{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# An Introduction to Bayesian Quadrature with Emukit" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Overview" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "# General imports\n", "%matplotlib inline\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "from matplotlib import colors as mcolors\n", "\n", "# Figure config\n", "LEGEND_SIZE = 15\n", "FIGURE_SIZE = (12, 8)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Navigation\n", "\n", "1. [What is Bayesian quadrature?](#1.-What-is-Bayesian-quadrature?)\n", "\n", "2. [The ingredients of Bayesian quadrature](#2.-The-quadrature-of-Bayesian-optimization)\n", "\n", "3. [Emukit's Bayesian quadrature interface](#3.-Emukit's-Bayesian-quadrature-interface)\n", "\n", "4. [References](#4.-References)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 1. What is Bayesian quadrature?" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We wish to integrate a function $f: \\mathbb{X} \\rightarrow \\mathbb{R}$, $x\\mapsto f(x)$ which is defined on some input space $\\mathbb{X}\\subseteq\\mathbb{R}^D$\n", "\n", "$$\n", "F : = \\int_{\\mathbb{X}}f(x)\\mathrm{d}x.\n", "$$\n", "\n", "The domain $\\mathbb{X}$ can equally be defined by the integral bounds, i.e., $bounds = \\{(lower\\_bound_d, upper\\_bound_d)\\}_{d=1}^D$. The function $f$ is called the *integrand*. Integration problems occur for example when computing estimators of some quantity or when marginalizing a probability distribution. Numerical solvers are needed whenever $f(x)$ is not integrable analytically.\n", "\n", "Bayesian quadrature (BQ) [[1, 2]](#4.-References) is a numerical method that infers the value of the integral $F$ from a finite number of usually noise-free integrand evaluations $f(x_n)$, at locations $x_n$, $n=1, ...,N$. It does so by first emulating the integrand function $f$ with a surrogate model.\n", "Then, an estimate for $F$ is obtained by integrating the surrogate model of $f$. \n", "The key point is that the integration of the surrogate model is much easier, often analytic, in comparison to the original integration problem. Hence BQ shifts the problem of solving a hard integration problem to a regression problem on the integrand and an easier, often analytic integration problem of the regression model.\n", "\n", "\n", "#### Surrogate model of the integrand\n", "The surrogate for the integrand $f$ is often a Gaussian process (GP) which can be integrated analytically if the kernel of the GP can be integrated analytically; an example of such a kernel is the RBF/Gaussian kernel. Sometimes also a process related to a Gaussian process is used as surrogate (e.g., [[3]](#4.-References)), then the surrogate is approximated with yet another GP which can then be integrated again. \n", "\n", "#### Distribution over the integral value\n", "Bayesian quadrature returns a *distribution* over the integral value $F$, not only an estimate of the integral value. An estimate can then be deduced, e.g., by taking the maximum a posteriori (MAP). If a GP is used as surrogate for $f$ then the integral distribution is of Gaussian form $F\\sim\\mathcal{N}(\\mathfrak{m}_n, \\mathfrak{v}_n)$. We obtain a distribution on $F$ because the model on the integrand $f$ was a distribution in the first place. A benefit of a distribution as return type in contrast to an estimator only is that a distribution also quantifies the uncertainty on the integral estimation. \n", "\n", "The integral distribution $F\\sim\\mathcal{N}(\\mathfrak{m}_n, \\mathfrak{v}_n)$ is exact and a Gaussian due to the closeness property of GPs under affine transformations. The univariate mean and variance of the integral distribution are respectively\n", "\n", "$$\n", "\\mathfrak{m}_n = \\int_{\\mathbb{X}} \\mu_n(x)\\mathrm{d}x, \\qquad\\qquad\n", "\\mathfrak{v}_n = \\int_{\\mathbb{X}} \\int_{\\mathbb{X}}^3 k_n(x, x')\\mathrm{d}x\\mathrm{d}x'.\n", "$$\n", "\n", "We can obtain the mean $\\mathfrak{m}_n$ and variance $\\mathfrak{v}_n$ of the integral distribution analytically if we know the analytic forms of the integral over the GP posterior mean function $\\mu_n(x)$ and the double integral over the posterior covariance function $k_n(x, x')$; this is fulfilled e.g., by the RBF kernel. \n", "\n", "#### Acquiring data\n", "\n", "In practice, integrand evaluation $f(x_n)$ can be expensive and we are restricted to a limited budged of $N$ choices of locations $x_n$ at which we can evaluate $f$.\n", "Thus we would like to choose these locations wisely, or some best way possible. What 'best' means is encoded in a user-defined utility which is equal to, or approximated by an *acquisition* function $a_n(x)$. The acquisition function always has knowledge of the current model of the integrand, in this case the GP on $f$ with mean $\\mu_n$ and kernel $k_n$.\n", "\n", "The integral $F$ is a global property of $f$, meaning that local information of $f$ can not be used alone to meaningfully guess $F$. This is reflected in the acquisition functions that are commonly used in BQ--they, too, are commonly global quantities. Examples are the integral-variance-reduction or the mutual information between the integral value and an additional hypothetically collected point at location $x$, i.e., \n", "\n", "$$\n", "x_{n+1} \\in \\operatorname*{arg\\:max}_{x \\in \\mathbb{X}} a_n(x).\n", "$$\n", "\n", "\n", "\n", "Given the surrogate GP on $f$, the acquisition function $a$, and a function handle to $f(x)$, BQ essentially iterates the following three steps until the budget of $N$ evaluations is used up: \n", "1. fit the GP $p(f|D_n)$ on the currently available dataset $D_n\\{(f(x_i), x_i)\\}_{i=1}^n$.\n", "2. condition the acquisition function $a_n(x)$ on $p(f|D_n)$ and find the maximizer, i.e., $x_{n+1} = \\operatorname*{arg\\:max}_{x \\in \\mathbb{X}} a_n(x)$.\n", "3. evaluate the objective function at $x_{n+1}$ to obtain $f(x_{n+1})$, and add the new observation to the dataset $D_{n+1} \\leftarrow D_{n} \\cup \\{x_{n+1}, f(x_{n+1})\\}$.\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 2. The ingredients of Bayesian quadrature" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

The Objective Function and the Input Space

" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As an example let's assume we want to integrate the one-dimensional function $f(x) = e^{-x^2 - \\sin^2(2x)}$ over the interval $\\mathbb{X}=[-3, 3]$, i.e.,\n", "\n", "$$\n", "F = \\int_{-3}^{3}e^{-x^2 - \\sin^2(2x)}\\mathrm{d}x.\n", "$$\n", "\n", "Conveniently, this function is already implemented in Emukit. " ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "from emukit.test_functions.quadrature import hennig1D\n", "\n", "user_function, integral_bounds = hennig1D()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Of course in reality, evaluating $f$ on a grid wouldn't be possible, but since the hennig1D function is a synthetic function we can evaluate it here for visualization purposes on the interval defined by the integral bounds. " ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "image/png": 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UFnb2P9qbNWumiIgILVq0yIvJACA0UKwBIAjk5eVp8eLF5zQNRJJKly6tZs2aMWINAGeBYg0AQSA1NVXZ2dleuZtpixYttHDhQllrvZAMAEIHxRoAgoA3Llz0aNmypXbu3KnNmzef874AIJRQrAEgCCxatEjR0dFKSko65315yjnzrAGgZCjWABAEFi5cqOTk5LO64+LxkpOTZYxhnjUAlBDFGgBczlqr33//3SvzqyWpTJkySkpKYsQaAEqIYg0ALrdlyxbt27dPzZs399o+mzVrphUrVnhtfwAQCijWAOByngLctGlTr+2zadOmWrdunXJycry2TwAIdhRrAHA5XxXrgoICrV692mv7BIBgR7EGAJdbsWKFKlWqpPj4eK/t01PSmQ4CAMVHsQYAl1uxYoWaNm0qY4zX9tmoUSOFhYVRrAGgBCjWAOBi1lotX77cq9NApMJbmzdo0IBiDQAlQLEGABfbsWOH9uzZ4/ViLRVOB6FYA0DxUawBwMV8ceGiR9OmTbVmzRodPnzY6/sGgGBEsQYAF/N1sc7Ly9PatWu9vm8ACEYUawBwsRUrVqh8+fKqXr261/fNyiAAUDIUawBwMV+sCOKRlJQkYwzFGgCKiWINAC7mKda+EBMTo4SEBIo1ABQTxRoAXGrXrl3asWOHmjRp4rNjNGnShGINAMVEsQYAl1q1apUk+bxYp6amKj8/32fHAIBgQbEGAJdas2aNpMK7JPpKo0aNdPjwYW3cuNFnxwCAYEGxBgCXWr16tSIiIlSvXj2fHaNhw4ZFxwIAnB7FGgBcas2aNUpMTFRERITPjuEZDfeMjgMATo1iDQAutWbNmqIRZV+pXr26YmNjKdYAUAwUawBwoYKCAr8Ua2OMGjRowFQQACgGijUAuNCWLVuUnZ3t0wsXPRo1asSINQAUA8UaAFzIU3R9PWLtOUZ6erpyc3N9fiwAcDOKNQC4kGdqhr9GrPPz85Wenu7zYwGAm1GsAcCF1qxZo6ioKNWqVcvnx/KMijMdBABOj2INAC60Zs0a1a9fX2Fhvv8xTrEGgOKhWAOAC61evdov00AkqXLlyoqLi2NlEAA4A4o1ALhMfn6+1q1b55cLF6XCJfcaNmzIiDUAnAHFGgBcZsOGDcrNzfVbsZYKp4MwYg0Ap0exBgCX8Ywc+2sqiOdYGzduVE5Ojt+OCQBuQ7EGAJfx5xrWHg0bNpS1VuvWrfPbMQHAbSjWAOAy69atU0xMjKpVq+a3Y9avX1+SlJaW5rdjAoDbUKwBwGXS0tKUmJgoY4zfjpmYmFh0bADAyVGsAcBl1q1bV1R0/aVy5cqKjY2lWAPAaVCsAcBFrLVKS0srmprhL8YYJSYmcltzADgNijUAuMi2bduUnZ3t92ItFU4HYcQaAE6NYg0ALuJZlcPfU0E8x0xLS5O11u/HBgA3oFgDgIt4RoydGrHOzs7W9u3b/X5sAHADijUAuMi6detkjFHdunX9fuyEhARJYp41AJwCxRoAXCQtLU21a9dW6dKl/X5sltwDgNOjWAOAizix1J5HvXr1JFGsAeBUKNYA4CJOLLXnER0drRo1alCsAeAUKNYA4BL79+/X9u3bHRuxlsRa1gBwGhRrAHAJT6F1asRaKryAkRFrADg5ijUAuIRnDWsni3ViYqI2bdqkQ4cOOZYBAAIVxRoAXMLJm8N4JCYmylqrjIwMxzIAQKCiWAOAS6SlpSkuLk4VK1Z0LANL7gHAqfmtWBtjuhljUo0xa40x95/k7XWMMXOMMYuMMUuMMT38lQ0A3CAtLa3oJi1O8RyfYg0AJ/JLsTbGhEsaI6m7pKaSBhljmh632UOSPrPWtpB0jaRX/ZENANxi/fr1jk4DkaTq1aurdOnSFGsAOAl/jVi3kbTWWptmrT0s6VNJfY7bxkoqd+T18pK2+CkbAAQ8a63Wr19fdJMWp4SFhSkhIYEl9wDgJCL8dJyakjYe9XiTpIuO2+ZRSV8ZY4ZLipXU+WQ7MsYMljRYkuLj45WSkuLtrPCT/fv3c/5cinPnf3/88YdycnKUm5t7zp/7cz1/5cuX15IlS/gacADfe+7G+Qt+/irWxTFI0vvW2ueMMe0kfWiMaWatLTh6I2vtm5LelKSkpCTbsWNH/yeFV6SkpIjz506cO//76aefJEldu3Y958/9uZ6/Cy+8UGPHjlWHDh1kjDmnLCgZvvfcjfMX/Pw1FWSzpNpHPa515Lmj3SbpM0my1v4kKUpSZb+kA4AA55l64fTFi54MmZmZ2rNnj9NRACCg+KtY/yqpoTEmwRhTSoUXJ045bpsMSZdLkjGmiQqL9U4/5QOAgLZ+/XpJUt26dZ0Nov8tucc8awA4ll+KtbU2T9IwSbMkrVTh6h/LjTGPGWN6H9lshKTbjTGLJX0i6WZrrfVHPgAIdOnp6apSpYpiY2OdjsJa1gBwCn6bY22tnS5p+nHPPXzU6yskXeKvPADgJoGwIogHa1kDwMlx50UAcIH09PSAmF8tSWXLllV8fDzFGgCOQ7EGgACXn5+vjIyMgCnWkljLGgBOgmINAAFuy5Ytys3NDZipIFLhPGtGrAHgWBRrAAhwgbTUnkdiYqI2bNigvLw8p6MAQMCgWANAgPMstRdoI9Z5eXnatGmT01EAIGBQrAEgwHlGrANhDWsPz+g586wB4H8o1gAQ4NavX68aNWqodOnSTkcpwlrWAHAiijUABLhAWmrPo1atWoqIiKBYA8BRKNYAEODWr18fcMU6IiJCdevWpVgDwFEo1gAQwHJzc7Vx48aAunDRo169ekUXVgIAKNYAENA2btyogoKCgBuxlrhJDAAcj2INAAEsEJfa80hISND27dt18OBBp6MAQECgWANAAAvEm8N4eMr+hg0bnA0CAAGCYg0AAWz9+vUKCwtTrVq1nI5yAtayBoBjUawBIIClp6erdu3aioyMdDrKCTwj1lzACACFKNYAEMACcak9j2rVqikqKooRawA4gmINAAEsPT09IC9clCRjjOrWrcuINQAcQbEGgACVk5OjLVu2BOyItcSSewBwNIo1AASojIwMSYG51J4HxRoA/odiDQABKpCX2vOoV6+edu/erczMTKejAIDjKNYAEKAC+eYwHp7SzzxrAKBYA0DASk9PV2RkpGrUqOF0lFNiyT0A+B+KNQAEqPXr16tu3boKDw93OsopcZMYAPgfijUABKhAXmrPo1KlSipTpgwj1gAgijUABKz09PSAvnBRKlzLul69eoxYA4Ao1gAQkA4cOKCdO3cG/Ii1xJJ7AOBBsQaAAOSZWhHoI9ZS4QWM69evl7XW6SgA4CiKNQAEIDcsteeRkJCgzMxM7dmzx+koAOAoijUABCA33BzGgyX3AKAQxRoAAtD69esVFRWlqlWrOh3ljFhyDwAKUawBIAB5ltozxjgd5YwYsQaAQhRrAAhA69evd8U0EEmKi4tTXFwcI9YAQh7FGgACkBtuDnM0ltwDAIo1AAScffv2ac+ePa4ZsZb+t+QeAIQyijUABBg3LbXnkZCQwFrWAEIexRoAAoybltrzqFevng4ePKidO3c6HQUAHEOxBoAA46a7Lnqw5B4AUKwBIOCkp6erTJkyqlixotNRis1TrJlnDSCUUawBIMB4ltpzwxrWHnXr1pXEiDWA0EaxBoAA47al9iSpTJkyio+Pp1gDCGkUawAIINZapaenu2p+tQdL7gEIdRRrAAggu3fv1v79+103Yi1xkxgAoFgDQABx41J7HvXq1dOGDRtUUFDgdBQAcATFGgACiBtvDuORkJCgw4cPa+vWrU5HAQBHUKwBIIC4ecSaJfcAhDqKNQAEkLS0NFWsWFHly5d3OkqJeUbZmWcNIFRRrAEggKSlpSkxMdHpGGeFtawBhDqKNQAEELcutSdJUVFRql69OlNBAIQsijUABIj8/HytX7/etSPWEkvuAQhtFGsACBCbN29Wbm6u64s1I9YAQhXFGgAChJtXBPGoV6+eMjIylJeX53QUAPA7ijUABIi0tDRJcv2IdX5+vjZt2uR0FADwO4o1AASItLQ0hYWFqU6dOk5HOWueJfeYDgIgFFGsASBApKenq3bt2oqMjHQ6ylnzTGPhAkYAoYhiDQABws1rWHvUrl1bYWFhjFgDCEkUawAIEMFQrCMjI1WrVi1GrAGEJIo1AASAgwcPavv27a5eEcSDJfcAhCqKNQAEAM8Ir9tHrKXCCxgZsQYQiijWABAAgmGpPY+EhARt3rxZhw4dcjoKAPgVxRoAAkAw3BzGo169erLWauPGjU5HAQC/olgDQABIS0tTbGys4uPjnY5yzlhyD0CoolgDQADwrAhijHE6yjmjWAMIVRRrAAgA6enpQTENRJJq1KihUqVKFc0bB4BQQbEGAIdZa4NiDWuP8PBw1atXj2INIORQrAHAYTt37tTBgweDZsRaKlzdhGININRQrAHAYcG01J5H/fr1tW7dOqdjAIBfUawBwGHBWKwTExO1d+9e7dmzx+koAOA3FGsAcJhn9Yx69eo5G8SLPL8kMB0EQCihWAOAw9LS0lStWjXFxMQ4HcVrPMWa6SAAQgnFGgAcFkwrgngwYg0gFPmtWBtjuhljUo0xa40x959im6uNMSuMMcuNMR/7KxsAOCmY1rD2KFOmjKpUqUKxBhBSIvxxEGNMuKQxkrpI2iTpV2PMFGvtiqO2aSjpAUmXWGv3GGOq+CMbADjp8OHD2rhxY9CNWEuFo9ZMBQEQSvw1Yt1G0lprbZq19rCkTyX1OW6b2yWNsdbukSRr7Q4/ZQMAx2RkZKigoCBoizUj1gBCib+KdU1JG496vOnIc0drJKmRMeYHY8x8Y0w3P2UDAMd4VgQJtqkgUuFa1hkZGcrNzXU6CgD4hV+mghRThKSGkjpKqiVprjGmubV279EbGWMGSxosSfHx8UpJSfFvSnjN/v37OX8uxbnznhkzZkiStm/f7rfPqb/O3+HDh1VQUKDPPvtMNWseP5aCs8H3nrtx/oKfv4r1Zkm1j3pc68hzR9sk6Wdrba6kdGPMahUW7V+P3sha+6akNyUpKSnJduzY0VeZ4WMpKSni/LkT5857ZsyYoVKlSql///4KDw/3yzH9df7CwsL01FNPKT4+nq8XL+F7z904f8HPX1NBfpXU0BiTYIwpJekaSVOO2+YLFY5WyxhTWYVTQ5icByCopaenq27dun4r1f7EknsAQo1firW1Nk/SMEmzJK2U9Jm1drkx5jFjTO8jm82S9IcxZoWkOZL+bq39wx/5AMApwbiGtUeNGjVUunRpVgYBEDL8NsfaWjtd0vTjnnv4qNetpHuPvABA0LPWat26dWrTpo3TUXwiLCxMCQkJWrt2rdNRAMAvuPMiADhk9+7d2rt3rxo0aOB0FJ9p0KABI9YAQgbFGgAc4hnJbdiwocNJfKdhw4Zau3atCv8oCQDBjWINAA7xFOtgH7HOzs7W1q1bnY4CAD5HsQYAh6xdu1bGmKC8OYyH55cG5lkDCAUUawBwyNq1a1W7dm1FRUU5HcVnKNYAQgnFGgAcsnbt2qCeBiJJderUUUREBMUaQEigWAOAQ0KhWEdERLDkHoCQQbEGAAfs3btXu3btCvpiLRVOB6FYAwgFFGsAcEAorAji0aBBA61Zs4Yl9wAEPYo1ADgg1Ir1/v37tWPHDqejAIBPUawBwAGeYl2/fn2Hk/ie5wY4TAcBEOwo1gDggLVr16pmzZqKiYlxOorPseQegFBBsQYAB4TCiiAedevWVXh4OMUaQNCjWAOAA0KpWJcqVUp169alWAMIehRrAPCzrKwsbd++PWSKtfS/lUEAIJhRrAHAzzwFM5SKdcOGDVlyD0DQo1gDgJ+tXr1akpSUlORwEv9p1KiRMjMzWXIPQFCjWAOAn6WmpsoYE1Ij1p5fIlJTUx1OAgC+Q7EGAD9bvXq16tSpo+joaKej+E2jRo0k/W+0HgCCEcUaAPwsNTU1pKaBSFKdOnVUunRpRqwBBDWKNQD4kbVWq1evLhrBDRXh4eFq0KABI9YAghrFGgD8aNu2bcrKygq5EWupcJ41I9YAghnFGgD8yDNiG2oj1lLhx7xu3Trl5eU5HQUAfIJiDQB+5BmxDdUR67y8PKWnpzsdBQB8gmINAH60evVqRUVFqXbt2k5H8TtWBgEQ7CjWAOBHqampatiwocLCQu/HL2tZAwh2ofeTHQAcFIorgnhUqlRJFStWZMQaQNAqcbE2xsQaY8J9EQYAgllubq7S0tJCcn61ByuDAAhmZyzWxpgwY8y1xphpxpgdklZJ2mqMWWGMecYYEzr35AWAc5Cenq68vLyQHbGWCudZM2INIFgVZ8R6jqT6kh6QVM1aW9taW0XSpZLmS3rKGHO