{ "metadata": { "name": "", "signature": "sha256:d5bb33ca912678d7713eb88b7fe2604530cb89be2eefa8bce0075e1aa2806c0d" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Introduction to GPy: Gaussian Process Regression in GPy\n", "\n", "# Gaussian Process Summer School, Melbourne, Australia\n", "### 25th-27th February 2015\n", "### Neil D. Lawrence and Nicolas Durrande\n" ] }, { "cell_type": "code", "collapsed": false, "input": [ "%matplotlib inline\n", "import numpy as np\n", "import pods\n", "import pylab as plt\n", "import GPy\n", "from IPython.display import display" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stderr", "text": [ "/Users/neil/Library/Enthought/Canopy_64bit/User/lib/python2.7/site-packages/pytz/__init__.py:29: UserWarning: Module pods was already imported from /Users/neil/sods/ods/pods/__init__.pyc, but /Users/neil/Library/Enthought/Canopy_64bit/User/lib/python2.7/site-packages is being added to sys.path\n", " from pkg_resources import resource_stream\n" ] } ], "prompt_number": 1 }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Covariance Function Parameter Estimation\n", "\n", "In this session we are going to optimize the parameters of the Gaussian process using gradient based optimization approaches. These maximize the likelihood function: which is defined as the probability of the model given the parameters, $p(\\mathbf{y}|\\mathbf{X}, \\boldsymbol{\\theta})$. \n", "\n", "First we'll load in the olympic marathon data." ] }, { "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": 2 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Then we'll construct a Gaussian process model with an exponentiated quadratic covariance function." ] }, { "cell_type": "code", "collapsed": false, "input": [ "k = GPy.kern.RBF(1)\n", "model = GPy.models.GPRegression(x, y, k)\n", "display(model)\n", "model.plot()" ], "language": "python", "metadata": {}, "outputs": [ { "html": [ "\n", "\n", "

\n", "Model: GP regression
\n", "Log-likelihood: -118.821194703
\n", "Number of Parameters: 3
\n", "

\n", "\n", "\n", "\n", " \n", " \n", " \n", " \n", " \n", "\n", "\n", "\n", "\n", "
GP_regression.ValueConstraintPriorTied to
rbf.variance 1.0 +ve
rbf.lengthscale 1.0 +ve
Gaussian_noise.variance 1.0 +ve
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dPWir8+t5xzxetwN9sVEUigru/5HVwgGAj376JgBqJLhh/TOGHgWlFK+/sh4f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\nF4tY53xzxcFjmtFs1FFmc7BDTlZCjO9egqQfuBNkfS0GAYn94Ag7DjG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"text": [ "" ] } ], "prompt_number": 3 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Rather sensibly, we've given the model an initial plot, and we can clearly see that the inital length scale is too low. This makes sense, our prior says that the length scale is 1 year, which means that athletic performance varies across very short time scales. This is perhaps unlikely, let's choose a larger lengthscale and try again.\n" ] }, { "cell_type": "code", "collapsed": false, "input": [ "model.rbf.lengthscale = 10.\n", "model.plot()" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 4, "text": [ "{'dataplot': [],\n", " 'gpplot': [[],\n", " [],\n", " [],\n", " []]}" ] }, { "metadata": {}, "output_type": "display_data", "png": 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9aJuSt2h7+7w8t+kAAB+5OT5LrwohzptRksu/fuFW/vG+60hPdbHvcD1/969P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\nRvr9BlWludhs8d36fnvvCf7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"text": [ "" ] } ], "prompt_number": 4 }, { "cell_type": "markdown", "metadata": {}, "source": [ "That seems better, now we can think about optimization. First though we have to consider the fact that some of the parameters are constrained (for example lengthscales and variances can only be positive). GPy allows the user to specify such constraints when constructing the model.\n", "\n", "### Parameter Constraints\n", "\n", "As we have seen during the lectures, the parameters values can be estimated by maximizing the likelihood of the observations. Since we don\u2019t 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", "collapsed": false, "input": [ "model.constrain_positive('.*') # Constrains all parameters matching .* to be positive, i.e. everything" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "WARNING: reconstraining parameters GP_regression\n" ] } ], "prompt_number": 5 }, { "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.\n", "\n", "Now we can optimize the model using the \n", "\n", "model.optimize()\n", " method." ] }, { "cell_type": "code", "collapsed": false, "input": [ "model.optimize()\n", "model.plot()\n", "display(model)" ], "language": "python", "metadata": {}, "outputs": [ { "html": [ "\n", "\n", "

