHfBfxJqqv0CZre+xPA\n++vyx4CVMebZjvf+RN3Woq8GPqvnIZ9CQwz8GHUZeFdTGvgrsR0rn4VyDLw8NLkkUHbvw91+odAO\nqDxsbMw/WdUyOsX+k3XAw8bs7uQ8eNu9zzz4MQY+9F6OQHfkyaHhDpvOf7IOedhY4J+sT/5FePIV\nwBpungXXG8Ov/NsVX/ki+4R6ffU17j/DsZv8I8AHgP+5LMvfMsZ8DHgZ8BsANUD9Uqo4PcB7qU75\nZcBP1H2eD3wu8Mv9T+FcdY6QtStEI+tP7MG7hte9qLQyOvkgqyzXHnxKyBpaJxlklWVlyDqHh41F\nQ1bo/7CxHpB1c31Gz5Ypy/IZ4DdlnTHmGeAPy7L8QF31ZuB7jTEfAj4CvBH4HeAd9TaeNsb8MPAm\nY8zHgU8CbwHePc+ZMtrqMvCa224z/qG6kIH3tdltwLHvhedYbF2EB9/mzbteutsW6rcVfY+8eZPs\nn6x2HenBL2vPP8k/Wd2wgkweMvKfrO4S0R/83vVYA++7D5SS+3CHkD0v4PifrNahkIb7cDfH6H+y\nXu08EwoUpWFFGkdYluX3G2MeAD9E9SemXwBeXpbltej2WqrTfzvV0Hon8J0Kx3JmukuQVWoCyCr/\n3BTy5uXm+kBWWZ4AsobWSQZZZVmuowBZoRoNFwFZoR2ojoSsy7SO+3jjXpblX/DUvR54fcs6O+C7\n69cdUIas/eV48NKbHvqwsbbwjVtWyOgUC1m71lGHrLKvMmSF2xBNl6YI0RSMgKyHBpJAVtKF2xu7\nykquc4CsbcqQtVGeELKqZXSy5ydDND7IOuBhYxAHWaWxRqyeCrL6goNyP2Mgq1pGp9DjgmUsI4Gy\ncZ9Up4asQ0I0sv7EHnwoRBMKywyFrG5fnHLtwWtBVlk/CWSVZZ/77dtOEQdZZXnukBXQyei09PRb\nkj33LOjvhY/ZdoasjfIEkNUm8ZgMslpmkQCyytCHNdbuEtEfxkFWK9fA++4DpWIga2HvWNzxoAVZ\n0/5BNRv36ZUh6zB5PHjpuWtCVlmeALKCP+aeDLLKsjJkfRTYdSrI2jYq2xQDWdnRmAOvDlmz536p\nypC1vwIhGm3I6rZbJYKszfYJIGu1oeZS9h0BWeVm3Pj63CAroJPRKQRZs3HPOp36GHh3nb4G/owg\nayiUkwiyamV0ioasXfPgR0BWGaKZO2SVIRpIAFkzUL1kpQzR+LarFaKR9bEhmhlBVl+72xenXHvw\nQyAr9H/Y2CjIWnW2O7mVAmTtmgc/J8gqy0kga/bc74JShGjatjs2RGPbziREYw+r62FjEiaGjPfQ\nh40d+t2GaPZFfSWLEM2qYdCHP2zMl9FpbV1BEaJZbsSnFGvcfQ8bk3WLZl2fefA3DH/YmK2LWS+W\n8NgQTQi9tM6Dj83o5DPuG7Jxvzs6h3nwbccQatM28G13Ffa4EX17hmh8992Fpx+BdjfWb8vuLInt\nmseb3VGI5po1S2yoZvjDxoBD+MaGaHZwFKJh+7gyQqEQTezDxuxShmhsXSBEY3cnQzT2IwyNMp9b\nIb+SWLmj1Z2/ZSVHqRyd7lCxx9T5sDGoILTrCOydsn0ufEJl435WypC1vwIhGuuFD4GsShmdYiEr\n6GR0ioas8niVISswy4xO1oNPktEpBFmz5551XtKcB99l4Nsgq6xXhqzuOj7P3dYpQNYhDxsbBVnl\n+StD1iEPG+N29bOCrF3z4GEkZE2bHzsb9/PTXZoHf6aQ1ZYngqzVZsLz4NUhqzzu2Dh8K2dotqfK\n6DQ1ZFXL6BSCrNlzv6vKIZr+UoKs8jQngKzQ/2FjYyBr5zz4MZC13uZUkHWIge+SL0STBLLGnPAI\nZeN+1poTZE1p4H2Xlqx33euRkNW9zU4MWbUyOkEcZFXL6OSDrAMeNma7D4GsQwy8730oJGPfpnLx\nWwAACbJJREFUy6GhBllzWOauK3vw/TUSssrTmwCyds2D14asahmdfJBVthfzhqxWySBr/hNT1vnr\nFJAV2j37kZAVZ+mu4/PcbV1PyKqV0SkWsqpldPJBVtegFWkha+h9m2Ihqyt1yJqnQmZlyDoxZNXK\n6BQJWaH/w8bGQFaGPGwsFrJWOzqqSwVZ5Xqzg6w7kiob91kph2j6awBkxWmXm/L1I9DPZ7U8kFUr\no1MsZD30TQFZ5XYyZAVaIGuOuWc1lSHrrdrmwbvu9QkyOkEUZNXK6BQLWdUyOvkg64CHjdndDYGs\ncDuCtCGr3E8SyDrEV+mhbNxnqaEefFeIhsB2Yzz4rhCNrD+xB+8aXheyamV0ioSsWhmdYiErKGV0\n8kFWWc6QtR2yOv6GtrJxv1PqMvCa204NWXHq5TbwHIutmzCjk6xrg6xKGZ1iIataRic4hqzuw7IS\nQ1bbH/QhK/jvA6VGQdZs3LP8uuuQdagiIKtWRqdYyAoqGZ1iISvc/mioQ1ZZlutkyFqVfZA1kbJx\nn70yZO2vDsiqldEpFrIeytNAVllWh6yy78wha9foKhgJWbPnntWtc4CsbcqQtVGXKKNTLGRVy+jk\ng6wDHjYGwyGrfO/G6TUNfArImvqSzcb9YnRqyDokRCPrT+zBh0I0obCMJmSV5dqDTwlZQ+uoQFZZ\n9rnfypD13B421geyFvlPTFlp1dcLH7NtTcjqa7PbgOZlduaQVZYhOWS16ySBrJZZTARZ3SWiP4yD\nrFaugdeCrDc5LJMVr7sEWaUSQFbpuaeGrLI8AWQNraMCWWV5AsgK1WhIAVnbRmWbYiHrrozY2Ahl\n436RypC1vwIhmikgK6hkdIqFrF3rjIKs1YaaS9lXGbLCec2DL4iHrLv8D9WsYZoasvZVhqyN8oSQ\nVS2jkz2/UIgGkkNWaawRq88Bso6514xRNu4XrSkhq1aIRtafkQefErK6fXHKtQevBVllvTpkrTrb\nndwqEWSV5blB1sTPDcvG/fKVIkTTtt2xIRrb5hptWXfiefChsIyb0ck13qHwjSy3Gr/2jE6rRsx9\n0ViCfkan5UZ8SrHGPTajk/3TD7chmqLgYBF9H9OYefC2Lma9WMJjQzQ+9HJFNu5ZKjqHefBtxxBq\n89WPMfBtdxX2uBF9R2Z0wimHwjfuffrAjE7XrFliQzWrQ/glVUYnto+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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.matshow(C)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Exercise 3: \n", "Try a range of different covariance functions and hyper-parameter values and plot the corresponding sample paths for each using the same approach given above. Compare these to the shapes of the covariance functions you found in Exercise 2. Can you see any relationship?" ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# Try plotting sample paths here" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Exercise 4:" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The sample paths from a GP inherit their properties (such as continuity, differentiability, smoothness etc) from the particular covariance function used.\n", "\n", "Can you tell the covariance structures \n", "that have been used for generating the\n", "sample paths shown in the figure below?\n", "
