{ "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)

\"Open

\"Download\"" ] }, { "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": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "x_plot = np.linspace(lb, ub, 100)[:, None]\n", "\n", "y_plot = f(x_plot)\n", "\n", "X_init = np.array([-2,1,2])\n", "\n", "Y_init = 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=\"$f(x) = x^2 e^{-x^2-2 cos^2(x)}$\")\n", "plt.legend(loc='lower right', prop={'size': LEGEND_SIZE}, borderpad=0.8)\n", "plt.xlabel(r\"$x$\", fontsize=15)\n", "plt.ylabel(r\"$f(x)$\", fontsize=15)\n", "plt.grid(True)\n", "plt.xlim(lb, ub)\n", "plt.show()\n" ] }, { "cell_type": "markdown", "metadata": { "nbpages": { "level": 4, "link": "[10.2.3.1 Take the GPR model as the surrogate](https://ndcbe.github.io/cbe67701-uncertainty-quantification/10.02-Bayesian-quadrature.html#10.2.3.1-Take-the-GPR-model-as-the-surrogate)", "section": "10.2.3.1 Take the GPR model as the surrogate" } }, "source": [ "#### 10.2.3.1 Take the GPR model as the surrogate" ] }, { "cell_type": "code", "execution_count": 127, "metadata": { "nbpages": { "level": 4, "link": "[10.2.3.1 Take the GPR model as the surrogate](https://ndcbe.github.io/cbe67701-uncertainty-quantification/10.02-Bayesian-quadrature.html#10.2.3.1-Take-the-GPR-model-as-the-surrogate)", "section": "10.2.3.1 Take the GPR model as the surrogate" } }, "outputs": [], "source": [ "import GPy\n", "X_init = X_init.reshape(-1,1)\n", "Y_init = f(X_init)\n", "## the squared-exponential kernel\n", "gpy_model = GPy.models.GPRegression(X=X_init, Y=f(X_init), kernel=GPy.kern.RBF(\n", " input_dim=X_init.shape[1], lengthscale=0.5, variance=1.0))\n", "\n", "from emukit.model_wrappers.gpy_quadrature_wrappers import BaseGaussianProcessGPy, RBFGPy\n", "from emukit.quadrature.kernels import QuadratureRBFLebesgueMeasure\n", "\n", "emukit_rbf = RBFGPy(gpy_model.kern)\n", "emukit_qrbf = QuadratureRBFLebesgueMeasure(emukit_rbf, integral_bounds=[[lb, ub]])\n", "emukit_model = BaseGaussianProcessGPy(kern=emukit_qrbf, gpy_model=gpy_model)" ] }, { "cell_type": "markdown", "metadata": { "nbpages": { "level": 3, "link": "[10.2.4 Result](https://ndcbe.github.io/cbe67701-uncertainty-quantification/10.02-Bayesian-quadrature.html#10.2.4-Result)", "section": "10.2.4 Result" } }, "source": [ "### 10.2.4 Result" ] }, { "cell_type": "code", "execution_count": 128, "metadata": { "nbpages": { "level": 3, "link": "[10.2.4 Result](https://ndcbe.github.io/cbe67701-uncertainty-quantification/10.02-Bayesian-quadrature.html#10.2.4-Result)", "section": "10.2.4 Result" } }, "outputs": [ { "data": { "image/png": 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\n", 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "The initial estimated integral is: 0.35\n", "with a confidence interval: 3.36 .\n", "The ground truth rounded to 2 digits for comparison is: 0.54 .\n" ] } ], "source": [ "from emukit.quadrature.methods import VanillaBayesianQuadrature\n", "\n", "emukit_method = VanillaBayesianQuadrature(base_gp=emukit_model, X=X_init, Y=Y_init)\n", "\n", "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(np.concatenate([x_plot, x_plot[::-1]]),\n", " np.concatenate([mu_plot[:, 0] - 1.9600 * np.sqrt(var_plot)[:, 0],\n", " (mu_plot[:, 0] + 1.9600 * np.sqrt(var_plot)[:, 0])[::-1]]),\n", " alpha=.6, fc='b', ec='None', label='95% confidence interval')\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()\n", "\n", "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(benchmark_solution[0], color=\"blue\", label=\"benchmark solution\", 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()\n", "\n", "print('The initial estimated integral is: ', round(initial_integral_mean, 2))\n", "print('with a confidence interval: ', round(2*np.sqrt(initial_integral_variance), 2), '.')