\n", "Model: GP regression
\n", "Log-likelihood: -6.94713791215
\n", "Number of Parameters: 3
\n", "

\n", "\n", "\n", "\n", " \n", " \n", " \n", " \n", " \n", "\n", "\n", "\n", "\n", "
GP_regression.ValueConstraintPriorTied to
rbf.variance 25.3995048241 +ve
rbf.lengthscale 152.045313 +ve
Gaussian_noise.variance0.048506484546 +ve
" ], "metadata": {}, "output_type": "display_data", "text": [ "" ] }, { "metadata": {}, "output_type": "display_data", "png": 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ereC51z+hoqYZgNm5qdx18zLm5qV5Nc6JYGhNeVUzvVYrESEWFkxPISVeJtQS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\nKv2OJ4GOlOBHuv5kKMF39Vh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"text": [ "" ] } ], "prompt_number": 6 }, { "cell_type": "markdown", "metadata": {}, "source": [ "The parameters obtained after optimisation can be compared with the values selected by hand above. As previously, you can modify the kernel used for building the model to investigate its influence on the model.\n", "\n", "By adding covariance functions together we can try and decompose the observation in to a longer lengthscale process and a shorter lengthscale process. Below we consider a GP that is initialised with a long lengthscale exponentiated quadratic, and a Matern $\\frac{5}{2}$ covariance to take account of shorter lengthscale effects. We also add a bias term to allow for an overall average." ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Exercise 5 a) answer \n", "kern = GPy.kern.RBF(1, lengthscale=80) + GPy.kern.Matern52(1, lengthscale=10) + GPy.kern.Bias(1)\n", "model = GPy.models.GPRegression(x, y, kern)\n", "model.optimize()\n", "model.plot()# Exercise 5 d) answer\n", "model.log_likelihood()\n", "display(model)" ], "language": "python", "metadata": {}, "outputs": [ { "html": [ "\n", "\n", "

\n", "Model: GP regression
\n", "Log-likelihood: -5.99078279431
\n", "Number of Parameters: 6
\n", "

\n", "\n", "\n", "\n", " \n", " \n", " \n", " \n", " \n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "
GP_regression.ValueConstraintPriorTied to
Gaussian_noise.variance0.0368133074589 +ve
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hEmy3khxUy6cv/4S7vvp1/vnffgrQndCfeXH9gLX98cRlGJwurCImzMaq+Rmy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\n82V1FBRVkl9URWllAwdOXOD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"text": [ "" ] } ], "prompt_number": 7 }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Exercise 2\n", "\n", "Now model Model the data with a product of an exponentiated quadratic covariance function and a linear covariance function. Fit the covariance function parameters. Why are the variance parameters of the linear part so small? How could this be fixed?" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Exercise 2 answer" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 8 }, { "cell_type": "markdown", "metadata": {}, "source": [ "DRAFT\n", "===\n", "\n", "## Gene Expression Example\n", "\n", "We now look at a real data example where there are multiple modes to the solution. In [Kalaitzis and Lawrence](http://www.biomedcentral.com/1471-2105/12/180) the objective was to understand when a temporal gene expression was either *noise* or had some underlying signal. To determine this Gaussian process models were fitted with and without a temporal kernel, and the likelihoods were compared. In the thousands of genes they considered, there were some where the posterior error surface for the lengthscale and the signal/noise ratio was multi modal. We will consider one of those genes. The example can also be rerun as\n", "python\n", "GPy.examples.regression.multiple_optima()\n", "\n", "The first thing to do is write a helper function for computint the likelihoods add different signal/noise ratios and different lengthscales. This is to allow us to visualize the error surface. " ] }, { "cell_type": "code", "collapsed": false, "input": [ "def contour_objective(x, y, log_length_scales, log_SNRs, kernel_call=GPy.kern.RBF):\n", " '''Helper function to contour an objective function in a set up where there \n", " is a kernel for signal corrupted by noise.'''\n", " lls = []\n", " num_data=y.shape[0]\n", " kernel = kernel_call(1, variance=1., lengthscale=1.)\n", " model = GPy.models.GPRegression(x, y, kernel=kernel)\n", " y = y - y.mean()\n", " for log_SNR in log_SNRs:\n", " SNR = 10.**log_SNR\n", " length_scale_lls = []\n", " for log_length_scale in log_length_scales:\n", " model['.*lengthscale'] = 10.**log_length_scale\n", " model.kern['.*variance'] = SNR\n", " Kinv = GPy.util.linalg.pdinv(model.kern.K(x)+np.eye(num_data))[0]\n", " total_var = 1./num_data*np.dot(np.dot(y.T, Kinv), y)\n", " noise_var = total_var\n", " signal_var = SNR*total_var \n", " model.kern['.