\n", "
\n", " \n", "\n", " \n", "\n", " \n", "\n", "
\n" ] }, { "cell_type": "raw", "metadata": {}, "source": [ "# Exercise 4 answer" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 3. A Gaussian Process Regression Model" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We will now combine the Gaussian process prior with some data to form a GP regression model with GPy. We will generate data from the function $f ( x ) = 0.3\\cos(1.3 x ) + \\sin(0.3x )$ over $[0, 10]$, adding some noise to give $y(x) = f(x) + \\epsilon$, with the noise being Gaussian distributed, $\\epsilon \\sim \\mathcal{N}(0, 0.01)$. " ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "X = np.random.uniform(0, 10, (200, 1))\n", "f = np.sin(.3*X) + .3*np.cos(1.3*X)\n", "Y = f+np.random.normal(0, .1, f.shape)\n", "plt.scatter(X, Y)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "A GP regression model based on an exponentiated quadratic covariance function can be defined by first defining a covariance function, " ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "collapsed": false }, "outputs": [], "source": [ "k = GPy.kern.RBF(input_dim=1, variance=1., lengthscale=1.)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "And then combining it with the data to form a Gaussian process model," ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\n", "Name : GP regression\n", "Objective : 199.15646490667305\n", "Number of Parameters : 3\n", "Number of Optimization Parameters : 3\n", "Updates : True\n", "Parameters:\n", " \u001b[1mGP_regression. \u001b[0;0m | value | constraints | priors\n", " \u001b[1mrbf.variance \u001b[0;0m | 1.0 | +ve | \n", " \u001b[1mrbf.lengthscale \u001b[0;0m | 1.0 | +ve | \n", " \u001b[1mGaussian_noise.variance\u001b[0;0m | 1.0 | +ve | \n" ] } ], "source": [ "m = GPy.models.GPRegression(X,Y,k)\n", "print(m)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Just as for the covariance function object, we can find out about the model using the command print m. " ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\n", "Name : GP regression\n", "Objective : 199.15646490667305\n", "Number of Parameters : 3\n", "Number of Optimization Parameters : 3\n", "Updates : True\n", "Parameters:\n", " \u001b[1mGP_regression. \u001b[0;0m | value | constraints | priors\n", " \u001b[1mrbf.variance \u001b[0;0m | 1.0 | +ve | \n", " \u001b[1mrbf.lengthscale \u001b[0;0m | 1.0 | +ve | \n", " \u001b[1mGaussian_noise.variance\u001b[0;0m | 1.0 | +ve | \n" ] } ], "source": [ "print(m)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Note that by default the model includes some observation noise\n", "with variance 1. We can see the posterior mean prediction and visualize the marginal posterior variances using m.plot()." ] }, { "cell_type": "code", "execution_count": 17, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 17, "metadata": {}, "output_type": "execute_result" }, { "name": "stderr", "output_type": "stream", "text": [ " /Users/pmzrdw/anaconda/lib/python3.5/site-packages/matplotlib/figure.py:1742: UserWarning:This figure includes Axes that are not compatible with tight_layout, so its results might be incorrect.