\n", "print('The ground truth rounded to 2 digits for comparison is: ', round(benchmark_solution[0], 2), '.')" ] }, { "cell_type": "markdown", "metadata": { "nbpages": { "level": 4, "link": "[10.2.4.1 Find the next quadrature point by minimizing the posterior variance ](https://ndcbe.github.io/cbe67701-uncertainty-quantification/10.02-Bayesian-quadrature.html#10.2.4.1-Find-the-next-quadrature-point-by-minimizing-the-posterior-variance)", "section": "10.2.4.1 Find the next quadrature point by minimizing the posterior variance " } }, "source": [ "#### 10.2.4.1 Find the next quadrature point by minimizing the posterior variance \n", "* The variance $v$ of the posterior $F$ is indenpent of the function value $f(x_n)$. \n", "\n", "* The goal of the next step is to find $x_{n+1}$ which minimizes ${v}_n - v[\\{x_i\\}_{i=1}^n\\cup x]$.\n", "\n", "\n", "\n", "\n" ] }, { "cell_type": "code", "execution_count": 136, "metadata": { "nbpages": { "level": 4, "link": "[10.2.4.1 Find the next quadrature point by minimizing the posterior variance ](https://ndcbe.github.io/cbe67701-uncertainty-quantification/10.02-Bayesian-quadrature.html#10.2.4.1-Find-the-next-quadrature-point-by-minimizing-the-posterior-variance)", "section": "10.2.4.1 Find the next quadrature point by minimizing the posterior variance " } }, "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", "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 = {}\".format(x_new), 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()\n" ] }, { "cell_type": "code", "execution_count": 141, "metadata": { "nbpages": { "level": 4, "link": "[10.2.4.1 Find the next quadrature point by minimizing the posterior variance ](https://ndcbe.github.io/cbe67701-uncertainty-quantification/10.02-Bayesian-quadrature.html#10.2.4.1-Find-the-next-quadrature-point-by-minimizing-the-posterior-variance)", "section": "10.2.4.1 Find the next quadrature point by minimizing the posterior variance " } }, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "y_new = f(x_new)\n", "X = np.append(X_init, x_new, axis=0)\n", "Y = np.append(Y_init, y_new, axis=0)\n", "\n", "emukit_method.set_data(X, Y)\n", "\n", "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] + 1.96*np.sqrt(var_plot)[:, 0],\n", " mu_plot[:, 0] - 1.96*np.sqrt(var_plot)[:, 0], color=\"C0\", alpha=0.6, label = '95% conifdence interval')\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": 143, "metadata": { "nbpages": { "level": 4, "link": "[10.2.4.1 Find the next quadrature point by minimizing the posterior variance ](https://ndcbe.github.io/cbe67701-uncertainty-quantification/10.02-Bayesian-quadrature.html#10.2.4.1-Find-the-next-quadrature-point-by-minimizing-the-posterior-variance)", "section": "10.2.4.1 Find the next quadrature point by minimizing the posterior variance " } }, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "The initial estimated integral is: 0.35\n", "with a confidence interval: 3.36 .\n", "The second estimated integral is: 0.39\n", "with a confidence interval: 2.29 .\n", "The benchmark solution rounded with 2 digits is: 0.54 .\n" ] } ], "source": [ "integral_mean, integral_variance = emukit_method.integrate()\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(benchmark_solution[0], color=\"blue\", label=\"benchmark 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()\n", "print('The initial estimated integral is: ', round(initial_integral_mean, 2))\n", "print('with a confidence interval: ', round(2*np.sqrt(initial_integral_variance), 2),'.')\n", "print('The second estimated integral is: ', round(integral_mean, 2))\n", "print('with a confidence interval: ', round(2*np.sqrt(integral_variance), 2),'.')\n", "print('The benchmark solution rounded with 2 digits is: ', round(benchmark_solution[0], 2),'.')" ] }, { "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)

\"Open

\"Download\"" ] } ], "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 }