*variance'] = signal_var\n", " model.Gaussian_noise = noise_var\n", " length_scale_lls.append(model.log_likelihood())\n", " print SNR, 10.**log_length_scale\n", " display(model)\n", " lls.append(length_scale_lls)\n", " \n", " return np.array(lls)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 9 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now we load in the data and compute the likelihood values." ] }, { "cell_type": "code", "collapsed": false, "input": [ "data = pods.datasets.della_gatta_TRP63_gene_expression(gene_number=937)\n", "x = data['X']\n", "y = data['Y']\n", "y = y - y.mean()\n", "kern = GPy.kern.RBF(input_dim=1)\n", "model = GPy.models.GPRegression(x, y, kern)\n", "resolution = 2\n", "log_lengthscales = np.linspace(1, 3.5, resolution)\n", "log_SNRs = np.linspace(-2.5, 1., resolution)\n", "lls = contour_objective(x, y, log_lengthscales, log_SNRs)" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "0.00316227766017 10.0\n" ] }, { "html": [ "\n", "\n", "

\n", "Model: GP regression
\n", "Log-likelihood: -2.10275061954
\n", "Number of Parameters: 3
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GP_regression.ValueConstraintPriorTied to
rbf.variance 0.00025506380619 +ve
rbf.lengthscale 10.0 +ve
Gaussian_noise.variance 0.0806582576232 +ve
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\n", "Model: GP regression
\n", "Log-likelihood: -2.12547857371
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GP_regression.ValueConstraintPriorTied to
rbf.variance 0.000255972082804 +ve
rbf.lengthscale 3162.27766017 +ve
Gaussian_noise.variance 0.0809454799079 +ve
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\n", "Model: GP regression
\n", "Log-likelihood: -1.41450534969
\n", "Number of Parameters: 3
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GP_regression.ValueConstraintPriorTied to
rbf.variance 0.0671183959588 +ve
rbf.lengthscale 10.0 +ve
Gaussian_noise.variance0.00671183959588 +ve
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\n", "Model: GP regression
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GP_regression.ValueConstraintPriorTied to
rbf.variance 0.779949847367 +ve
rbf.lengthscale 3162.27766017 +ve
Gaussian_noise.variance0.0779949847367 +ve
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\n", "Model: GP regression
\n", "Log-likelihood: -16.7147336689
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GP_regression.ValueConstraintPriorTied to
rbf.variance 1.0 +ve
rbf.lengthscale 1.0 +ve
Gaussian_noise.variance 1.0 +ve
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Vy76iVAHdAqxw95vNbDCwjbtvVrib2SvAT9x9rpkNBdq6+6AGtiu6KiAIvXmO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\nQESkTCkBiIiUKSUAEZEypQQgIlKm/j97/HKURg95ZwAAAABJRU5ErkJggg==\n", "text": [ "" ] } ], "prompt_number": 38 }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Sampling with Hamiltonian Monte Carlo" ] }, { "cell_type": "code", "collapsed": false, "input": [ "model.kern.lengthscale=30.\n", "model.kern.variance=0.5\n", "model.Gaussian_noise=0.01\n", "model.kern.lengthscale.set_prior(GPy.priors.InverseGamma.from_EV(30.,100.))\n", "model.kern.variance.set_prior(GPy.priors.InverseGamma.from_EV(0.5, 1.)) #Gamma.from_EV(1.,10.))\n", "model.Gaussian_noise.set_prior(GPy.priors.InverseGamma.from_EV(0.01,1.))\n", "_ = model.plot()" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "WARNING: reconstraining parameters GP_regression.rbf.lengthscale\n", "WARNING: reconstraining parameters GP_regression.rbf.lengthscale\n", "WARNING: reconstraining parameters GP_regression.rbf.variance\n", "WARNING: reconstraining parameters GP_regression.rbf.variance\n", "WARNING: reconstraining parameters GP_regression.Gaussian_noise\n", "WARNING: reconstraining parameters GP_regression.Gaussian_noise\n" ] }, { "metadata": {}, "output_type": "display_data", "png": 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HXBMnH/3eN/n9E4/z+G+fZcM11/LWO8W8uD+f2sb3c1JcVCgbVi5hZWYiq7KSiJ3i/2lL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\nH4/y3N6z+FnNfO9Lt7I6e26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"text": [ "" ] } ], "prompt_number": 50 }, { "cell_type": "code", "collapsed": false, "input": [ "hmc = GPy.inference.mcmc.HMC(model, stepsize=5e-2)\n", "s = hmc.sample(num_samples=1000)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 51 }, { "cell_type": "code", "collapsed": false, "input": [ "plt.plot(s)" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 52, "text": [ "[,\n", " ,\n", " ]" ] }, { "metadata": {}, "output_type": "display_data", "png": 