9DzMCQFAI5RVBPJKSkrRlyxZlZWU5HQUAvC6iGNt0ttbmHv+ktXa3pImSJhpjIr2eDACCzMqVKyWFdrFu3LixJGnVqlW68MILHU4DAN51xhFrT6k2xrxkjDGn2wYAcGorV65UtWrVVKFCBaejOKZJkyaS/vdLBgAEk5JcvJglaYoxJlaSjDFXGGN+8E0sAAg+K1asUNOmTZ2O4aj69esrMjJSK1ascDoKAHhdsYu1tfYhSZ9ISjlSqO+VdL+vggFAMLHWauXKlSFfrCMjI9WoUSNGrAEEpeLMsZYkGWMul3S7pAOSqku61VrLmkkAUAybN29WVlZW0VSIUNakSRP9/vvvTscAAK8ryVSQByWNstZ2lDRA0n+NMZf5JBUABBnPCG2oj1hLhZ+DtLQ05eTkOB0FALyqJFNBLrPWfn/k9aWSukt63FfBACCYeOYUM2Jd+DkoKChgPWsAQac4N4g51UogWyVdfrptAACFVq5cqYoVK6pKlSpOR3GcZ9SeedYAgk1xRqy/NcYMN8bUOfpJY0wpSe2MMR9Iuskn6QAgSHhWBGEcovDui2FhYawMAiDoFOfixTWS8iV9boypLmmvpChJ4ZK+kvSitXaRzxICQBBYuXKlrrrqKqdjBISoqCglJiYyYg0g6BSnWF9orR1sjPmLpDqS4iVlW2v3+jQZAASJnTt3ateuXVy4eJSmTZsyYg0g6BRnKshsY8xPkqpKulFSDUnZPk0FAEHEUyAp1v/TtGlTrV69Wnl5eU5HAQCvKc4tzUdKul6F00ESJI2StMwYs9wY818f5wMA1/NMeWBFkP9p0qSJcnNztW7dOqejAIDXFOsGMdbadcaYztbaorWRjDFlJDXzWTIACBIrVqxQmTJlVKtWLaejBAzP6P3y5cuVlJTkcBoA8I6SrGO9+rjH+621870fCQCCy9KlS9WsWTNWBDmKZ4WUZcuWOR0FALymJHdeBACUkLVWS5cuVfPmzZ2OElBiYmJUv359LV261OkoAOA1FGsA8KGtW7fqjz/+UHJystNRAk5ycrKWLFnidAwA8BqKNQD4kGdElhHrEzVv3lxr167VwYMHnY4CAF5BsQYAH/KMyFKsT5ScnKyCggLWswYQNCjWAOBDS5cuVc2aNVWxYkWnowQczy8bzLMGECwo1gDgQ0uWLGF+9SkkJiYqJiaGedYAggbFGgB8JDc3VytXrmQayCmEh4frvPPOY8QaQNCgWAOAj6xevVqHDx9mxPo0WBkEQDChWAOAj7AiyJk1b95cO3fu1Pbt252OAgDnjGINAD6yZMkSRUREqHHjxk5HCVie0XxGrQEEA4o1APjI0qVL1bhxY5UqVcrpKAGLlUEABBOKNQD4yOLFi5lffQaVK1dW9erV9fvvvzsdBQDOGcUaAHxg586d2rhxo1q2bOl0lIDXsmVLLVy40OkYAHDOKNYA4AOeotiqVSuHkwS+Vq1aaeXKldzaHIDrUawBwAc8xfqCCy5wNogLtGzZUgUFBVzACMD1KNYA4AMLFy5U/fr1FRcX53SUgOeZLsN0EABuR7EGAB9YuHAh86uLqVatWqpcuTLFGoDrUawBwMv27NmjtLQ0inUxGWPUsmVLLViwwOkoAHBOKNYA4GWLFi2SxIWLJdGqVSstW7ZMhw4dcjoKAJw1ijUAeJlnSkOLFi0cTuIeLVu2VF5enpYtW+Z0FAA4axRrAPCyhQsXqk6dOqpcubLTUVyDCxgBBAOKNQB42YIFC5hfXUIJCQkqX74886wBuBrFGgC8KDMzU6tXr6ZYlxAXMAIIBhRrAPCi3377TZLUpk0bh5O4T5s2bbR48WLl5OQ4HQUAzgrFGgC8aP78+ZIo1mejbdu2ys3NLVpVBQDcxm/F2hjTzRiTaoxZa4y5/zTb9TfGWGNMa39lAwBvmT9/vho3bqwKFSo4HcV1LrroIkn/++UEANzGL8XaGBMuaYyk7pKaShpkjGl6ku3KSvqbpJ/9kQsAvMlaq/nz56tt27ZOR3Gl6tWrq27duhRrAK7lrxHrNpLWWmvTrLWHJX0qqc9Jthst6SlJTLAD4Drp6enauXMnxfoctG3blmINwLX8VaxrStp41ONNR54rYoxpKam2tXaanzIBgFd5CiHF+uy1bdtWGRkZ2rJli9NRAKDEIpwOIEnGmDBJz0u6uRjbDpY0WJLi4+OVkpLi02zwnf3793P+XIpzd3ITJkxQVFSUdu3aFdCfn0A+f6VKlZIkvfPOO2rfvr3DaQJPIJ87nBnnL/gZa63vD2JMO0mPWmuvOPL4AUmy1j5x5HF5Sesk7T/yLtUk7ZbU21r726n2m5SUZFNTU30ZHT6UkpKijh07Oh0DZ4Fzd3Jt2rRRbGys5syZ43SU0wrk83fo0CGVK1dOd999t5566imn4wScQD53ODPOn7sZYxZYa0+7uIa/poL8KqmhMSbBGFNK0jWSpnjeaK3dZ62tbK2tZ62tJ2m+zlCqASCQZGdna9GiRUwDOUelS5dWixYtmGcNwJX8UqyttXmShkmaJWmlpM+stcuNMY8ZY3r7IwMA+NLChQuVl5dHsfaCtm3b6tdff1Vubq7TUQCgRPy2jrW1drq1tpG1tr619l9HnnvYWjvlJNt2ZLQagJvMmzdPktSuXTuHk7jfJZdcouzsbC1cuNDpKABQItx5EQC84LvvvlPTpk1VpUoVp6O43p/+9CdJhZ9TAHATijUAnKO8vDx9//336tChg9NRgkLVqlXVuHFjijUA16FYA8A5Wrhwofbv38/V/l7UsWNHzZs3T3l5eU5HAYBio1gDwDnyjKx6pjDg3HXo0EFZWVn6/fffnY4CAMUWEDeIAeBuubm5mjJlihYuXKiVK1eqTp066tChgy6//HKVK1fO6Xg+99133ykpKUnVqlVzOkrQ8Eyr+e6779S69WmXjQ0KmzZt0tdff625c+fq0KFDatasmS699FJ+WQNchhFrAOfk559/VuvWrTVgwAA99dRTWr58ud544w3169dPDRo00EcffSR/3IjKKfn5+Zo3bx7zq72sevXqatiwYdDPs87OztZDDz2kxMRE3XrrrZo6dap+/PFHPfjgg+rQoYP69++vzZs3Ox0TQDFRrAGctRdffFHt2rXTH3/8oYkTJ+rAgQNKTU3V3r179e233yoxMVHXX3+9evbsqaysLKfj+sTixYuVmZlJsfaBDh06aN68ecrPz3c6ik+sXLlSycnJ+te//qVBgwZp6dKl2rFjh9avX6+9e/fqiSee0PTp09W0adOi5RwBBDaKNYCzMnbsWN1zzz266qqrtHLlSvXr10+lS5eWVHj3vE6dOumHH37Qyy+/rK+//lqdO3fW7t27HU7tfSkpKZJEsfaBjh07au/evVqyZInTUbxu0aJF+tOf/qT9+/dr9uzZ+uCDD9SsWTOFhRX+t1y+fHndf//9WrZsmapXr65evXpp6dKlDqcGcCYUawAlNn/+fN16663q3LmzPv74Y5UtW/ak24WHh2v48OGaOHGifv/9d3Xq1CnoyvU333yjRo0aqWbNmk5HCTqdOnWSVPg5Dia//fabOnXqpJiYGM2bN0+XXXbZKbetX7++Zs2apTJlyuiKK67Qtm3b/JgUQElRrAGUyI4dO/TEE08oOTlZkyZNKhqlPp3evXvryy+/1KpVq3T11VcHzRJq2dnZmjNnjrp37+50lKBUo0YNJScna8aMGU5H8ZrNmzerd+/eiouL09y5c9WgQYMzvk/dunU1a9YsHTx4UE8++aQKCgr8kBTA2aBYAyiRe+65RwcPHtS4ceNOOVJ9Ml26dNHrr7+u2bNna8SIET5M6D9z585VTk6OunXr5nSUoNWtWzd9//33QTFHPzs7W1dddZWysrI0depU1a1bt9jve9555+nZZ5/V4sWL9e677/owJYBzQbEGUGzTp0/Xxx9/rOuvv15NmzYt8fvfcsstuueee/Tyyy9r7NixPkjoXzNnzlRUVBTzq32oW7duys3N1Zw5c5yOcs6GDh2qX3/9VePGjVPz5s1L/P633XabLrjgAo0cOVJbt271QUIA54piDaBYDh06pLvuuktNmzbVoEGDzno/Tz/9tDp06KChQ4cqLS3Niwn9b+bMmerQoYOio6OdjhK0LrnkEsXGxmrmzJlORzkn48eP13vvvaeHHnpIffr0Oat9GGM0YsQI5eTk6N577/VyQgDeQLEGUCzvvPOONmzYoJdeekmlSpU66/1ERERo7NixCg8P14033uja+dbr16/XqlWrmAbiY6VKldLll1+uGTNmuHY99M2bN+uOO+5QmzZt9PDDD5/TvmrVqqURI0bov//9r5YtW+alhAC8hWIN4IwOHTqkf//737rkkkt0+eWXn/P+6tSpozFjxuiHH37Q008/7YWE/jdr1ixJolj7Qbdu3bR+/XqtWbPG6SglZq3VLbfcokOHDmncuHGKjIw8533ee++9io2N1ejRo72QEIA3UawBnNE777yjzZs369FHH5Uxxiv7vPbaazVw4EA99thjWr16tVf26U8zZsxQ3bp1lZSU5HSUoHfFFVdIkitXB3nvvff09ddf69lnn1XDhg29ss9KlSrpr3/9q8aPH6/ly5d7ZZ8AvINiDeC0Dh06pCeeeEIXX3yxV0arPYwxeumllxQVFaU777zTVX/mP3DggL766iv17NnTa79o4NQSExPVtGlTffHFF05HKZFt27ZpxIgRat++ve644w6v7tszav3YY495db8Azg3FGsBpffbZZ9q0aZNGjRrl9RJZvXp1Pfnkk5ozZ44+/PBDr+7bl2bOnKns7GwNGDDA6Sgho3///po7d6527tzpdJRi++tf/6qDBw/qrbfeKrqjordUqlRJQ4cO1fjx47V+/Xqv7hvA2aNYAzitMWPGKCkpqejP8d42ePBgtWvXTvfee6927drlk2N428SJE1W5cmW1b9/e6Sgho3///iooKHDNqPW0adM0fvx4jRo1ymfThe666y4ZY/TGG2/4ZP8ASo5iDeCUFixYoJ9//llDhgzx2ZSHsLAwvfHGG9q3b5/uu+8+nxzDm3JycjR16lT17dtXERERTscJGcnJyapfv74mTJjgdJQzys7O1vDhw9WkSROffk3XqVNHvXr10ttvv61Dhw757DgAio9iDeCUXnvtNcXExOimm27y6XGaN2+ukSNH6r333lNKSopPj3Wuvv76a+3fv59pIH5mjNGAAQP07bffas+ePU7HOa0nnnhC6enpGjNmzDktTVkcQ4cO1a5du1zxCwcQCijWAE5qz549+vjjj3XdddcpLi7O58cbNWqUEhISdOeddwb06NvEiRMVFxenTp06OR0l5PTv3195eXmaMmWK01FOac2aNXrqqad07bXX+uVr5PLLL1fDhg316quv+vxYAM6MYg3gpD788ENlZ2dryJAhfjleTEyMXnvtNaWmpurZZ5/1yzFL6vDhw5oyZYp69+7t85FInKh169aqU6eOxo8f73SUk7LWatiwYYqKivLb13BYWJiGDBmiH3/8UUuWLPHLMQGcGsUawEmNHTtWLVu2VIsWLfx2zCuuuEIDBw7U448/HpC3O586dar27NlzTrd0x9kzxuiaa67RzJkztW3bNqfjnGDixIn66quv9Pjjj6t69ep+O+4NN9ygiIgIV62sAwQrijWAE6xcuVILFizQDTfc4Pdjv/DCC4qIiNDw4cMDbm3rd999VzVr1lSXLl2cjhKybrnlFuXn52vcuHFORzlGVlaW7r77bl1wwQV++yuPR+XKldWjRw99/PHHys/P9+uxARyLYg3gBB9++KHCwsJ0zTXX+P3YNWvW1D//+U9Nnz5dkydP9vvxT2Xz5s2aOXOmbrrpJoWHhzsdJ2Q1btxY7dq107vvvhtQv3j985//1ObNm/Xaa685slrM9ddfry1btujbb7/1+7EB/A/FGsAxCgoK9NFHH6lr166qVq2aIxmGDx+u5s2b669//asOHDjgSIbjffjhhyooKNAtt9zidJSQd+utt2rlypX65ZdfnI4iSVq0aJFefPFFDR48WG3btnUkQ69evVS+fPmAG8kHQg3FGsAx5s2bp4yMDEemgXhERkbqtdde08aNGwPils3WWr377rtq3769GjRo4HSckHf11VcrOjpa7777rtNRlJ+fr9tvv12VK1fWk08+6ViOqKgoDRw4UBMnTgyYX0aBUESxBnCMcePGqUyZMurbt6+jOS655BLdeuutev7557V8+XJHs8ydO1dr1qzRrbfe6mgOFCpXrpwGDhyoTz75RFlZWY5m+c9//qMFCxbo5ZdfVoUKFRzNcsMNN+jAgQMBNYUKCDUUawBFcnNzNWnSJPXu3VsxMTFOx9FTTz2lcuXK6Y477lBBQYFjOZ5//nlVqlRJV199tWMZcKyhQ4cqKytL77zzjmMZMjIy9NBDD6lnz54aOHCgYzk8Lr30UtWsWTNglyMEQgHFGkCR7777Trt37w6IkiAVrnbw3HPP6YcfftDrr7/uSIbU1FRNmTJFQ4cODYhfNlCoTZs2at++vV544QXl5eX5/fjWWt11112y1mrMmDEyxvg9w/HCwsLUv39/zZgxw/GRfCBUUawBFJkwYYJiY2N1xRVXOB2lyE033aQuXbro//7v/5SRkeH34z/33HOKiorS0KFD/X5snN7IkSOVkZHhyAjthAkTNG3aND3++OOqW7eu349/KgMGDNChQ4c0ffp0p6MAIYliDUBS4UVYkyZN0pVXXqno6Gin4xQxxujNN9+UtVZ33HGHX5dY2759u8aOHaubbrpJVapU8dtxUTxXXnmlkpKS9Oyzz/r162L37t3661//qlatWmn48OF+O25xXHzxxapWrZomTJjgdBQgJFGsAUgqXA1k586dGjBggNNRTlCvXj09+eSTmjlzpl+nhLzwwgs6fPiw7rnnHr8dE8UXFhamESNGaOHChZo1a5Zfjmmt1Z133qldu3bprbfecmTN6tMJDw9Xv379NH36dFYHARxAsQYgqfBP29HR0erevbvTUU7qrrvuUteuXTVixAilpqb6/HgZGRl68cUXdf311yspKcnnx8PZufHGG5WYmKj77rvPL3cdHDdunMaPH6/Ro0erRYsWPj/e2RgwYIAOHjyomTNnOh0FCDkUawAqKCjQpEmT1L17d8XGxjod56TCwsL03nvvKTo6Wtddd50OHz7s0+P94x//kDFGjz/+uE+Pg3NTunRpPfnkk1q6dKnef/99nx4rPT1dQ4cOVfv27fX3v//dp8c6F+3bt1d8fDzTQQAHUKwB6LffftPWrVvVr18/p6OcVo0aNfT2229rwYIFuvfee312nN9++00fffSR7rnnHtWpU8dnx4F3DBgwQO3atdOoUaO0f/9+nxwjOztbAwYMUFhYmMaOHRvQt7WPiIhQr169NGPGDOXm5jodBwgpFGsAmjx5ssLDwwN2GsjRrrrqKo0cOVJjxozRhx9+6PX95+Xlafjw4YqPj9f999/v9f3D+4wxeu6557R161aNHj3a6/u31mro0KFauHChxo0bp3r16nn9GN525ZVXat++ffr++++djgKEFIo1AE2ZMkXt27dXxYoVnY5SLE888YQ6deqkwYMH67fffvPqvp988knNnz9fL730ksqVK+fVfcN32rVrp9tvv13PPPOM5s6d69V9v/rqq3rvvff08MMP68orr/Tqvn2lS5cuKlWqlKZOnep0FCCkUKyBEJeWlqZly5apT58+TkcptoiICH366aeqVq2aunfv7rWLGX/55Rc9+uijGjRokAYNGuSVfcJ/nn/+edWvX1833HCD9u3b55V9TpgwQcOHD1evXr30yCOPeGWf/lCmTBlddtll+vLLL52OAoQUijUQ4qZMmSJJ6tWrl8NJSqZKlSr66quvZIxR165dtWnTpnPa365du3TdddepRo0aGjNmjJdSwp/KlCmjDz/8UJs3b9Ztt912zquEfPPNN7r22mt18cUX69NPP1VYmLv+y+zVq5fWrFnjl1V0ABRy108JAF43efJknXfeeapfv77TUUqsYcOGmjlzpvbs2aP27dufdYHIzMxUt27dtGnTJn3yySeqUKGCl5PCX9q2baunn35aEydO1NChQ8/6xjGff/65evXqpaSkJE2dOtWVt7Pv2bOnJDEdBPAjijUQwvbs2aN58+a5ahrI8Vq2bKnZs2fr4MGDuvjii0t8sVZWVpZ69+6txYsXa8KECbrkkkt8lBT+cu+99+r+++/XG2+8ofvuu08FBQXFfl9rrV555RX1799f559/vr799lvX/qJVt25dJScnU6wBP6JYAyFs1qxZys/Pd80FWady4YUX6qefflKlSpXUsWNHPfDAA8rJyTnj+y1cuFAtW7bUvHnzNHbs2KIRPrjfv//9bw0ZMkTPPvusevbsqZ07d57xfTZv3qw+ffoUzan+9ttvFR8f74e0vtOrVy/98MMP2r17t9NRgJBAsQZC2LRp01S5cmW1adPG6SjnLDExUb/88otuvvlmPfnkk2revLnGjBmjzMzME7Zdu3at7rnnHrVr107Z2dlKSUnhYsUgY4zRmDFj9Oqrr2rOnDlKTk7Wc889pz179pyw7YYNG/Tggw/qvPPO09dff63nnntOkyZNcuX0j+P16tVL+fn5mjFjhtNRgJAQ4XQAAM7Iz8/XzJkz1a1bt4C+2UVJxMXF6e2339bVV1+tf/zjHxo2bJjuu+8+NWvWTA0bNtTBgweVlpamJUuWKDw8XIMGDdILL7ygSpUqOR0dPmCM0ZAhQ3TxxRdr+PDhGjlypEaNGqXzzz9fCQkJOnz4sFavXq3ly5dLKiyhzzzzjBo2bOhwcu+58MILVaVKFX355Ze67rrrnI4DBD2KNRCifvvtN+3atUs9evRwOorXde3aVV27dtWvv/6qcePGafny5Zo3b55iY2OVmJiofv366S9/+Ytq1KjhdFT4wfnnn6+5c+fq999/17vvvqvly5dr/vz5ioyMVFJSkvr3769bbrklKO+yGRYWpp49e2rSpEnKzc1VZGSk05GAoEaxBkLU9OnTFRYWpiuuuMLpKD5z4YUX6sILL3Q6BgLEBRdcoJdfftnpGH7Xq1cvvffee/r+++/VqVMnp+MAQY051kCImjZtmtq1a+eauy0CODvchRHwH4o1EIK2bdumBQsWBOU0EADHKlOmjDp16qSpU6ee9breAIqHYg2EoJkzZ0oSxRoIEb169dLatWu1evVqp6MAQY1iDYSgadOmqUaNGjr//POdjgLADzxrtE+fPt3hJEBwo1gDISY3N1dfffWVevToIWOM03EA+EG9evXUtGlTTZs2zekoQFCjWAMh5scff1RmZibTQIAQ06NHD82dO1dZWVlORwGCFsUaCDHTpk1TZGSkOnfu7HQUAH7Uo0cP5ebmavbs2U5HAYIWxRoIMdOnT9ef/vQnlS1b1ukoAPzo0ksvVdmyZZkOAvgQxRoIIRs2bNDy5cuZBgKEoMjISHXt2lXTp09n2T3ARyjWQAiZMWOGJJbZA0JVz549tWXLFi1ZssTpKEBQolgDIWTatGlKTExUUlKS01EAOKBbt26SxHQQwEco1kCIyMnJ0ezZs1lmDwhh1atXV8uWLVnPGvARijUQIr777jtlZ2czDQQIcT179tRPP/2k3bt3Ox0FCDoUayBETJs2TdHR0erYsaPTUQA4qEePHiooKNCsWbOcjgIEHYo1EAKstZo2bZouu+wyRUdHOx0HgIMuvPBCVa5cmekggA9QrIEQsGbNGqWlpTENBIDCw8PVrVs3zZw5U/n5+U7HAYIKxRoIAZ6RKYo1AKnwZ8GuXbv066+/Oh0FCCoUayAETJs2TU2bNlW9evWcjgIgAFxxxRUKCwtjOgjgZRRrIMhlZmbqu+++Y7QaQJGKFSuqXbt2FGvAyyjWQJD7+uuvlZubq169ejkdBUAA6dmzpxYsWKCtW7c6HQUIGhRrIMhNnTpVFSpU0MUXX+x0FAABxPNXrJkzZzqcBAgeFGsgiOXn52vatGnq0aOHIiIinI4DIIAkJyerZs2aTAcBvMhvxdoY080Yk2qMWWuMuf8kb7/XGLPCGLPEGDPbGFPXX9mAYPXzzz9r165duvLKK52OAiDAGGPUo0cPffXVV8rNzXU6DhAU/FKsjTHhksZI6i6pqaRBxpimx222SFJra22ypAmSnvZHNiCYTZ06VREREerWrZvTUQAEoB49eigzM1M//PCD01GAoOCvEes2ktZaa9OstYclfSqpz9EbWGvnWGsPHnk4X1ItP2UDgtaXX36p9u3bKy4uzukoAAJQ586dFRkZyXQQwEv8VaxrStp41ONNR547ldskzfBpIiDIrV+/XsuWLWM1EACnVKZMGXXo0EFffvml01GAoBBwVzMZY66X1FpSh1O8fbCkwZIUHx+vlJQU/4WDV+3fv5/z50OTJk2S5JvvE86du3H+3MsX565Jkyb65ptvNG7cONWqxR+LfYnvveBnrLW+P4gx7SQ9aq294sjjByTJWvvEcdt1lvQfSR2stTvOtN+kpCSbmprqg8Twh5SUFHXs2NHpGEGra9euysjI0KpVq7y+b86du3H+3MsX5y4jI0N169bV008/rb///e9e3TeOxfeeuxljFlhrW59uG39NBflVUkNjTIIxppSkayRNOXoDY0wLSW9I6l2cUg3g1DIzM5WSksI0EABnVKdOHbVs2VJffPGF01EA1/NLsbbW5kkaJmmWpJWSPrPWLjfGPGaM6X1ks2cklZE03hjzuzFmyil2B+AMuNsigJLo27evfvrpJ23bts3pKICr+W0da2vtdGttI2ttfWvtv44897C1dsqR1ztba6taay848tL79HsEcCrcbRFASVx11VWy1mrKFMa0gHPBnReBIOO522L37t252yKAYjnvvPNUv359poMA54hiDQQZz90WmQYCoLiMMerbt69mz56tzMxMp+MArkWxBoLMF198wd0WAZRY3759dfjwYc2YwW0kgLNFsQaCiLVWkyZN0uWXX87dFgGUSLt27RQfH890EOAcUKyBILJkyRKtW7dO/fv3dzoKAJcJDw9Xnz59NG3aNB06dMjpOIArUayBIDJp0iSFhYWpT58+TkcB4EJ9+/ZVVlaW5syZ43QUwJUo1kAQmThxotq3b68qVao4HQWAC11++eWKjY1lOghwlijWQJBITU3V8uXL1a9fP6ejAHCpqKgode/eXZMnT1ZBQYHTcQDXoVgDQeLzzz+XVHijBwA4W1dddZW2bdumn3/+2ekogOtQrIEg8dlnn+miiy5S7dq1nY4CwMV69uypUqVKafz48U5HAVyHYg0EgdTUVC1atEiDBg1yOgoAlytfvry6d++u//73v0wHAUqIYg0Egf/+978yxmjgwIFORwEQBK655hpt2bJF33//vdNRAFehWAMuZ63VJ598og4dOqhGjRpOxwEQBHr16qWYmBh9+umnTkcBXIViDbjc0qVLtWrVKl1zzTVORwEQJGJjY9WrVy9NmDBBeXl5TscBXINiDbjcp59+qvDwcO62CMCrrrnmGu3cuZObxQAlQLEGXKygoECffPKJOnfurMqVKzsdB0AQ6datm8qVK6ePPvrI6SiAa1CsARebN2+e1q9frxtuuMHpKACCTFRUlAYOHKiJEyfqwIEDTscBXIFiDbjYBx98oLJly3JTGAA+cdNNN2n//v2aNGmS01EAV6BYAy514MABjR8/XgMHDlRMTIzTcQAEoUsvvVSJiYn64IMPnI4CuALFGnCpSZMmaf/+/brpppucjgIgSBljdOONN+rbb79VRkaG03GAgEexBlzqgw8+UEJCgi699FKnowAIYjfeeKOstfrwww+djgIEPIo14EIbNmzQt99+qxtvvFFhYXwbA/CdhIQEdejQQe+//z63OAfOgP+RARd66623ZIzRrbfe6nQUACHgL3/5i9auXcua1sAZUKwBl8nNzdXbb7+tHj16qE6dOk7HARACBgwYoIoVK+r11193OgoQ0CjWgMtMnjxZ27dv15133ul0FAAhIioqSrfccou++OILbd261ek4QMCiWAMu8/rrr6tOnTrq1q2b01EAhJDBgwcrLy9P7777rtNRgIBFsQZcZPXq1Zo9e7YGDx6s8PBwp+MACCGNGjXS5ZdfrjfffFP5+flOxwECEsUacJGXX35ZkZGRXLQIwBFDhgxRRkaGvvjiC6ejAAGJYg24xO7du/Xee+/p2muvVfXq1Z2OAyAE9e3bVwkJCXr++eedjgIEJIo14BJvvPGGDh48qHvvvdfpKABCVHh4uO6++279+OOPmj9/vtNxgIBDsQZc4PDhw/rPf/6jLl26KDk52ek4AELYrbfeqri4OEatgZOgWAMu8Omnn2rr1q0aMWKE01EAhLgyZcrojjvu0MSJE5Wenu50HCCgUKyBAJefn69///vfat68ubp27ep0HADQ8OHDFRERoSeffNLpKEBAoVgDAe6///2vUlNT9cgjj8gY43QcAFDNmjV1++23691339WGDRucjgMEDIo1EMDy8/M1evRoNWvWTFdddZXTcQCgyP3336+wsDA98cQTTkcBAgbFGghgn332mVatWqVHHnlEYWF8uwIIHLVq1dJf/vIXRq2Bo/A/NRCgcnNz9eijj6pZs2bq16+f03EA4AT333+/jDF67LHHnI4CBASKNRCg3njjDa1evVpPPPEEo9UAAlLt2rU1bNgwvffee1q8eLHTcQDH8b81EID27t2rRx99VJdffrl69uzpdBwAOKWHHnpIFSpU0MiRI2WtdToO4CiKNRCA/vWvf2n37t167rnnWAkEQECrUKGCHnnkEX3zzTeaMWOG03EAR1GsgQCzatUqvfzyy7r55pt1/vnnOx0HAM5oyJAhatSoke655x7l5OQ4HQdwDMUaCCAFBQUaPHiwYmNjWcIKgGtERkbqP//5T9F1IUCoolgDAeTdd9/VvHnz9Oyzz6pq1apOxwGAYuvatauuv/56PfHEE1qxYoXTcQBHUKyBALF161b9/e9/V8eOHXXLLbc4HQcASuz5559X2bJldfvttys/P9/pOIDfUayBAFBQUKCbb75Zhw4d0htvvMEFiwBcKT4+Xi+++KJ+/PFHPf30007HAfyOYg0EgBdeeEFfffWVXnjhBTVq1MjpOABw1q6//nr9+c9/1qhRo/Tzzz87HQfwK4o14LAFCxbogQce0FVXXaXBgwc7HQcAzokxRq+//rpq1aqlQYMGad++fU5HAvyGYg04aMeOHerXr5+qVq2qt956iykgAIJCXFycPvroI2VkZOi6665jvjVCBsUacMjhw4fVr18/7dy5U1988YUqVarkdCQA8JpLLrlEL7/8sqZNm6YHH3zQ6TiAX0Q4HQAIRZ71qn/44Qd9+umnatWqldORAMDr7rrrLi1dulRPPfWUGjdurJtvvtnpSIBPUawBP7PW6t5779UHH3ygRx99VH/+85+djgQAPvPyyy9r3bp1uu2221S2bFn179/f6UiAzzAVBPAja60eeeQRvfTSS7r77rv18MMPOx0JAHwqMjJSn3/+udq2batBgwZpxowZTkcCfIZiDfhJQUGBRo4cqdGjR+vWW2/V888/z8WKAEJCbGyspk2bpmbNmqlv376aMGGC05EAn6BYA35w+PBh3XLLLXr++ec1fPhwVgABEHLi4uI0e/ZsXXjhhbr66qv1+uuvOx0J8DqKNeBj27Zt0+WXX66xY8fqscce00svvaSwML71AISeChUq6KuvvlKPHj00ZMgQDR06VIcPH3Y6FuA1/O8O+NDcuXPVqlUrLViwQB9//LFGjRrFSDWAkBYTE6MvvvhCI0eO1KuvvqpOnTopIyPD6ViAV1CsAR/IycnRiBEj1LFjR0VHR2v+/PkaNGiQ07EAICBERETomWee0aeffqrFixerefPmev/992WtdToacE4o1oCXTZ8+XcnJyXr++ed1xx136Pfff1dycrLTsQAg4Pz5z3/WkiVLdMEFF+iWW27RFVdcoZUrVzodCzhrFGvASxYsWKAePXqoZ8+eCgsL01dffaXXXntNZcqUcToaAASsxMREzZkzR//5z3/066+/Kjk5WcOGDdOWLVucjgaUGMUaOAfWWn333Xfq3bu3Wrdurfnz5+uZZ57RkiVL1KVLF6fjAYArhIWFadiwYVq9erVuu+02vfHGG0pMTNTw4cO1Zs0ap+MBxUaxBs7Crl279Morr+iCCy5Qx44d9cMPP2j06NFav369Ro4cqVKlSjkdEQBcJz4+Xq+//rpSU1N13XXX6Y033lCjRo3Uo0cPjR8/Xjk5OU5HBE6LYg0Ug7VWqampevHFF3XFFVeoevXqGj58uMLCwvT2229r06ZNeuihh1SuXDmnowKA6yUmJuqdd95RRkaGHn30US1evFhXX321qlWrpmuvvVZjx47V9u3bnY4JnCDC6QBAIMrLy9PKlSv122+/6ZdfftGsWbOUnp4uSWrcuLHuvfdeXX/99WrevLnDSQEgeFWrVk2PPPKIHnroIc2ZM0cff/yxpk+frk8++USS1KpVK3Xu3FmtW7dWq1atVK9ePZY0haMo1ghZ1lplZmYqLS1Na9eu1bp167Ru3TotW7ZMixcvVnZ2tiSpbNmy6tSpk+677z5169ZN9erVczY4AISY8PBwde7cWZ07d1ZBQYF+//13zZgxQzNmzNDzzz+v3NxcSVLFihXVqlUrJSUlqUGDBqpfv74aNGigunXrKjo62uGPAqGAYg1XKygo0IEDB5SZmal9+/YpMzOz6OXox57Xd+/erW3bthW9eMqzR9WqVZWUlKQ777yzaASkYcOG3CkRAAJEWFiYWrZsqZYtW+rBBx/UoUOHtHTpUi1YsEC//fabFi1apLFjxyozM/OY9ytfvryqVaumatWqqWrVqqpQoYLKly9/2pdy5cqpXLlyioigLqF4+EpBwLDW6o8//tDmzZu1ZcsWbd68WTt27NCePXu0Z88e7d69+5jXPaW5ODcUKFOmjMqVK6cKFSqoWrVquuSSS4p+wCYkJKh+/fpKTExU2bJl/fCRAgC8pXTp0mrdurVat26tO+64Q1Lh/ye7du0q+kvkhg0btH37dm3btk1bt27VokWLtG/fPu3bt0+HDh064zFiYmKKivbR/5YvX15VqlRR1apViwq756VixYpMSwlBFGv4lbVWW7Zs0fLlyzV58mR9+OGHWr16dVGZPtkPuOjoaFWoUEEVK1ZUhQoVVLduXV1wwQWKi4srGk04emTh+Mdly5ZVeHi4Ax8tAMAJxhjFx8crPj5ebdu2Pe22hw4dKirZx78c/RfP4//dsmWL9u7dqx07digvL++E/ZYuXfqYgZvExEQdOHBAlStXVoMGDRQVFeWrDx8OoljDZ3bs2KHly5dr2bJlx/y7d+/eom2qVq2qxo0b6+KLL1bNmjVVo0YN1axZs+ilSpUq/PABAPhM6dKlVaVKFVWpUuWs3t9aqz179mjbtm3avn170cumTZuUnp6udevWae7cucrKypIkPfTQQwoLC1P9+vXVrFkznXfeeUX/NmrUiOVaXY5ijXO2e/duLV++/JjyvHz5cu3cubNomwoVKqhZs2YaNGhQ0Q+RvXv3qk+fPg4mBwDg3BhjVLFiRVWsWFFNmzY96TaeqY7jx49XXFycVq1aVfT/5eTJk1VQUCBJioiIUOPGjdW8eXMlJycXvdSsWZNpJS5BsUaxZWZmasWKFSeMQm/durVom7Jly+q8885Tnz59jvktvFq1aif8UEhJSfHzRwAAgP8ZY1S5cmU1adJEHTt2POZtOTk5Sk1N1bJly7Rs2TItXbpU33//fdGSgpIUFxdXVLI9pbtZs2YqU6aMnz8SnInfirUxppuklySFS3rbWvvkcW8vLWmspFaS/pD0Z2vten/lQ6GCggJt3LhRqampJ7xs3LixaLvo6Gidd9556tq16zEFunbt2vxWDQBAMUVFRen888/X+eeff8zze/fu1dKlS7V06VItWbJES5cu1fvvv6/9+/cXbZOYmKjk5GQ1bdpUDRs2VIMGDdSgQQNVrVqV/4sd4pdibYwJlzRGUhdJmyT9aoyZYq1dcdRmt0naY61tYIy5RtJTkv7sj3yhwrNu844dO7Rx40Zt3LhRGRkZysjIKHp9/fr1xyxBV65cOSUlJalDhw5q0qSJmjVrpmbNmqlevXosQQcAgI/ExcWpffv2at++fdFzBQUF2rBhwzFle/HixZo6dary8/OLtouNjS0q2XXq1Cm6funof2NiYpz4sIKev0as20haa61NkyRjzKeS+kg6ulj3kfTokdcnSHrFGGNscdZSCzLWWuXm5io3N1eHDx8+6esHDhzQ/v37T/mSlZWl3bt3a9euXdq5c6d27dqlXbt2FS2if7QqVaqoTp06aty4sbp166akpCQlJSWpcePG/NYLAECACAsLU0JCghISEtS7d++i53Nzc7VhwwatXbv2mJelS5dq+vTpJ9yzQSpc17tSpUpFK2555olXqFBBcXFxio2NVUxMzDEvRz8XFRWlyMjIE15CfdDNX8W6pqSNRz3eJOmiU21jrc0zxuyTVEnSrlPtdNOmTerataustad8ObK/gNnm+O0KCgpOKM4nW7anJKKjo1WmTBlVrFhRlStXVv369XXRRRepcuXKqly5suLj41W7dm3VqVNHNWvWZNUNAABcLDIysmiE+niev1Z7lrU9+mX37t1F94jYsGFD0etHj36XVFhY2AllOyIiQmFhYQoLC5Mx5ph/T/bc6d7med0z6Hf04N/xz3l7m+Iw/hgQNsYMkNTNWvuXI49vkHSRtXbYUdssO7LNpiOP1x3ZZtdx+xosabAkRUREtGrUqNExH/jxn+yTfXK8uc3Jtj/dPo7fJiwsTOHh4UVfeCd7PTw8XBEREce8HhUVpejo6GNePL9BumXN5v3793PhhUtx7tyN8+denDt3c8P5s9YqJydHOTk5OnToUNHrxz8+dOiQ8vPzlZ+fr7y8POXl5R3z+tGP8/PzjxlQPH7A8VTPSTrt207WYY8ewPT2NqtWrVpgrW19us+fv0asN0uqfdTjWkeeO9k2m4wxEZLKq/AixmNYa9+U9KYkJSUl2eXLl/skMHwvJSXlhKuj4Q6cO3fj/LkX587dOH/uVpyRa39NhPlVUkNjTIIxppSkayRNOW6bKZJuOvL6AEnfhuL8agAAALiTX0asj8yZHiZplgqX23vXWrvcGPOYpN+stVMkvSPpQ2PMWkm7VVi+AQAAAFfw2zrW1trpkqYf99zDR72eI2mgv/IAAAAA3hTaa6IAAAAAXkKxBgAAALyAYg0AAAB4AcUaAAAA8AKKNQAAAOAFFGsAAADACyjWAAAAgBdQrAEAAAAvoFgDAAAAXkCxBgAAALyAYg0AAAB4AcUaAAAA8AKKNQAAAOAFFGsAAADACyjWAAAAgBcYa63TGc6aMSZLUqrTOXDWKkva5XQInBXOnbtx/tyLc+dunD93S7LWlj3dBhH+SuIjqdba1k6HwNkxxvzG+XMnzp27cf7ci3Pnbpw/dzPG/HambZgKAgAAAHgBxRoAAADwArcX6zedDoBzwvlzL86du3H+3Itz526cP3c74/lz9cWLAAAAQKBw+4g1AAAAEBBcX6yNMaONMUuMMb8bY74yxtRwOhOKxxjzjDFm1ZHz97kxJs7pTCg+Y8xAY8xyY0yBMYar3F3AGNPNGJNqjFlrjLnf6TwoPmPMu8aYHcaYZU5nQckZY2obY+YYY1Yc+bn5N6czoXiMMVHGmF+MMYuPnLt/nnZ7t08FMcaUs9ZmHnn9r5KaWmvvdDgWisEY01XSt9baPGPMU5Jkrf0/h2OhmIwxTSQVSHpD0khr7RmXIYJzjDHhklZL6iJpk6RfJQ2y1q5wNBiKxRjzJ0n7JY211jZzOg9KxhhTXVJ1a+1CY0xZSQsk9eX7L/AZY4ykWGvtfmNMpKTvJf3NWjv/ZNu7fsTaU6qPiJXk7t8UQoi19itrbd6Rh/Ml1XIyD0rGWrvSWssNmtyjjaS11to0a+1hSZ9K6uNwJhSTtXaupN1O58DZsdZutdYuPPJ6lqSVkmo6mwrFYQvtP/Iw8sjLKbum64u1JBlj/mWM2SjpOkkPO50HZ+VWSTOcDgEEsZqSNh71eJP4jx3wO2NMPUktJP3scBQUkzEm3Bjzu6Qdkr621p7y3LmiWBtjvjHGLDvJSx9JstY+aK2tLekjScOcTYujnencHdnmQUl5Kjx/CCDFOX8AgOIxxpSRNFHS3cf9xR0BzFqbb629QIV/WW9jjDnldCxX3NLcWtu5mJt+JGm6pEd8GAclcKZzZ4y5WdKVki63bp/wH4RK8L2HwLdZUu2jHtc68hwAPzgyP3eipI+stZOczoOSs9buNcbMkdRN0kkvJHbFiPXpGGMaHvWwj6RVTmVByRhjukm6T1Jva+1Bp/MAQe5XSQ2NMQnGmFKSrpE0xeFMQEg4cgHcO5JWWmufdzoPis8YE+9ZtcwYE63CC8BP2TWDYVWQiZKSVLg6wQZJd1prGYVxAWPMWkmlJf1x5Kn5rOjiHsaYqyT9R1K8pL2SfrfWXuFoKJyWMaaHpBclhUt611r7L2cTobiMMZ9I6iipsqTtkh6x1r7jaCgUmzHmUknzJC1VYV+RpH9Ya6c7lwrFYYxJlvSBCn9uhkn6zFr72Cm3d3uxBgAAAAKB66eCAAAAAIGAYg0AAAB4AcUaAAAA8AKKNQAAAOAFFGsAAADACyjWAAAAgBdQrAEAAAAvoFgDQIgwxswxxnQ58vrjxpj/OJ0JAIJJhNMBAAB+84ikx4wxVSS1kNTb4TwAEFS48yIAhBBjzHeSykjqaK3NcjoPAAQTpoIAQIgwxjSXVF3SYUo1AHgfxRoAQoAxprqkjyT1kbTfGNPN4UgAEHQo1gAQ5IwxMZImSRphrV0pabQK51sDALyIOdYAAACAFzBiDQAAAHgBxRoAAADwAoo1AAAA4AUUawAAAMALKNYAAACAF1CsAQAAAC+gWAMAAABeQLEGAAAAvOD/AUpWIjbfbRIiAAAAAElFTkSuQmCC\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "lb = integral_bounds[0][0] # lower bound\n", "ub = integral_bounds[0][1] # upper bound\n", "\n", "x_plot = np.linspace(lb, ub, 300)[:, None]\n", "y_plot = user_function.f(x_plot)\n", "\n", "plt.figure(figsize=FIGURE_SIZE)\n", "plt.plot(x_plot, y_plot, \"k\", label=\"The Integrand\")\n", "plt.legend(loc=2, prop={'size': LEGEND_SIZE})\n", "plt.xlabel(r\"$x$\")\n", "plt.ylabel(r\"$f(x)$\")\n", "plt.grid(True)\n", "plt.xlim(lb, ub)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Ground truth\n", "\n", "For the sake of demonstration we compute the ground truth integral here to high precision. In real-world tasks, this is not possible which is why we need a method like BQ in the first place." ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "from emukit.test_functions.quadrature.baselines import univariate_approximate_ground_truth_integral\n", "\n", "ground_truth = univariate_approximate_ground_truth_integral(user_function.f, (lb, ub))[0]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

The Intial Design

" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Usually, before we start the actual BQ loop we need to gather a few observations such that we can fit an initial GP-model. This is called the initial design and common strategies are either a predefined grid or sampling points uniformly at random. " ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "X_init = np.array([[-2.],[-0.5], [-0.1]])\n", "Y_init = user_function.f(X_init)\n", "\n", "plt.figure(figsize=FIGURE_SIZE)\n", "plt.plot(X_init, Y_init, \"ro\", markersize=10, label=\"Initial observations\")\n", "plt.plot(x_plot, y_plot, \"k\", label=\"The Integrand\")\n", "plt.legend(loc=2, prop={'size': LEGEND_SIZE})\n", "plt.xlabel(r\"$x$\")\n", "plt.ylabel(r\"$f(x)$\")\n", "plt.grid(True)\n", "plt.xlim(lb, ub)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

The Model

\n", " " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now we can start with the BQ loop by first fitting a model on the collected data. \n", "The arguably most popular model for BQ is a Gaussian process (GP) which defines a probability distribution across classes of functions, such that each linear finite-dimensional restriction is multivariate Gaussian (see e.g., [[4]](#4.-References)). GPs are fully parametrized by a mean function $\\mu(x)$ and a covariance function $k(x,x')$. \n", "\n", "In BQ, the kernel choice is more restricted than, for example in Bayesian optimization, since BQ requires access to analytic integrals of the kernel function. Luckily, the RBF-kernel \n", "\n", "$$ \n", "k(x,x') = \\theta_0 \\cdot \\exp{ \\left(-\\frac{\\|x-x'\\|^2}{\\theta_1}\\right)}\\quad \\text{with}\\quad \\theta_0,~\\theta_1\\quad \\text{hyperparameters},\n", "$$\n", "\n", "is integrable analytically and is also a standard choice in many applications.\n", "To denote that $f$ is a sample from a GP conditioned on the dataset $D_n$ with mean function $\\mu_n(x)$ and covariance function $k_n(x, x')$ we write $f \\sim \\mathcal{GP}(\\mu_n,k_n).$\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Note that the Gaussian process model class can also be characterized by its hyperparameters $\\theta = \\{\\theta_0, ... \\theta_k\\}$ such as for instance the kernel lengthscales. For simplicity we keep these hyperparameters fixed here. However, we usually either optimize or sample these hyperparameters using the marginal log-likelihood of the GP. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Make your GP model \n", "\n", "We use a GPy GP regression model with RBF kernel as surrogate for $f$." ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [], "source": [ "import GPy\n", "\n", "# GPy takes X and Y values at initialization. Those will be overwritten later when the emukit model is initialized.\n", "gpy_model = GPy.models.GPRegression(X=X_init, Y=Y_init, kernel=GPy.kern.RBF(\n", " input_dim=X_init.shape[1], lengthscale=0.5, variance=1.0))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Convert to Emukit quadrature model\n", "\n", "We use the GPy GP wrapper which is already in Emukit to convert the GPy model into an Emukit model. But you can also use your own model and wrap it using Emukit interfaces.\n", "\n", "We first wrap the RBF kernel of GPy and obtain the Emukit RBF kernel `emukit_rbf`. Then we create the quadrature RBF kernel `emukit_qrbf` which has additional functionality needed for BQ. Then we create an Emukit GP `emukit_model` with this quadrature kernel. Note that we need to wrap the kernel, too, since the integration that BQ performs is essentially equal to integrating the kernel." ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [], "source": [ "from emukit.model_wrappers.gpy_quadrature_wrappers import BaseGaussianProcessGPy, RBFGPy\n", "from emukit.quadrature.kernels import QuadratureRBFLebesgueMeasure\n", "from emukit.quadrature.measures import LebesgueMeasure\n", "\n", "emukit_rbf = RBFGPy(gpy_model.kern)\n", "emukit_measure = LebesgueMeasure.from_bounds(integral_bounds)\n", "emukit_qrbf = QuadratureRBFLebesgueMeasure(emukit_rbf, emukit_measure)\n", "emukit_model = BaseGaussianProcessGPy(kern=emukit_qrbf, gpy_model=gpy_model)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Choose the quadrature method: Vanilla BQ\n", "\n", "The vanilla BQ method performs GP regression on the integrand $f$ itself which is the most simple way of doing BQ; then this GP is integrated. \n", "Emukit can perform the integration of the GP without approximations. But first, we plot the marginal distributions of the GP alongside the integrand, as well as the distribution over the integral value $F$. " ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [], "source": [ "from emukit.quadrature.methods import VanillaBayesianQuadrature\n", "\n", "emukit_method = VanillaBayesianQuadrature(base_gp=emukit_model, X=X_init, Y=Y_init)" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "mu_plot, var_plot = emukit_method.predict(x_plot)\n", "\n", "plt.figure(figsize=FIGURE_SIZE)\n", "plt.plot(X_init, Y_init, \"ro\", markersize=10, label=\"Observations\")\n", "plt.plot(x_plot, y_plot, \"k\", label=\"The Integrand\")\n", "plt.plot(x_plot, mu_plot, \"C0\", label=\"Model\")\n", "plt.fill_between(x_plot[:, 0],\n", " mu_plot[:, 0] + np.sqrt(var_plot)[:, 0],\n", " mu_plot[:, 0] - np.sqrt(var_plot)[:, 0], color=\"C0\", alpha=0.6)\n", "plt.fill_between(x_plot[:, 0],\n", " mu_plot[:, 0] + 2 * np.sqrt(var_plot)[:, 0],\n", " mu_plot[:, 0] - 2 * np.sqrt(var_plot)[:, 0], color=\"C0\", alpha=0.4)\n", "plt.fill_between(x_plot[:, 0],\n", " mu_plot[:, 0] + 3 * np.sqrt(var_plot)[:, 0],\n", " mu_plot[:, 0] - 3 * np.sqrt(var_plot)[:, 0], color=\"C0\", alpha=0.2)\n", "plt.legend(loc=2, prop={'size': LEGEND_SIZE})\n", "plt.xlabel(r\"$x$\")\n", "plt.ylabel(r\"$f(x)$\")\n", "plt.grid(True)\n", "plt.xlim(lb, ub)\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "initial_integral_mean, initial_integral_variance = emukit_method.integrate()\n", "\n", "x_plot_integral = np.linspace(initial_integral_mean-3*np.sqrt(initial_integral_variance), \n", " initial_integral_mean+3*np.sqrt(initial_integral_variance), 200)\n", "y_plot_integral_initial = 1/np.sqrt(initial_integral_variance * 2 * np.pi) * \\\n", "np.exp( - (x_plot_integral - initial_integral_mean)**2 / (2 * initial_integral_variance) )\n", "plt.figure(figsize=FIGURE_SIZE)\n", "plt.plot(x_plot_integral, y_plot_integral_initial, \"k\", label=\"initial integral density\")\n", "plt.axvline(initial_integral_mean, color=\"red\", label=\"initial integral estimate\", \\\n", " linestyle=\"--\")\n", "plt.axvline(ground_truth, color=\"blue\", label=\"ground truth integral\", \\\n", " linestyle=\"--\")\n", "plt.legend(loc=2, prop={'size': LEGEND_SIZE})\n", "plt.xlabel(r\"$F$\")\n", "plt.ylabel(r\"$p(F)$\")\n", "plt.grid(True)\n", "plt.xlim(np.min(x_plot_integral), np.max(x_plot_integral))\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We observe that the error in the integral value is still large after only three initial evaluations, but the true integral value is well within the error bars. " ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "The initial estimated integral is: 0.9\n", "with a credible interval: 3.86 .\n", "The ground truth rounded to 2 digits for comparison is: 1.14 .\n" ] } ], "source": [ "print('The initial estimated integral is: ', round(initial_integral_mean, 2))\n", "print('with a credible interval: ', round(2*np.sqrt(initial_integral_variance), 2), '.')\n", "print('The ground truth rounded to 2 digits for comparison is: ', round(ground_truth, 2), '.')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