\n" ] }, { "data": { "image/png": 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nc889lx9//LHOOXfu3MmIESPo0KEDNpuNM844gzlz5oSUycrKYuzYsTgcDiwW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\nbdrE7bdvB+ae1cbjCarVar2AXTab5aGHHsL3feL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j2Zx11lmnPAOtVc5dyOweMqC+QOnw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\naNI+Zocoay25QpnJTJGp6Sx+EP49Fo0Qi3pt27tZrlQpV3x83yfwAyw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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "m.plot()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The actual predictions of the model for a set of points Xstar\n", "(an $m \\times p$ array) can be computed using \n", "\n", "Ystar, Vstar = m.predict(Xstar)" ] }, { "cell_type": "code", "execution_count": 18, "metadata": { "collapsed": false }, "outputs": [], "source": [ "Xp = np.linspace(-2,12)[:,None]\n", "Ystar, Vstar = m.predict(Xp, full_cov=True)\n", "up95, lo95 = m.predict_quantiles(Xp, quantiles=(2.5,97.5))\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Note that the inputs to GPy need to be 2-d arrays." ] }, { "cell_type": "code", "execution_count": 19, "metadata": { "collapsed": true }, "outputs": [], "source": [ "Xp = np.linspace(-2,12)[:,np.newaxis]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Exercise 5" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "a) What do you think about this first fit? Does the prior given by the GP seem to be\n", "adapted?" ] }, { "cell_type": "raw", "metadata": {}, "source": [ "# Exercise 4 a) answer" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "b) The parameters of the models can be modified using a regular expression matching the parameters names (for example m['.*noise'] = 0.001 ), or by m.Gaussian_noise.variance=0.001. Change the values of the parameters to obtain a better fit, replotting your fitted model." ] }, { "cell_type": "code", "execution_count": 20, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# Exercise 4 b) answer" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "c) As in Section 2, random sample paths from the conditional GP can be obtained using\n", "np.random.multivariate_normal(mu[:,0],C) where the mean vector and covariance\n", "matrix mu and C are obtained through the predict function mu, C = m.predict(Xp,full_cov=True). Obtain 10 samples from the posterior sample and plot them alongside the data below." ] }, { "cell_type": "code", "execution_count": 21, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# Exercise 4 c) answer" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Note that the GPy.models commands are wrappers for a collection of commands. GPRegression makes two default choices here:\n", "\n", "1. Specifies a Gaussian likelihood, i.e., we assume that $y=f(x) + e$ where $f$ is the GP, and $e\\sim N(0, \\sigma^2)$ is the Gaussian noise term (referred to as the likelihood in GPy), sometimes called a **nugget** in spatial statistics.\n", "2. Specifies an inference scheme, i.e., a way of calculating the posterior distribution of $f$ given the training data. Because we are using a Gaussian likelihood here, the posterior distribution of $f$ is also a Gaussian process, and so inference can be done exactly.