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DmQJvjitES7Nuxh/0k+hMtB6wXZE/Jp9Pt33aresIgjDw9LnA/+K9XzDqsVFkeDP498X/\ntgY9odWCd9lc5Cbl9nVTLEYkj2BX9S5r4lNhTaE1DgDGA+GUiacwMmUkn2//3Fr/yZZPAGPSVix4\nbeVrrCpexemTTgeMyVjRumjM4tjVDdXduqYZOZOgEqIW+Jl5M2P6UBMEoX/oc4Gfv3E+YPjdnTan\nlbkQWgU+WqGJFcOThrOrepdV3OLRrx+1xgFCmZU3K8yCT3ImkaASYhYnv3T3UqYNm2b50bsTc25O\nyKqu757A+4N+Kx3EyRNOtlITdMbwpOF7XY4eQYgH+jwOvthvWJpmhEoolgVvbz+ztC/JS85jR9UO\nKxSyoLqAy2dc3m6/W464hfP2O4+fvf0zyurKqLy5kme+e4Zlhcti0o6KQAVXH3I12b5s9s3a14g5\nj9JFYxZK6a4F//svfk9pXSkAz5/+fFSDtNm+bIpqimjWzSSoBNRdipVXrWTfYXtf9k1BGEr0WxSN\nGTkTipl3JlLqgL5kUsYkvt75NUW1RYDhkjFDN8P2y5zE3PFzLYtdKYXX4aW+qb7dvj2hsKaQ3MRc\nzpxyJvcfdz8euydqF836MiNE0syQGS2hIZJKqahy47vsLhKdiZT6S611CzYv6NZ1BUHof/pc4Mem\njgUIy3diMlAuGtMdMzNvJgA+h6/TYt2hPneXzdWulmxPKawpJDux1ffvtrujdtHsrNrJrLxZbKvc\n1uW+zbq51zH8EzImsK50nTWoaw7yCoIweOlzgb/9qNuByFb6QLloTMxfFWYahY4I9bm77K6YWvA5\niTnWcncSexVUFXDk6CPZWLaxy30f+/oxvPd5w8YTusu0YdNYuWclKfcbYyixesgJgtB39LkP3iwm\n0TZUEcDn9AH976IB2HX9Ltx2N49+/WiXwqfRVhK0WFnwWmv21O4Ji96JdpA12BSktK6UQ4Yfwt9W\n/K3L/beUbwG6ntTUGTmJOWEpHrobntmWF5e9yNtr3ybLm8VBuQdx1SFX9ep8giC0p88FflzaOOwJ\n9ogx7k6bk9VXr2Zs2ti+bkY7zLDMu4++u8t97z3mXmtSUKws+Mr6Spw2Z1guGI8jOh98YU0hw3zD\nyPJlUR5onzitLeY1Ao0BkpxJrLx6Zbfbm+pO5ZuC1tJ9Xf3q6Yym5iZ+/o+fA0bI6vxN87nqkKt4\n8tsneXP1m3x4wYf97rYThHikzwV+atZUgrd1HDc+JWtKXzeh18ybM8963V0LvrCmkEBjgDGpY8LW\nF9UUhfnfIXoffEF1AcOThpPuSaesrqzL/U2xDDQGSHYlMyplVNTtN0l1p1q59aF7Ar+2ZC1rS9Zy\nxuQzACNVgsmSK5ZYtXDvWHQHZXVlPL34aa6ffX232ygIQjid+uCVUm6l1DdKqWVKqdVKqf9pWZ+u\nlFqglFqvlPpIKdV+BLX1HLFu84DSXQv+4D8dzPRnp7db33ZyFRB15sbXVr5Gti+72wLvD/p7bBmn\nulPZXrndWu5O9M5DXz7Ema+faS3XNNRYr0Mjh0xX2fKi5T3KsSPAD0U/oO5SzP7L7IFuijAI6FTg\ntdYB4Git9YHA/sDRSqkjgJuBBVrricAnLct7BS6bix+KfohqwPK9de9RUF2Az+Frt62otihsgBUM\nV0p1QzVXv391p+ddXrScE8edSIYng1J/aVi6g1DqG+spqCqwooBK/aU9FnizGtYRo44A4KudX3HR\n3y+K6ljzmua8AzOD5YzcGbjt7nYC/9flf+XrnV/3qJ17O++vfx9A+k8Aooii0Vqb+WSdgA0oB04H\nXmxZ/yJwRp+0bhAyJnUMDU0NLNm1pMt9X1j+AjNyZ1jhmCZ/Xf5Xzn3z3LC8PGBYs5vKNvHMd8+E\nWcttqW2oZdaIWXgcHrJ8WWyp2BJxvzsW3cGIR1sTmBX7i3scsTTMNwyAiw+4mPKbDL//Sz9EVxTF\nFG77PXY2l2+mNljLUaOP4qvLvsKeYKdZN1NcW2wJ/1lTzurX7JUfb/6YHZU7+u16fUmsIryE+KBL\ngVdKJSillgFFwEKt9SogW2td1LJLEZDd4QnijBR3CmdMPsNKoFYZqOwwVHFdyTrO2/c8q5IUGCGX\nd316F3ccdQf3HXtf2P5uu9uaZWrmha8L1rWz0CsCFZZFvX/2/qwoWhHx+ma+mo82fWQt99SCN/32\no1JGWdeOltBxhXUl6/AH/aS4U3DanCilcNvdYf79HF+ONQmtLbuqd0XlluoOx790PNd+eG1MzzlQ\nmO4vM3pN2LuJxoJvbnHRjACOVEod3Wa7BiL7COKUEUkjLNG8fv71THhiQsT9SutKGZs2NixfzL82\n/IvN5ZvJ9Ga2G58Ijagxv6je+7w8tfipsP0q6yutnD7JruSwB0goZminmSis2N9zgTcnqmV4MsLa\nHU1eHn/Qz+EjDweMCVr+oD/MbeW2u/mh6AcuOfASqm+pJjsxu8PcN+MeH8dP3/ppVG3+6Vs/jTrN\ncTQzen/5r1/y2srXADp0iw0kZXVlrC9dz6UHXtpuUF/YO4k6ikZrXamUeh84CChSSuVorQuVUrlA\n+xp4Ldx5553W6/z8fPLz83ve2kHCkaOP5Ip/XsGzpz3L0sKlEffRWlPqL2V0yuiwfDGmW8P0R4di\npm6A8IHIbRWts1VXF69mT+0eS3A7i+ppW8D89oW3c/y447u6vYgopVh8+WJm5M4AoPn2ZoY/MpwS\nf0mXhVr8QT+3HHELS3cv5a8//JWzp5xtJTwDQ+C3VmxleNJwEp2J5CTmhFn0oQQaA1GXNXx15ask\nOZPIH5Pf5b6R5mm05anFT7Fizwr8QT+XvXsZ+o7BJfKnvnIqX+38ilvn3Mp/tv9noJsjdINFixax\naNGimJ+300+1UioTaNRaVyilPMDxwF3Au8DFwAMt/9/p6ByhAh8vnDbpNPx/96O1piJQARiCHmrZ\n1jTU4LQ5yfJlUVhTSFNzE7YEG6uLVwNEDFUMzbQZKvChfvNXV7wKhKd5iBQ7v7ZkbVh7Ep2J1DTU\n9Go2q1n+EAzBz/Jmsad2T1QC73F4uPbQa3ngiwfIS8qzfPrmPRT7ixmXPg4wJlV15KIBY+JZZ1TV\nV1kzbrdVbuPhLx/mhsNu6PSY99a91+49jITH7uH9De93uk9/0tTchEZjT7BbfZaXnBexsLwweGlr\n/N51110xOW9XLppc4N8tPvhvgPe01p8A9wPHK6XWA8e0LO81uO1uI/lWXanlfmnrJimrKyPNk8bo\nlNH4g36u+/A6wAiPLPptEWdOObPdeb0OL59f8jlXH3x1mMDblI01xWuoDBiTo+Yd0SYuP2RgbVf1\nLhqaGpjy1JQw4TcfKG2t+t6Q5cuy/PydUResw+vwkuxK5pixx7C1Yms7C77YX2xV/Mr2deyiAboM\noQy1/udvms9vF/y2y7TKtcHasP7qqFat2+62Zgb3RShnY3Mj/9kWvfX907d/yoF/PBAwPicAo1NG\nU1VfFZZDqS5YJ+kl9kK6CpNcobWeobU+UGu9v9b6wZb1ZVrr47TWE7XWJ2itK/qnuYOH3MRcCqoK\nqAhUkOXNsix5k7rGOiuJ2UtnvsSOqh2U+EuoCFREzFxpcviow0l0JjLv3/Msobr7P3cz/dnp/Pwf\nP6e0rpQMb4a1v8ve6qIJNAbIeySP3dVGrnhTJP3z/Pzz/H/y8AkP86dT/xSzPsjyZlnpoDviiW+e\noKi2yHI/DfMNY2PZxrCBWo/dQ1FNkVWAJScxh6KaTiz4Lvzfa0vWtlvXUVK2UFeZKfDBpiC++3wR\nRf77wu9ZV7qOZFdy1K6i7vDdru846oWjok4r8cX2L1hVvAp1l7IemuPSx5Hly7Is+q0VW/He52XE\noyOY8ewMfij6Iebt7kv21O5B3aU6/UwIkRmQotvxQKY307JEs3xZ7Sb+1AXrLDfKqJRRbK/czvEv\nHc+Y1DFdWtGbyjcBcMorp1jrLj7gYj7c+CF/+OYPZHhaBT7URWNG9phhk1sqtvDKWa/gcXgYmzaW\n62dfz8iUkb2881aG+Ybx1+V/7XSfX3/4a7ZWbLWiOgprCimtKw2rD2CKfpKrxYJPzKaotqhDIe/K\nco5k/YeOY4TyztpW76IZ7WNGRYXm2zFdW9srt3P+fuczd/xcFm5Z2Gk7eoL5wFlfuj6q/UPHDpYX\nLWftNWuZmDGRnMQc60H/1uq3cCQ4KPGXsLFsoxUrP1QwH0idue2EyIjA95AMbwYbyjaQ5kkjxZUS\n0YI3o2JGJI+wCoy8c26HwxUWx+9jDISGpuSdlDmJzb/ezOTMyUzNmmqtD3XRmLHcpgthfen6dukQ\nYsll0y9j4daFHfr1Q4XY/NVi5v4JTR+dl5SHRlsWvNvuxmP3tOtTk4588M8sfoZr3r+mncA7bU4+\n2PgBD3/5cLtjzMpY0GrBmw/YUIEPzYU/OmU0Z085m7fXvh3erhhE1piuvo5cRG1pG/1jjmOkudOs\n/iutK2XenHncdPhN3HjYjVYtgaGC+X72pMD83o4IfA/J8GSwsWwj6Z50Ut2pVAQqeOjLh6z4dbP2\nKRjiVhGooKq+ysqg2Rn/dfB/8f1/GaGNM3JnMCljEr+e9Wtyk3JZc80aDsk7xNo31EVjWjihScHa\npkOIJQfkHMCkjEl47/Wyq3pXu+2hA33mw256jpG2IdTyNEsnmrUDwLDiP9