The Acquisition Function

" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In the second step of our BQ loop we use our model to compute the acquisition function. In BQ, the acquisition function is ideally a global property of the integrand $f$ since the integral $F$ is, too. Two common acquisition functions of BQ are:\n", "\n", "\n", "**Integral variance reduction (IVR)**: The IVR is the difference between the current variance $\\mathfrak{v}_n$ of the integral distribution and the variance of the integral distribution after another hypothetically collected datapoint at $x$\n", "That is, IVR maximizes\n", "\n", "$$\n", "a_n^{IVR}(x) = \\mathfrak{v}_n - v[\\{x_i\\}_{i=1}^n\\cup x]= \\mathfrak{v}_n \\rho^2(x),\n", "$$ \n", "\n", "where $v[\\{x_i\\}_{i=1}^n\\cup x]$ is the integral variance under the newly collected point $x$, and \n", "$$\n", "\\rho^2(x) = \\frac{\\left(\\int_{\\mathbb{X}} k_n(z, x)\\mathrm{d}z\\right)^2}{\\mathfrak{v}_n v_n(x)}\n", "$$ \n", "\n", "is the squared correlation between the integral value and the hypothetical integrand value at $x$, and $v_n(x)$ is the variance of $f(x)$. Note that we can normalize the IVR by the current variance $\\mathfrak{v}_n$ of the integral which does not depend on $x$. Like this, the normalized IVR ranges between 0 and 1 and is indeed equal to the squared correlation itself.\n", "\n", "\n", "\n", "**Mutual Information (MI)**: This acquisition function builds on an information theoretic approach. MI is the mutual information $I(F; f(x))$ between the integral value and the value of the hypothetically collected datapoint $f(x)$. That is, MI maximizes\n", "\n", "$$\n", "a_n^{MI}(x) = I(F; f(x)) = -\\frac{1}{2}\\log\\left[1-\\rho^2(x)\\right].\n", "$$\n", "\n", "In vanilla BQ, both IVR and MI are identical in the sense that their armax that yields $x_{n+1}$ is identical, i.e., the location of their global optimum is the same. This can be seen since IVR is a transformation of MI by the strictly monotonic function $1-e^{-2a^{MI}}$.\n", "Since the policy of the acquisition scheme (choosing the argmax of $a_n(x)$) is independent of the values of $a_n(x)$ we can thus use IVR and MI interchangeably for vanilla BQ (note that this might be not the case for cost-sensitive models). In this tutorial we will use the normalized IVR.\n", "\n", "The acquisition functions presented here only rely on the model and hence are cheap to evaluate. Furthermore we can easily compute the gradients and use a simple gradient based optimization method to find $x_{n+1} \\in \\operatorname*{arg\\:max}_{x \\in \\mathbb{X}} a_n(x)$." ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "scrolled": false }, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "from emukit.quadrature.acquisitions import IntegralVarianceReduction\n", "\n", "ivr_acquisition = IntegralVarianceReduction(emukit_method)\n", "\n", "ivr_plot = ivr_acquisition.evaluate(x_plot)\n", "\n", "plt.figure(figsize=FIGURE_SIZE)\n", "plt.plot(x_plot, (ivr_plot - np.min(ivr_plot)) / (np.max(ivr_plot) - np.min(ivr_plot)), \n", " \"green\", label=\"integral variance reduction\")\n", "\n", "plt.legend(loc=0, prop={'size': LEGEND_SIZE})\n", "plt.xlabel(r\"$x$\")\n", "plt.ylabel(r\"$acquisition(x)$\")\n", "plt.grid(True)\n", "plt.xlim(lb, ub)\n", "plt.ylim(0, 1.04)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

Evaluating the objective function

" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To find the next point to evaluate we optimize the acquisition function using a standard gradient descent optimizer.\n", "\n", "The `space` object defines the input space for the optimizer which, in the case of BQ, is equal to the integration domain defined by the integral bounds, i.e., $\\mathbb{X} = [-3, 3]$. Note that the maximum of the acquisition does *not* appear at the integral bounds where the variance on $f$ is highest. This is because evaluations on the bounds would not maximally reduce what we learn about the integral, a global property; this behavior precisely illustrates the difference of a local vs a global acquisition strategy." ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "from emukit.core.optimization import GradientAcquisitionOptimizer\n", "from emukit.core.parameter_space import ParameterSpace\n", "\n", "space = ParameterSpace(emukit_method.reasonable_box_bounds.convert_to_list_of_continuous_parameters())\n", "optimizer = GradientAcquisitionOptimizer(space)\n", "x_new,_ = optimizer.optimize(ivr_acquisition)\n", "\n", "plt.figure(figsize=FIGURE_SIZE)\n", "plt.plot(x_plot, (ivr_plot - np.min(ivr_plot)) / (np.max(ivr_plot) - np.min(ivr_plot)), \n", " \"green\", label=\"integral variance reduction\")\n", "plt.axvline(x_new, color=\"red\", label=\"x_next\", linestyle=\"--\")\n", "plt.legend(loc=0, prop={'size': LEGEND_SIZE})\n", "plt.xlabel(r\"$x$\")\n", "plt.ylabel(r\"$f(x)$\")\n", "plt.grid(True)\n", "plt.xlim(lb, ub)\n", "plt.ylim(0, 1.04)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Afterwards we evaluate the true objective function and append it to our initial observations." ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [], "source": [ "y_new = user_function.f(x_new)" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [], "source": [ "X = np.append(X_init, x_new, axis=0)\n", "Y = np.append(Y_init, y_new, axis=0)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "After updating the model, you can see that the uncertainty about the true objective function in this region decreases and our model becomes more certain. We have also reduces the variance on the integral estimation as can be seen from the plot below." ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [], "source": [ "emukit_method.set_data(X, Y)" ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "mu_plot, var_plot = emukit_model.predict(x_plot)\n", "\n", "plt.figure(figsize=FIGURE_SIZE)\n", "plt.plot(emukit_model.X, emukit_model.Y, \"ro\", markersize=10, label=\"Observations\")\n", "plt.plot(x_plot, y_plot, \"k\", label=\"The Integrand\")\n", "plt.plot(x_plot, mu_plot, \"C0\", label=\"Model\")\n", "plt.fill_between(x_plot[:, 0],\n", " mu_plot[:, 0] + np.sqrt(var_plot)[:, 0],\n", " mu_plot[:, 0] - np.sqrt(var_plot)[:, 0], color=\"C0\", alpha=0.6)\n", "plt.fill_between(x_plot[:, 0],\n", " mu_plot[:, 0] + 2 * np.sqrt(var_plot)[:, 0],\n", " mu_plot[:, 0] - 2 * np.sqrt(var_plot)[:, 0], color=\"C0\", alpha=0.4)\n", "plt.fill_between(x_plot[:, 0],\n", " mu_plot[:, 0] + 3 * np.sqrt(var_plot)[:, 0],\n", " mu_plot[:, 0] - 3 * np.sqrt(var_plot)[:, 0], color=\"C0\", alpha=0.2)\n", "plt.legend(loc=2, prop={'size': LEGEND_SIZE})\n", "plt.xlabel(r\"$x$\")\n", "plt.ylabel(r\"$f(x)$\")\n", "plt.grid(True)\n", "plt.xlim(lb, ub)\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "integral_mean, integral_variance = emukit_method.integrate()\n", "\n", "y_plot_integral = 1/np.sqrt(integral_variance * 2 * np.pi) * \\\n", "np.exp( - (x_plot_integral - integral_mean)**2 / (2 * integral_variance) )\n", "plt.figure(figsize=FIGURE_SIZE)\n", "plt.plot(x_plot_integral, y_plot_integral_initial, \"gray\", label=\"initial integral density\")\n", "plt.plot(x_plot_integral, y_plot_integral, \"k\", label=\"new integral density\")\n", "plt.axvline(initial_integral_mean, color=\"gray\", label=\"initial integral estimate\", linestyle=\"--\")\n", "plt.axvline(integral_mean, color=\"red\", label=\"new integral estimate\", linestyle=\"--\")\n", "plt.axvline(ground_truth, color=\"blue\", label=\"ground truth integral\", \\\n", " linestyle=\"--\")\n", "plt.legend(loc=2, prop={'size': LEGEND_SIZE})\n", "plt.xlabel(r\"$F$\")\n", "plt.ylabel(r\"$p(F)$\")\n", "plt.grid(True)\n", "plt.xlim(np.min(x_plot_integral), np.max(x_plot_integral))\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "The estimated integral is: 0.93\n", "with a credible interval: 2.94 .\n", "The ground truth rounded to 2 digits for comparison is: 1.14 .\n" ] } ], "source": [ "print('The estimated integral is: ', round(integral_mean, 2))\n", "print('with a credible interval: ', round(2*np.sqrt(integral_variance), 2), '.')\n", "print('The ground truth rounded to 2 digits for comparison is: ', round(ground_truth, 2), '.')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 3. Emukit's Bayesian quadrature interface" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Of course in practice we don't want to implement all of these steps our self. Emukit provides a convenient and flexible interface to apply Bayesian quadrature. Below we can see how to run vanilla Bayesian quadrature on the exact same function for 20 iterations.\n", "\n", "We see that the model is now very certain about the integral value which can be seen from the narrow density. In comparison, the initial integral density using three points only (shown in gray) is very wide and flat and more uncertain." ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [], "source": [ "from emukit.examples.vanilla_bayesian_quadrature_with_rbf.vanilla_bq_loop_with_rbf import create_vanilla_bq_loop_with_rbf_kernel\n", "\n", "emukit_loop = create_vanilla_bq_loop_with_rbf_kernel(X=X_init, Y=Y_init, \n", " integral_bounds=integral_bounds,\n", " measure=None)\n", "emukit_loop.run_loop(user_function=user_function, stopping_condition=20)" ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "mu_plot, var_plot = emukit_loop.model.predict(x_plot)\n", "\n", "plt.figure(figsize=FIGURE_SIZE)\n", "plt.plot(emukit_loop.loop_state.X, emukit_loop.loop_state.Y, \"ro\", markersize=10, label=\"Observations\")\n", "plt.plot(x_plot, y_plot, \"k\", label=\"The Integrand\")\n", "plt.plot(x_plot, mu_plot, \"C0\", label=\"Model\")\n", "plt.fill_between(x_plot[:, 0],\n", " mu_plot[:, 0] + np.sqrt(var_plot)[:, 0],\n", " mu_plot[:, 0] - np.sqrt(var_plot)[:, 0], color=\"C0\", alpha=0.6)\n", "\n", "plt.fill_between(x_plot[:, 0],\n", " mu_plot[:, 0] + 2 * np.sqrt(var_plot)[:, 0],\n", " mu_plot[:, 0] - 2 * np.sqrt(var_plot)[:, 0], color=\"C0\", alpha=0.4)\n", "\n", "plt.fill_between(x_plot[:, 0],\n", " mu_plot[:, 0] + 3 * np.sqrt(var_plot)[:, 0],\n", " mu_plot[:, 0] - 3 * np.sqrt(var_plot)[:, 0], color=\"C0\", alpha=0.2)\n", "plt.legend(loc=2, prop={'size': LEGEND_SIZE})\n", "plt.xlabel(r\"$x$\")\n", "plt.ylabel(r\"$f(x)$\")\n", "plt.grid(True)\n", "plt.xlim(lb, ub)\n", "\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "integral_mean, integral_variance = emukit_loop.model.integrate()\n", "\n", "y_plot_integral = 1/np.sqrt(integral_variance * 2 * np.pi) * \\\n", "np.exp( - (x_plot_integral - integral_mean)**2 / (2 * integral_variance) )\n", "plt.figure(figsize=FIGURE_SIZE)\n", "plt.plot(x_plot_integral, y_plot_integral_initial, \"gray\", label=\"initial integral density\")\n", "plt.plot(x_plot_integral, y_plot_integral, \"k\", label=\"new integral density\")\n", "plt.axvline(initial_integral_mean, color=\"gray\", label=\"initial integral estimate\", linestyle=\"--\")\n", "plt.axvline(integral_mean, color=\"red\", label=\"new integral estimate\", linestyle=\"--\")\n", "plt.axvline(ground_truth, color=\"blue\", label=\"ground truth integral\", \\\n", " linestyle=\"--\")\n", "plt.legend(loc=2, prop={'size': LEGEND_SIZE})\n", "plt.xlabel(r\"$F$\")\n", "plt.ylabel(r\"$p(F)$\")\n", "plt.grid(True)\n", "plt.xlim(np.min(x_plot_integral), np.max(x_plot_integral))\n", "plt.ylim(-0.06, 1)\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "The estimated integral is: 1.12\n", "with a credible interval: 0.04 .\n", "The ground truth rounded to 2 digits for comparison is: 1.14 .\n" ] } ], "source": [ "print('The estimated integral is: ', round(integral_mean, 2))\n", "print('with a credible interval: ', round(2*np.sqrt(integral_variance), 2), '.')\n", "print('The ground truth rounded to 2 digits for comparison is: ', round(ground_truth, 2), '.')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 4. References\n", "\n", "- [1] O'Hagan (1991) [Bayes-Hermite Quadrature](https://www.sciencedirect.com/science/article/pii/037837589190002V), *Journal of Statistical Planning and Inference* 29, pp. 245--260.\n", "- [2] Diaconis (1988) [Bayesian numerical analysis](http://probabilistic-numerics.org/assets/pdf/Diaconis_1988.pdf), *Statistical decision theory and related topics* V, pp. 163--175.\n", "- [3] Gunter et al. (2014) [Sampling for Inference in Probabilistic Models with Fast Bayesian Quadrature](https://papers.nips.cc/paper/5483-sampling-for-inference-in-probabilistic-models-with-fast-bayesian-quadrature), *Advances in Neural Information Processing Systems*, 27, pp. 2789--2797.\n", "- [4] Rasmussen and Williams (2005) [Gaussian Processes for Machine Learning](http://www.gaussianprocess.org/gpml/chapters/RW.pdf) *Adaptive Computation and Machine Learning*, The MIT Press\n" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.9.5" } }, "nbformat": 4, "nbformat_minor": 2 }