{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "*This notebook contains material from [cbe67701-uncertainty-quantification](https://ndcbe.github.io/cbe67701-uncertainty-quantification);\n", "content is available [on Github](https://github.com/ndcbe/cbe67701-uncertainty-quantification.git).*" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "< [10.1 Using GPflow package for Gaussian Process Regression](https://ndcbe.github.io/cbe67701-uncertainty-quantification/10.01-Contributed-Example.html) | [Contents](toc.html) | [10.3 **Using scikit-learn for Gaussian Process Regression**](https://ndcbe.github.io/cbe67701-uncertainty-quantification/10.03-Gaussian-Process-Regression.html)
"
]
},
{
"cell_type": "markdown",
"metadata": {
"nbpages": {
"level": 1,
"link": "[10.2 A simple example of Bayesian quadrature](https://ndcbe.github.io/cbe67701-uncertainty-quantification/10.02-Bayesian-quadrature.html#10.2-A-simple-example-of-Bayesian-quadrature)",
"section": "10.2 A simple example of Bayesian quadrature"
}
},
"source": [
"# 10.2 A simple example of Bayesian quadrature"
]
},
{
"cell_type": "markdown",
"metadata": {
"nbpages": {
"level": 1,
"link": "[10.2 A simple example of Bayesian quadrature](https://ndcbe.github.io/cbe67701-uncertainty-quantification/10.02-Bayesian-quadrature.html#10.2-A-simple-example-of-Bayesian-quadrature)",
"section": "10.2 A simple example of Bayesian quadrature"
}
},
"source": [
"Created by Zhuogang Peng (zpeng5@nd.edu)\n",
"\n",
"These examples and codes were adapted from:\n",
"\n",
"O’Hagan (1991) Bayes-Hermite Quadrature, Journal of Statistical Planning and Inference 29, pp. 245–260.\n",
"\n",
"Diaconis, P. (1988). “Bayesian numerical analysis”. In:Statistical Decision Theory and Related Topics IV1,pp. 163–175.\n",
"\n",
"The Emukit authors (2018), Emukit: Emulation and Uncertainty Quantification for Decision Making, https://github.com/amzn/emukit\n",
"\n",
"McClarren, Ryan G (2018). Uncertainty Quantification and Predictive Computational Science: A Foundation for Physical Scientists and Engineers, Chapter 10 : Gaussian Process Emulators and Surrogate Models, Springer, https://link.springer.com/chapter/10.1007%2F978-3-319-99525-0_7\n"
]
},
{
"cell_type": "markdown",
"metadata": {
"nbpages": {
"level": 3,
"link": "[10.2.1 Bayesian quadrature uses Gaussian process regression as the approximation to the integrand](https://ndcbe.github.io/cbe67701-uncertainty-quantification/10.02-Bayesian-quadrature.html#10.2.1-Bayesian-quadrature-uses-Gaussian-process-regression-as-the-approximation-to-the-integrand)",
"section": "10.2.1 Bayesian quadrature uses Gaussian process regression as the approximation to the integrand"
}
},
"source": [
"### 10.2.1 Bayesian quadrature uses Gaussian process regression as the approximation to the integrand\n",
"\n",
"* We want to calculate the integral\n",
"$$\n",
"F = \\int_{\\mathbb{D}}f(x)\\mathrm{d}x.\n",
"$$\n",
" \n",
"\n",
"* Suppose we do not know the exact expression of $f$, but we do have some observations.\n",
"\n",
"* The conventional method (like trapezoid rule) cannot give the accuracy of the integration. \n",
"\n",
"* But the Bayesian method estimates the uncertainty, along with the result. It can even tell us how to select the observations."