z4YdjDw3xgRIpAAnh5\nxcs8/d3TvLXmrbD1J4w7gacWP8VvF/y23TGhD1EzTYQ5/hEq8KH7jUkdw+iU0WHjD1/v/JqEuxN6\nVa+3uLaYX33wK6BrgW9qbmJxweKwvpg2bJrVrz6nz3pYlNWVke3L5v7j7mdCxgRqG2rxB/1DJh2E\nKfDfFnxLsCnY4fsvtEcEvodkeDJ4dsmz2BPspLhTKKsr48YFN3Lf58bkpbpgneV3tifYrVwukdIW\nRMKMY77/2PtZ+8u1HYbxue1uy4I3LZxPt31q7d82HUKs+eGqH5iaNTWifzQ0vbCJGaUS+iV96ISH\n2H3DbkanjrbWnTPlHK798Fqrpi/Alzu+BOgwIZspWBWBCp486UlunXMrCy9eyMT0iR22v8RfwkPH\nP8SI5BH8c/0/gVZxDXW7FfuLyU00MpCOTh1Nsis57AFg3mtBdc9n4L63/j3LNdOVwL+95m1mPjcz\nbGzhvP3Os177HD7r8xA6buNzGGMLvvt8PLf0uR63tT8xBf66+dfh+m8Xp7566gC3aOggAt9DLp1+\nKWAMYKW6UrnoHSMvS4JK4A9f/4HbF90eNnEp1Z2KRpPoTIzq/KnuVMp+V8Zx+xzX6X4um8tyLZgW\n2/bK7VbUTKRauLEm2ZUcMbukGf8/bdi0sPX/+fl/OGvKWdZyuie93YPo3mPv5fIZl/Po149a6+b8\n7xyg47z2oaJ4zcxruOeYe8gfkx/W56FWq9aapxY/xbj0cWR4Mrj5k5upDFRa5wkV8OLaYitMdETy\nCJJdyVQEKlhRtIL6xnorSqcjt1I0hEb6dCXwbSe/gTHobVIRqOCCv1/AW6vf4s3VbzIieQRgWPZm\nmGc0EVADTUNTA2+vaXWFaTSfbv10AFs0tBCB7yETMozZqzUNNZY/OdWdypJdS7hu/nUs3b00bNbo\nrLxZAGHhgV2R5knrMi7bZXdZVpxpsfmDfsufHcuwyI5IcadELABS01DDUaOPstxNJnNGz8Fhc3R5\n3stmXMbn2z+3lkcmj+TxuY93GO7XUSbO0PchdB9/0I89wc6PJv3I8sUX1RZFFnh/MXlJebz54zcZ\nkzqGJFcSRbVF7P/H/Xlh2QvWw6w38eeh1+vM39zQ1GCNE5gcM/YYy+gw7w2MAcprZ11r1WMI/QU5\nFNIZvLvu3Xa5lvrjMx0vSE/1gpzEHJJdyZbA337k7awpWWNtD52ZeuZkI+49minx3WFy5mQ+3vwx\n9Y31YbH4psD3BymuFMudobW2onlqG2pJciX1+J4zPBlh4qyU4tSJp9LY3BjRf2yGprbFbE+WNyts\nfkFNQw3pnnSUUpaL5ePNH/PvLf8GDJH8zYe/4Y/f/ZHi2mIyvZmcPfVsElRC2K+CyvpKS5x7Y8GH\n5tjpyIJvbG4k4/cZ7KzayaKLF/HNL4zxln2z9g3rZzOFxN3/uTtsbCN0DCia2bsDTeh3yKQ2WMsn\nmz8ZgNZcbw4SAAAgAElEQVQMPUTge8HSK5ay9IqlliU0e2R4Du5QceorV8nMvJlk+7L5oegHahtq\nGZdmRFGYk4b6g1B/9Psb3mfko0YoZk1DTdRjDpFw2pxhk7iq66tJdiUb6yNY8XXBuohzDKZlT2NS\nxiQSnYlhUSqV9ZXt+umaf13D/E3zrfY/9s1jzPtkHgs2L7CKtUOrFZmgEvAH/ZZ7xayw1ZOBwNCI\nno4Efm3JWushNXvkbCtTqSMh/BdR6DhFaLvNX5A/nvrjqAu8DyTVDdU4bU5+Mf0XYevPf+v8AWrR\n0EIEvhfkJuWSl5xniffUrKlcsP8F1vZQd8ysvFlhM1BjSVFtETOfm0ltsJZfzDC+CGZMeX8wKmUU\nb699m2BTMMxCrg3WRj3mEAmnzWlZolprqhuqSXIldVh0xR/088iJj3DvMfeGrb/y4CtZ+8u1VroG\nAN99PuZ9Ms9q3+4bdvP43MetByQYA7Beh5fbjryNOaPmcMqEU8LO+9VlX3HT4TdR21BruWgqAhUs\n3LIQ+z32boVN7qjcweurXgeMeQEdCXyo39wsIwm0c3mZA8IQHkllHjM6ZXSnxWU2lG7ggw0fRN3+\nvqIyUMnFB1zMn0//MwsvXsh7578H9Ny9VBGo6FW6jqGGCHwMMEUiyZnEH0/5Ix/+7EMgPILF5/Rx\n77H3Rjw+VtQGa8lLymPJFUvCvvx9zeUzLmdF0QreWftO2HV7a8GbLoem5iYCjQESVAJOmzNsctfi\ngsWA8QAINAb40aQfhZVYDCVU4MGYJ2C+dzmJORw8/OAwP3hRbRGJzkR+M/s3/M9x/2PFmJscOuJQ\nhicNxx/0U+IvYVzaOMrryq1zdDR7ti0/FP3AqMdacxPNGTWnQ4FvW6jdpK275Y0fv0HxjcUsv3I5\nR405ylqfk5jDXfl34XV4qWus46XlL0WckTvruVmc/MrJUbW/L6msr7RmPeePyefUiUYETTQC36yb\n+X536/jPzqqdpD2Qxo0f3dg3jY0BsQ4BFYGPAaalppTC5/RZBb27SsIVKz782Yccv8/xRp54dwoz\ncmewT+o+/XJtMCZ9XXXwVdz8yc1WPpTG5kZqG3pnwYMRJdTQ1MBLP7xkWfNmBs3CmkJmPjeTYFOQ\n+qZ6HDZHp/7+tgJvS7CF+aS9Dq+VeuGiAy6isKawS1eXz+Fj4daF7K7ZzZSsKdZ8B4h+NqqZgO7K\ng65E36E5avRR+IN+Xv7h5XaDrcX+Ys6acharrl4Vtr6tiybRmUimN5P9s/cPE397gp3bj7odr8OL\nP+jnoncuYuwfxobVyQWiKubeH5if6VCePOlJpmS2r+VcUFXA3JfnWstfbP+CGX+aYfXhpjJjYPrL\nnV/2YYt7RlV9FRtKN2C/x24lFIwFIvAx4IhRR3BXfmv2NzNcLS8pr1+ub7osimuLLevu1iNvpfLm\n6Oum9pbz9jsPR4LD8utWBirZU7snLG9OTzD98JWBSq6dZRTlMO/XFOuNZRspqCoIy1AZiRR3Ck8t\nfoqch4xfVssKl4UN1oaGtR456kjLgu8Mt93NmpI1fLXjKyZnTKY8UG4NtJ748olRhSKa4jw2zRgM\n9Tq8lNaVcuHfLwyLIgJD8NLcaWGzmaG9i6YrPI7w+r9vrn6z3T6Kga+n/N2u79hv2H5h61LdqRHH\nDxZuXcj8TfOt+QxmwMP1869nW8U2lhct59ixx7Z7mA008zfOJ+P3GUx80piv0TZCqjeIwMeAJFcS\ntx91u7Wcm5TLiqtWcPiow/vl+qZFu6d2jyVytgRbv0bSmBOuTNGY+dxMHv/2cfZJ690vCdMPX9dY\nZ1nTpovGHNhcVbyK8U+Mt0JROyLDk8G7694Ny2ly/aHXW6/NMZNrZ12L1+GlqKaoy7EMswJXXWMd\nU7OmUhGoCIuk+Wz7Z3y146tOz2H+MjENA6/DaxVpCXXVFNcWc9vC2yLOhu5uREymN5MnFz9pLYd+\nVsxJa4MhHHF18WqrBoGJx+GxBH7lnpWWu87s99NePQ2tNbuqdzE8aTh/WvonZv9lNg9/9TCnTDiF\nikDFoCrY8n3h91w761oabm3gkRMeiThBsKcM/DsYp+w3bL9++4KYghcq8P2Ny+6iur7ack+YVlKs\nBD7QGLAsbPOBZl7r2SXPAl27xCKlEQi10E2Bv3T6paR70tldszsssVskQi3pfdL2oTxQTnmg3GrL\nT9/6KYc9fxj3/ude/rzkzxHPYU4SM/MGeR1eK6+Q+TB64psnrMl0bedSDE8azpxRczptZ1vO3681\nCuWmw28KC9G86v2rACOFxEAPtEYaqPfYW399THtmGjctuAkwrH2TwppCquurrRnh313xHduu28Zv\nZv8Gl80VVoRnoFlbspbJmZNx2Bxd1kLoLoM/EFboEpfdRVV9FY3NjVHluukLzHqy182/jhtm38Ds\nEbM55//OYVLGpF6d1wyJDDQGrBBI00Vjfkk/3vwx0LXFef9x93PVIVdxyJ9bc/m09cGDkahr2rBp\nFFxfEJYULRLHjD2GOaPm8Nn2z0j3pFMRqGBNyRoePuFhrnr/KsuqvHXhrWR6M7n8oMvbnaOqvopT\nJpzCSeNPstphhnM+tfgpvt75NS8uf9Hav+3AdcH13U+PoJTiz6cZD5yKQEVYgrb6pnp+PPXHHDn6\nSC78+4UU/rZwwGLmaxtq291vqAUPRijlA58/ENZHq4pXUVVfxchkI2Q3dJZvmieN8rpykl3JfLPz\nG5JcSe1cXv3JjqodjE4x0nSMTRsb1tbeIhZ8HOCyuSj2F7cbjOpPQmP+PXYP+w7bl5zEnLBqVD3B\nZXdZFrx5jVR3KqX+0nazZ2854pZOz5XlywqrSgXhFrzLZrQ1xZ2CUorhScOjmnk8McPwnaZ5jAyO\nywqXcdjIwzhr8llh+3UUnlcZqOTQEYdas5ZDr7lyz8ow4QJ6XFe3Lb+Y8Qt+MeMXpLnTwiz4QGOA\nKw66gl/O/CXDfMMGLH98sClIs25uFxHmsXvwB/3W4GljcyP3f9Fac8htd/PH7/7I1wVfW+9v6BhF\nuied8kA52yu3c+hfDrWK8QwUBVUFViqJQ0ccypMnP9nFEdEjAh8HuOwuahpq+tXn3q4NtlYhT3Yl\nMzlzMrtv2N3JEdER6oM3ZzVOyZzC6uLVYQJ/UO5B3UqNbIpkqMArpVh6xdJu9+MTJz3BkiuWkOpO\nZVf1LsrryhmRPIK85PBB9kgCH2wK8v6G98MmaJmCFtqnoXRVsrC7+JzhxU1CH6b7Dts36migWFMb\nrMXn9LVL1+FzGonUTF+1OfBscvmMy6luqGblnpXMHT+X//3R/4YdPzJ5JJvLN7OxbCM+hy+mPu+e\nYI4V9AUi8HGAKQQDKfCh4YmmRRsLzCiaUNGZmDGRTeWbqK6v5pIDLwG6PyA4Pn08QDv/7vTc6d1u\no8fhYUbuDMuVkJ2YTYJKsNxTZjRKJIH/05I/sbxoeZjAj08fzzlTz+GPp/4x4vViHSvtsYe7PEIz\noaa4Urosd9hXRHLPgDFYXlpXaqWorghUMDNvJg8e/yBgjC+YEVeZ3kx+fuDPw47P9mVz9htn84+1\n/yB/TD47qnb07Y10QrNupjZY22cTE0Xg4wDTDTKQAh/KtOxpXe8UJWa2zNBB1kxvJqV1hovGzLPS\nnXw3j899nOdOM1Ll9mYiVltMS3PuOCMW+6wpZ/Hpzz9l32H7Aq3RMqGYg9GhFmiaJ43/+/H/hc1G\nDSXWedw9Dk+HFnyyK3nABiS3VW6L+FDM8GZQVlfG9srtTM2ayrLCZby+6nWmZE5B36GZPXI2kzMn\nA0QMOvjvY/6bkckj+abgG/bP3p+q+qoBi6qpbajF6/D2WUCGCHwcYH4Zu5Opsq9445w3eh05E4qZ\nqTK0BGK6J93ywZuWT3ditn8161fMGjGL8pvKY578rf7Wep49zYjq8Tg8HDn6SCvML5IwmykXQmPw\nTTp6YOePyY9Raw1Co1IgvBpZ27z3/cncl+dGrPnrtDlpbG7kuvnXceK4E3n1bGNiUKgVvE/aPtT9\nv7qIg6e5SbkcNPwgVu5ZycSMidgT7FHXwI01NQ01vZ4M2Bki8HGAI8HB7w77HZceeGnXO/cxvR1U\nbUuKK4Uvtn/B/E3zrS+C+RO9uqHaEsGefEm6ipDpCZFSRNx51J08e+qz2JStXf6XmoYa7s6/m9kj\nZrc7LjRJmMnzpz/fLmVCbwmNSvlu13dsrdhqPUyTnEkD5qI5ecLJ/Gzazzrcvqd2D1cefCWnTDRy\nBLWN9OlsMNpMPDcqZdSAPsRE4IUuUUrxwPEP8ON9fzzQTbHCvWJFiiuF+7+4n+sPvd4SwQxvhmXB\nmwLf2xmzfcnYtLFccdAVjEwZyWsrXwvzodc01DAla0rEvP/j08e3G6iOlC2zt4Ra8LctvM1aBwNr\nwTfpJn406Ucdbs/wZFjjPYU3FEZ8SHaE6ZrL8mZ1WLCmP6huqO5TgZc4eCFmNN/e3GWBku6ys9rI\n5T5vzjzLnZLhMXywVfVV1uzWjvzVg4kUVwqXvnspY9PGWm6Wriy4tpWuzHC6WBJqwZu/QCwL3pVE\nVUPPBX5j2UbGpY3r8HPxs7d/xpTMKdx65K3ttoU+wNtyyxG3hPVbd4vLm8emulMH9CG2uGBxn6b2\nFoEXYkasxR2wIiVCLXSX3YXT5qSgusCYrPKLbwZ0okq0mOGNoQW8u/MTXd/RNwOBoRa8mRfHFHif\nw9dpWuGumPDEBP521t/46bSfRtz+yopXyPJmRRT4ykBlhwJ/37H39bhN0CrwaZ60dvMA+pMr37+y\nXSqGWCIuGmFQ8/KZL/P5JZ+3W5/hzWBrxVaSXEnMzJvZpz9zY0Wp38hbY7pBIDqBb769mS3Xbul0\nn97gcXgoqi2iMlBp+bHNh3XbCJvuYEYNdTVRqqPMlZ1Z8L3FDC32OXxkJ2ZHLBrf15iD7m0zgcYS\nEXhhUDMla0rEpG0Znoyw2rNDATMxWWg1qopAhZXvvCOUUlZOlb4g2ZVMpjeTBZsXUFVfZRXVAKy0\nwj3BLOO4oWxDp/tFjC5qrKegusBKvR1rzDBKpRQ5vhx2VO3gug+vC0vZ0NeYn4PuZgLtDiLwwpDE\n9E0PJYE3Q/HMNMdNzU3srtndb3UDOiJBJXDGpDMo9ZdSWlcalmCtVwLfMnDZUSHyDaWG8EeKdlm6\neykT0if0WWHw0yedzsKLFwLGZ+nbgm/5wzd/CEtY1teYn4fTJp7WZ9cQgReGJNOGGZOphoJrxuS1\ns1/jrZ+8ZaWrLawpJMOTEfPQ0p6Q4TVCT0v9pWGROrGw4DuKMf+24FsmZ06OOH9jZ9XOPv3VYkuw\nWQPdM3Jn8MFGI2tm6PhIX1PfVE+2L5vfHf67PruGCLwwJDkkz8gIOVBZDnvCufudy1lTzsKWYCPQ\nGGBtydqYx7T3lAxPRqsF7+29Bb+1YisH//ngsPKKbdlUvomTx59MZaCy3UzSXdW7+i0yakbuDGu8\nIJoCLbEidMZwXyECLwxJzph8Bn87628D3YwekeJKoSJQwafbPuXQvEMHujmAkVP+ka8foSJQETYB\nzMzc2F0+2/YZAA8d/1CHAr+5fDNTs6YSbA6ScHe4FPWn6yr0fmOZi92krK7Mqh0cigi8IHSAPcHe\nYejdYCfTm8me2j28uvJVztvvvIFuDgDnTzMKgByUe1BYXpTuWvANTQ3srNqJRnPB/hdw0oSTOhX4\njn7B9GWGxbaYEUM5iTk8vfhpa2wgVlz094uY+dzMdusDjYE+d8+JwAtCPzMqZRTvrX+PjWUbmZTZ\nu4IosSJBJfDMKc+0+1Xktrtp1s1hkT+dce9/7mXkoyON8E9HIm67m2J/MV/uaF/oelP5prC8RVpr\nbvv3bQx7cBhrStb0++DzSeNPYs7oOTGtiQp0OHArFrwgxCGjUkZZsfCDaZD4yoOvbPfAUUqR6k6N\nOqWuOTHNjO93293UNNRw+POH88KyF9BaU9NQQ12wjlJ/aVhh+kvfvZRlRcso9hfz3a7v+ixEMhJp\n7jTOmnKWkaOmpZBId4j0AGzWzdQF6yiqLbLyzi/ZtQQwfP3+oF8EXhDijb4Mi+sLiv3FTHhiQlT7\nNmojvW+owJs89vVjvLDsBZL+J4m1JWsZnToaW4KNDb8yXCKvrXyNLeVb+OySz3jsxMd6Xe6xO5Td\nVMapE0/t1CXV1NzE3Z/e3W59oDGA+143H236KGz9A58/gPc+I0IoLzmPuS/P5eA/H0xZXRnDHhrG\ni8tf7HOBHzohCIIQJxwz9hgALtz/wgFuSezYUbmDL3d8aRU2r2moYUTyCGvG6Ln7nsvrq17n0neN\njKcfb/7Ycs+YxVcCjQG2VGzhgOwDOGLUEQNwF+C1dyzwRbVF3LHoDnITc8Nq6xZUGTVx286GNX/N\ngDGLeWvDViZlTGLR1kUArCtZF9PU2pEQC14Q+hmPw4Pb7uaeo+8Z6KbEjHs/u5fz3jrPKtBRHijH\n5/BZCeLM4te/O+x3HD7ycBZtW8S4tNYB1sbbjOP8QX+fVTeKhs4seLOA+hX/vCJsvSnk1Q3VaK15\nY9UbQGu6Z6fNSWldKcN8wxjmG8bZb5wNwLLCZdbDra/oUuCVUiOVUguVUquUUiuVUr9uWZ+ulFqg\nlFqvlPpIKRX75NqCEKfU/b86RqfGNrVyX/HJRZ9w9JijO93Hpgwhb9JGKuR/rP0Hx+5zrLVdKcWe\n3+7h3mPvZd+sfVmwaQET0lvdPrYEGxcfcHG7ouj9TUcCr7Xm+e+fB4wUw6FYAl9fTbG/mHPfPJeX\nf3iZOxbdAbSmJk5yJnHT4Tfx+jmvM++IedQ31XNQ7kF9eTtRuWiCwG+01suUUonAEqXUAuASYIHW\n+vdKqZuAm1v+BEGII8zC551hhlaaLprK+krL/XDYyMOYkjnFsmgfPOFBfjnzl+1q975wxgsxbnn3\n8Tq81AZbB1nnvjyXCekTGJM6hoe/ehiAA3MOtLY362bOe8sIdd1RtYM/fP0HAJ5e/LS1j0bjtDnZ\nWLbRKk6yrmQdYKRM6Eu6FHitdSFQ2PK6Rim1BsgDTgeOatntRWARIvCCEHe4bC6rtGBHmK4Ycz+X\nzWWJ/heXfhG2b7IrOaZ1e2OJz+kLKxM4f9N85m+aT6o7lXRPOmV1ZWEWvplXCODlH1628u9sq9xm\nrW9oaqDmlpqwrJlm/v2+SLEdSrd88EqpMcB04BsgW2ttjioUAd3LuC8IwpCgOxa8mX9mqNKRi2ZW\n3iwKbyhk4cULw7abufJdNheV9ZVcN+s6RqeMDhtgrW+sx2FzhBUA702O/e4QtcC3uGfeAq7VWocV\nadRGIomBKUsuCEKf4rQ5u5zoZPrgzcpIA1XEureECnxofpzx6eNx2Bxk+7LDBN58vX/2/oAxr8Hn\nNHzuVx50JQD7Dduv3XXGpo3tmxtoQ1RhkkopB4a4v6S1fqdldZFSKkdrXaiUygX2RDr2zjvvtF7n\n5+eTn5/fqwYLgtC/uOyu6C34FheFHqL2XqjAh7pfzMRnPqcvosAfmHMgi3ctprqh2lr3zKnP8Pvj\nfx/xOr+a+SuuOKg1GmfRokUsWrQopvcCUQi8MpxEfwFWa60fC9n0LnAx8EDL/3ciHB4m8IIgDD2c\nNmeXPnizaEd/ZmPsC0IFvsRfwqiUUWyv3G49wEK3767ebT3QzFq2Ka4Utldut87XUcinUipsklNb\n4/euu+6Kyf1EY8EfDlwA/KCU+r5l3S3A/cAbSqnLgK3AT2LSIkEQBhUuW9cWvPkAqG+q556j7xmw\nIta9JTSKpsRfQpY3i