\n", "\n", "We could equivalently set up the model using the following:\n" ] }, { "cell_type": "code", "execution_count": 22, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\n", "Name : gp\n", "Objective : 199.15646490667305\n", "Number of Parameters : 3\n", "Number of Optimization Parameters : 3\n", "Updates : True\n", "Parameters:\n", " \u001b[1mgp. \u001b[0;0m | value | constraints | priors\n", " \u001b[1mrbf.variance \u001b[0;0m | 1.0 | +ve | \n", " \u001b[1mrbf.lengthscale \u001b[0;0m | 1.0 | +ve | \n", " \u001b[1mGaussian_noise.variance\u001b[0;0m | 1.0 | +ve | \n" ] } ], "source": [ "gauss = GPy.likelihoods.Gaussian(variance=1.0)\n", "exact = GPy.inference.latent_function_inference.ExactGaussianInference()\n", "m1 = GPy.core.GP(X=X, Y=Y, kernel=k, likelihood=gauss, inference_method=exact)\n", "print(m1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Covariance Function Parameter Estimation" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As we have seen during the lectures, the parameters values can be estimated by maximizing the likelihood of the observations. Since we donâ€™t want one of the variance to become negative during the optimization, we can constrain all parameters to be positive before running the optimisation." ] }, { "cell_type": "code", "execution_count": 23, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "WARNING: reconstraining parameters GP_regression\n" ] } ], "source": [ "m.constrain_positive()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The warnings are because the parameters are already constrained by default, the software is warning us that they are being reconstrained." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now we can optimize the model using the m.optimize() method. A number of optimizers are available, such as 'scg', 'lbfgs', 'org-bfgs', 'fmin_tnc', as well as stochastic optimizers if a dependency on a package 'climin' is satisfied, such as 'adadelta' and 'rprop'." ] }, { "cell_type": "code", "execution_count": 24, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\n", "Name : GP regression\n", "Objective : -151.23345681629752\n", "Number of Parameters : 1\n", "Number of Optimization Parameters : 1\n", "Updates : True\n", "Parameters:\n", " \u001b[1mGP_regression. \u001b[0;0m | value | constraints | priors\n", " \u001b[1mGaussian_noise.variance\u001b[0;0m | 0.00895683789669 | +ve | \n" ] }, { "name": "stderr", "output_type": "stream", "text": [ " /Users/pmzrdw/anaconda/lib/python3.5/site-packages/matplotlib/figure.py:1742: UserWarning:This figure includes Axes that are not compatible with tight_layout, so its results might be incorrect.\n" ] }, { "data": { "image/png": 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7W24sRDfk9XopLi4mEFBx1nrIL3Hw5fd72LynkF2Hytlf6OBwqZMf9uYxfuL9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\nwhe+wCOP/JgDBw6wZctmbrvt9uLWC+vWraO7u6u4Cuf+++/HX1bOwdY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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "m.optimize(messages=1, ipython_notebook=True) # Messages indicates you wish to see the progress of the optimizer, needs ipywidgets to be installed\n", "m.plot()\n", "print(m)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The parameters obtained after optimisation can be compared with the values you selected by hand. As previously, you can modify the kernel used for building the model to investigate its influence on the model." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Note what has happened outside the range of the data: the GP prediction returns to its prior mean value of 0. We could fix this by adding a prior mean." ] }, { "cell_type": "markdown", "metadata": { "collapsed": true }, "source": [ "## Problems with hyper-parameter optimization" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Unfortunately, optimization of GP hyper-parameters is not always without problems. The likelihood surface that is being maximized is often flat and multi-modal, and thus the optimizer can sometimes fail to converge, or gets stuck in local-maxima. You can see from the optimization output above, that the gradients at the optima are very small ($10^{-18}$), but not necessarily zero. This kind of problem is due to the use of numerical optimization. When using GPs this can type of problem is common, and so we must always sanity check our answers, and ideally run some diagnostic tests on the fitted model.