]
},
{
"cell_type": "markdown",
"metadata": {
"nbpages": {
"level": 3,
"link": "[10.2.2 The procedures of Bayesian Quadrature](https://ndcbe.github.io/cbe67701-uncertainty-quantification/10.02-Bayesian-quadrature.html#10.2.2-The-procedures-of-Bayesian-Quadrature)",
"section": "10.2.2 The procedures of Bayesian Quadrature"
}
},
"source": [
"### 10.2.2 The procedures of Bayesian Quadrature\n",
"\n",
"* Using the Gaussian process as a prior distribution of $f$.\n",
"\n",
"* Observe $f$ at $[x_1, x_2, ..., x_n]$ on the computational domain $\\mathbb{D}$.\n",
"\n",
"* Calculate the posterior distribution of $f$ with Gaussian process regression.\n",
"\n",
"* The posterior $F$ is a linear functional of $f$.\n",
"\n",
"* The posterior variance of $F$ does not depend on the observation $f$. This allows us to choose the quadrature points offline. \n"
]
},
{
"cell_type": "markdown",
"metadata": {
"nbpages": {
"level": 3,
"link": "[10.2.3 Implementation](https://ndcbe.github.io/cbe67701-uncertainty-quantification/10.02-Bayesian-quadrature.html#10.2.3-Implementation)",
"section": "10.2.3 Implementation"
}
},
"source": [
"### 10.2.3 Implementation"
]
},
{
"cell_type": "code",
"execution_count": 123,
"metadata": {
"nbpages": {
"level": 3,
"link": "[10.2.3 Implementation](https://ndcbe.github.io/cbe67701-uncertainty-quantification/10.02-Bayesian-quadrature.html#10.2.3-Implementation)",
"section": "10.2.3 Implementation"
}
},
"outputs": [],
"source": [
"## import all needed Python libraries here\n",
"%matplotlib inline\n",
"import matplotlib.pyplot as plt\n",
"from mpl_toolkits.mplot3d import Axes3D\n",
"import numpy as np\n",
"import math\n",
"from scipy.stats import norm\n",
"from scipy.integrate import quad\n",
"\n",
"# import sys\n",
"# !{sys.executable} -m pip install --user emukit\n",
"# !{sys.executable} -m pip install --user pyDOE\n",
"\n",
"from sklearn.gaussian_process import GaussianProcessRegressor\n",
"from sklearn.gaussian_process.kernels import RBF, ConstantKernel as C\n",
"\n",
"\n",
"# Figure config\n",
"LEGEND_SIZE = 16\n",
"FIGURE_SIZE = (10, 8)"
]
},
{
"cell_type": "markdown",
"metadata": {
"nbpages": {
"level": 3,
"link": "[10.2.3 Implementation](https://ndcbe.github.io/cbe67701-uncertainty-quantification/10.02-Bayesian-quadrature.html#10.2.3-Implementation)",
"section": "10.2.3 Implementation"
}
},
"source": [
"For example, we are interested in \n",
"the integral of \n",
"$$\n",
"f(x) = x^2 e^{-x^2-2 cos^2(x)}.\n",
"$$\n",
"over $[-3, 3]$.\n"
]
},
{
"cell_type": "code",
"execution_count": 124,
"metadata": {
"nbpages": {
"level": 3,
"link": "[10.2.3 Implementation](https://ndcbe.github.io/cbe67701-uncertainty-quantification/10.02-Bayesian-quadrature.html#10.2.3-Implementation)",
"section": "10.2.3 Implementation"
}
},
"outputs": [],
"source": [
"def f(x):\n",
" return x**2*np.exp(-x**2 - 2*(np.cos(x))**2)"
]
},
{
"cell_type": "code",
"execution_count": 125,
"metadata": {
"nbpages": {
"level": 3,
"link": "[10.2.3 Implementation](https://ndcbe.github.io/cbe67701-uncertainty-quantification/10.02-Bayesian-quadrature.html#10.2.3-Implementation)",
"section": "10.2.3 Implementation"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"(0.5369627263101916, 2.1141020263709753e-11)\n"
]
}
],
"source": [
"lb = -3 # lower bound\n",
"ub = 3 # upper bound\n",
"\n",
"benchmark_solution = quad(f, lb, ub)\n",
"print(benchmark_solution)"
]
},
{
"cell_type": "code",
"execution_count": 126,
"metadata": {
"nbpages": {
"level": 3,
"link": "[10.2.3 Implementation](https://ndcbe.github.io/cbe67701-uncertainty-quantification/10.02-Bayesian-quadrature.html#10.2.3-Implementation)",
"section": "10.2.3 Implementation"
}
},
"outputs": [
{
"data": {
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\n",
"text/plain": [
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]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"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": "3.6.5"
}
},
"nbformat": 4,
"nbformat_minor": 2
}