+2V28lLzrO2mwI//JHhHDHqCBKdidx7zL3cduRtpHnSuPs/dzMqZdSA3UMo\n0UTRfE7HvvrjYtscQRAGG1354LXWPPHtE9ZypALaQwVTwAtrCpn53EyO3+d46m+tDytGHmgMWL9Y\nPt9u1AtOcaeQglF68dSJp/LjqT8emBtog6QqEAShU1z2zsMkqxuqO9w21DAF3szf3tDUYLlfwBhr\ncNvdnUbBhNa0HWgkVYEgCJ3itDkJNgWt7IihPmYw/O6jU0Zz0QEXDVALY4fX4aUiUMHvPv4dc8fP\n5aETHoq4jzlLFeDI0Uf2ZxO7hVjwgiB0SoJKIMmVRFV9Fc9//zw3fHQDTbc3Mfzh4Wy9bivF/mKG\n+YZx51F3csyYYwa6ub0i0ZlIYU0hxbXFLPuvZRELcngdXr4vNIYjd9+w2yoAPxgRgRcEoUtS3alU\nBCqsGrhPL36aotoivtzxJZWBSrITsxmbNrbf4rv7ijR3GmDUae2o2pLP6SPRmcj0nOmDWtxBXDSC\nIERBqjuV8rpyrv3wWsamjuX3Xxjx3Ve9fxVnvXEWB+cObJKwWGGmXOismLvX4WVH5Q6uPPjK/mpW\njxGBFwShS1Ldqeyu2Q0YESNmhaf1pesBw+KNJ8zZqJHwOrysL11PpjezH1vUM0TgBUHokjR3mlWM\n2symeMqEU6ztbTNDDmV+su9PuP3I2zv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"text": [ "" ] } ], "prompt_number": 52 }, { "cell_type": "code", "collapsed": false, "input": [ "labels = ['kern variance', 'kern lengthscale','noise variance']\n", "samples = s[300:] # cut out the burn-in period\n", "from scipy import stats\n", "xmin = samples.min()\n", "xmax = samples.max()\n", "xs = np.linspace(xmin,xmax,100)\n", "for i in xrange(samples.shape[1]-1):\n", " kernel = stats.gaussian_kde(samples[:,i])\n", " plt.plot(xs,kernel(xs),label=labels[i])\n", "_ = plt.legend()" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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37vTt25cTTjiBRx55JNMlZR1N6xORrLB48eJMl5D1dIUtIhIQCmwRkYBISWDro+kiIumn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\n", "text": [ "" ] } ], "prompt_number": 53 }, { "cell_type": "code", "collapsed": false, "input": [ "fig = plt.figure(figsize=(14,4))\n", "ax = fig.add_subplot(131)\n", "_=ax.plot(samples[:,0],samples[:,1],'.')\n", "ax.set_xlabel(labels[0]); ax.set_ylabel(labels[1])\n", "ax = fig.add_subplot(132)\n", "_=ax.plot(samples[:,1],samples[:,2],'.')\n", "ax.set_xlabel(labels[1]); ax.set_ylabel(labels[2])\n", "ax = fig.add_subplot(133)\n", "_=ax.plot(samples[:,0],samples[:,2],'.')\n", "ax.set_xlabel(labels[0]); ax.set_ylabel(labels[2])" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 46, "text": [ "" ] }, { "metadata": {}, "output_type": "display_data", "png": 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eDyH6g8LS4TKIm2I/BWw1s/cDe4B3NdvwpZemfj/8cLjttjA/OamIkBCtMjkZ+j/kTS0t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\nIGY2H/h74Hfd/Wdmdug3d3cz86ztNm/efGh+fHy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"text": [ "" ] } ], "prompt_number": 46 }, { "cell_type": "markdown", "metadata": {}, "source": [ "## More Advanced: Uncertainty Propagation\n", "\n", "Let $x$ be a random variable defined over the real numbers, $\\Re$, and $f(\\cdot)$ be a function mapping between the real numbers $\\Re \\rightarrow \\Re$. Uncertainty\n", "propagation is the study of the distribution of the random variable $f ( x )$.\n", "\n", "We will see in this section the advantage of using a model when only a few observations of $f$ are available. We consider here the 2-dimensional Branin test function\n", "defined over [\u22125, 10] \u00d7 [0, 15] and a set of 25 observations as seen in Figure 3." ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Definition of the Branin test function\n", "def branin(X):\n", " y = (X[:,1]-5.1/(4*np.pi**2)*X[:,0]**2+5*X[:,0]/np.pi-6)**2\n", " y += 10*(1-1/(8*np.pi))*np.cos(X[:,0])+10\n", " return(y)\n", "\n", "# Training set defined as a 5*5 grid:\n", "xg1 = np.linspace(-5,10,5)\n", "xg2 = np.linspace(0,15,5)\n", "X = np.zeros((xg1.size * xg2.size,2))\n", "for i,x1 in enumerate(xg1):\n", " for j,x2 in enumerate(xg2):\n", " X[i+xg1.size*j,:] = [x1,x2]\n", "\n", "Y = branin(X)[:,None]" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 35 }, { "cell_type": "markdown", "metadata": {}, "source": [ "We assume here that we are interested in the distribution of $f (U )$ where $U$ is a\n", "random variable with uniform distribution over the input space of $f$. We will focus on\n", "the computation of two quantities: $E[ f (U )]$ and $P( f (U ) > 200)$.\n", "\n", "## Computation of $E[f(U)]$\n", "\n", "The expectation of $f (U )$ is given by $\\int_x f ( x )\\text{d}x$. A basic approach to approximate this\n", "integral is to compute the mean of the 25 observations: np.mean(Y). Since the points\n", "are distributed on a grid, this can be seen as the approximation of the integral by a\n", "rough Riemann sum. The result can be compared with the actual mean of the Branin\n", "function which is 54.31.