\n", "\n", "As an example, consider\n" ] }, { "cell_type": "code", "execution_count": 25, "metadata": { "collapsed": false }, "outputs": [], "source": [ "np.random.seed(16)\n", "X = np.linspace(0.05,0.95,10)[:,None]\n", "Y = -np.cos(np.pi*X) + np.sin(4*np.pi*X) + np.random.normal(loc=0.0, scale=0.1, size=(10,1)) " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "If we now fit a GP and optimize the hyper parameters, you may find some problems." ] }, { "cell_type": "code", "execution_count": 26, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 26, "metadata": {}, "output_type": "execute_result" }, { "name": "stderr", "output_type": "stream", "text": [ " /Users/pmzrdw/anaconda/lib/python3.5/site-packages/matplotlib/figure.py:1742: UserWarning:This figure includes Axes that are not compatible with tight_layout, so its results might be incorrect.\n" ] }, { "data": { "image/png": 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i7jq7A9QBBxyw3fq2bNlCY2Mjv/71r6mpqUnrdjNFwUlERCRDCgoK2Guvvfj3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\nMJWVlZSXlxMIBAAIBAKUl5dTWVmp8CQ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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "m = GPy.models.GPRegression(X,Y) # this will automatically use a RBF covariance function\n", "m.optimize(messages=1)\n", "m.plot()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Exercise 5:\n", "What may have happened here?\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [] }, { "cell_type": "markdown", "metadata": {}, "source": [ "One way to fix this is to change the parameter settings so that the optimizer starts in a more sensible location as described above. \n", "\n", "Another option is to run the optimizer multiple times from multiple different starting points, and pick the best possible (I'd recommend this as good practice). This can be done in GPy as follows:" ] }, { "cell_type": "code", "execution_count": 27, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Optimization restart 1/10, f = 11.96887713535652\n", "Optimization restart 2/10, f = 7.969923622373031\n", "Optimization restart 3/10, f = 7.969923622373408\n", "Optimization restart 4/10, f = 7.969923622374876\n", "Optimization restart 5/10, f = 11.968877507245928\n", "Optimization restart 6/10, f = 7.969923622373341\n", "Optimization restart 7/10, f = 7.969923622373198\n", "Optimization restart 8/10, f = 7.969923622377622\n", "Optimization restart 9/10, f = 7.96992362237698\n", "Optimization restart 10/10, f = 7.969923622373035\n" ] }, { "data": { "text/plain": [ "" ] }, "execution_count": 27, "metadata": {}, "output_type": "execute_result" }, { "name": "stderr", "output_type": "stream", "text": [ " /Users/pmzrdw/anaconda/lib/python3.5/site-packages/matplotlib/figure.py:1742: UserWarning:This figure includes Axes that are not compatible with tight_layout, so its results might be incorrect.\n" ] }, { "data": { "image/png": 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FaTum87bvLeVfH+1gS+6hep/XaRRC1S5CAT9oNGi0BrSmpFo7zeeXeMlfs4MV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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "m.optimize_restarts(10) # try 10 different starting locations \n", "m.plot()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The fit chosen is the one with the highest maximum likelihood. This is not always what we want, and so we may choose to use methods such as looking at prediction error on a held out dataset, or cross-validation to choose the hyper parameters. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can also do things like fix certain parameters, constrain them to lie in a given range, and put prior distributions over them. Notice how this information is reported when you type print(m)." ] }, { "cell_type": "code", "execution_count": 28, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Warning: changing parameters to satisfy constraints\n", "WARNING: reconstraining parameters GP_regression.rbf.lengthscale\n", "WARNING: reconstraining parameters GP_regression.rbf.variance\n", "\n", "Name : GP regression\n", "Objective : 12.012149258332974\n", "Number of Parameters : 3\n", "Number of Optimization Parameters : 2\n", "Updates : True\n", "Parameters:\n", " \u001b[1mGP_regression. \u001b[0;0m | value | constraints | priors \n", " \u001b[1mrbf.variance \u001b[0;0m | 1.42852320245 | +ve | Ga(3.2, 2.1)\n", " \u001b[1mrbf.lengthscale \u001b[0;0m | 0.200000007687 | 0.2,1.0 | \n", " \u001b[1mGaussian_noise.variance\u001b[0;0m | 0.1 | +ve fixed | \n" ] }, { "name": "stderr", "output_type": "stream", "text": [ " /Users/pmzrdw/GPy/GPy/core/parameterization/priors.py:301: RuntimeWarning:divide by zero encountered in log\n" ] }, { "data": { "image/png": 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CJgglBZ06wYABwQYjTbbxyCOZ7B93poQZTNZqXSIijVBSsA39gI7V2+oefzx0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\nUsZwNCVoyqCIRCvhk4JBYcd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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "m.Gaussian_noise.variance.fix(0.1)\n", "m.rbf.lengthscale.constrain_bounded(lower=0.2, upper=1)\n", "\n", "gamma_prior = GPy.priors.Gamma.from_EV(1.5, 0.7)\n", "gamma_prior.plot()\n", "m.rbf.variance.set_prior(gamma_prior)\n", "m.optimize()\n", "print(m)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To remoe these constraints and priors, we can do something like the following:" ] }, { "cell_type": "code", "execution_count": 29, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\n", "Name : GP regression\n", "Objective : 11.016765214370487\n", "Number of Parameters : 3\n", "Number of Optimization Parameters : 3\n", "Updates : True\n", "Parameters:\n", " \u001b[1mGP_regression. \u001b[0;0m | value | constraints | priors\n", " \u001b[1mrbf.variance \u001b[0;0m | 1.42852320245 | | \n", " \u001b[1mrbf.lengthscale \u001b[0;0m | 0.200000007687 | | \n", " \u001b[1mGaussian_noise.variance\u001b[0;0m | 0.1 | | \n" ] } ], "source": [ "m.unconstrain()\n", "m.rbf.variance.unset_priors()\n", "print(m)\n", "m.constrain_positive() # we've removed the postive constraint above, so we should reset this constraint.\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Exercise 6:\n", "Generate some data from the model $$y = x*sin(x)+e \\qquad e \\sim N(0,0.1^2)$$ for x in the range $[0,5]$. Fit a GP regression model. Do your hyperparameter estimates look reasonable? Try constraining the noise variance to be $0.1^2$. Predict the function in the range $[-5,10]$. Do your predictions look reasonable? What could you do to fix this?" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [] } ], "metadata": { "anaconda-cloud": {}, "kernelspec": { "display_name": "Python [conda root]", "language": "python", "name": "conda-root-py" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.5.2" }, "widgets": { "state": { "18254e5c823e4e98b16a1fa1ba2f0601": { "views": [ { "cell_index": 74 } ] }, "1f7845e1830243379232e8c4e97eaa41": { "views": [ { "cell_index": 67 } ] } }, "version": "1.2.0" } }, "nbformat": 4, "nbformat_minor": 0 }
indexrbf.lengthscaleconstraintspriors
[0] 0.20000000 +ve