\n", "\n", "Alternatively, we can fit a GP model and compute the integral of the best predictor\n", "by Monte Carlo sampling:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Fit a GP\n", "# Create an exponentiated quadratic plus bias covariance function\n", "kg = GPy.kern.RBF(input_dim=2, ARD=True)\n", "kb = GPy.kern.Bias(input_dim=2)\n", "k = kg + kb\n", "\n", "# Build a GP model\n", "model = GPy.models.GPRegression(X,Y,k)\n", "\n", "# fix the noise variance to something low\n", "model.Gaussian_noise.variance = 1e-5\n", "model.Gaussian_noise.variance.constrain_fixed()\n", "display(model)\n", "\n", "# optimize the model\n", "model.optimize()\n", "\n", "# Plot the resulting approximation to Brainin\n", "# Here you get a two-d plot becaue the function is two dimensional.\n", "model.plot()\n", "display(model.add.rbf.lengthscale)\n", "\n", "# Compute the mean of model prediction on 1e5 Monte Carlo samples\n", "Xp = np.random.uniform(size=(1e5,2))\n", "Xp[:,0] = Xp[:,0]*15-5\n", "Xp[:,1] = Xp[:,1]*15\n", "Yp = model.predict(Xp)[0]\n", "np.mean(Yp)" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "WARNING: reconstraining parameters GP_regression.Gaussian_noise.variance\n" ] }, { "html": [ "\n", "\n", "

\n", "Model: GP regression
\n", "Log-likelihood: -74285.8774977
\n", "Number of Parameters: 5
\n", "

\n", "\n", "\n", "\n", " \n", " \n", " \n", " \n", " \n", "\n", "\n", "\n", "\n", "\n", "
GP_regression.ValueConstraintPriorTied to
" ], "metadata": {}, "output_type": "display_data", "text": [ "\u001b[1mGP_regression.add.rbf.lengthscale\u001b[0;0m:\n", "Param([ 28.98116529, 303.00020102])" ] }, { "metadata": {}, "output_type": "pyout", "prompt_number": 36, "text": [ "58.283419091796873" ] }, { "metadata": {}, "output_type": "display_data", "png": 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dmsGBKVJI5akPIcZFZZ+8QFCADPnL0MuMyAzXJsJliaLIepFLusPA5VKb2ORC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"text": [ "" ] } ], "prompt_number": 36 }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Exercise 6\n", "\n", "a) Has the approximation of the mean been improved by using the GP model?" ] }, { "cell_type": "raw", "metadata": {}, "source": [ "# Exercise 6 a) answer " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "b) One particular feature of GPs we have not use for now is their prediction variance. Can you use it to define some confidence intervals around the previous result?" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Exercise 6 b) answer" ], "language": "python", "metadata": {}, "outputs": [] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Computation of $P( f (U ) > 200)$\n", "\n", "In various cases it is interesting to look at the probability that $f$ is greater than a given\n", "threshold. For example, assume that $f$ is the response of a physical model representing\n", "the maximum constraint in a structure depending on some parameters of the system\n", "such as Young\u2019s modulus of the material (say $Y$) and the force applied on the structure\n", "(say $F$). If the later are uncertain, the probability of failure of the structure is given by\n", "$P( f (Y, F ) > \\text{f_max} )$ where $f_\\text{max}$ is the maximum acceptable constraint.\n", "\n", "### Exercise 7\n", "\n", "a) As previously, use the 25 observations to compute a rough estimate of the probability that $f (U ) > 200$." ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Exercise 7 a) answer" ], "language": "python", "metadata": {}, "outputs": [] }, { "cell_type": "markdown", "metadata": {}, "source": [ "b) Compute the probability that the best predictor is greater than the threshold." ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Exercise 7 b) answer" ], "language": "python", "metadata": {}, "outputs": [] }, { "cell_type": "markdown", "metadata": {}, "source": [ "c) Compute some confidence intervals for the previous result" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Exercise 7 c) answer" ], "language": "python", "metadata": {}, "outputs": [] }, { "cell_type": "markdown", "metadata": {}, "source": [ "These two values can be compared with the actual value {$P( f (U ) > 200) = 1.23\\times 10^{\u22122}$ .\n", "\n", "We now assume that we have an extra budget of 10 evaluations of f and we want to\n", "use these new evaluations to improve the accuracy of the previous result.\n", "\n", "### Exercise 8\n", "\n", "a) Given the previous GP model, where is it interesting to add the new observations if we want to improve the accuracy of the estimator and reduce its variance?" ] }, { "cell_type": "raw", "metadata": {}, "source": [ "# Exercise 8 a) answer" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "b) Can you think about (and implement!) a procedure that updates sequentially the model with new points in order to improve the estimation of $P( f (U ) > 200)$?" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Exercise 8 b) answer" ], "language": "python", "metadata": {}, "outputs": [] } ], "metadata": {} } ] }