{ "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", "< [10.2 A simple example of Bayesian quadrature](https://ndcbe.github.io/cbe67701-uncertainty-quantification/10.02-Bayesian-quadrature.html) | [Contents](toc.html) | [11.0 Predictive Models Informed by Simulation, Measurement, and Surrogates](https://ndcbe.github.io/cbe67701-uncertainty-quantification/11.00-Predictive-Models-Informed-by-Simulation-Measurement-and-Surrogates.html)

\"Open

\"Download\"" ] }, { "cell_type": "markdown", "metadata": { "colab_type": "text", "id": "AUdBNLwRIufS", "nbpages": { "level": 1, "link": "[10.3 **Using scikit-learn for Gaussian Process Regression**](https://ndcbe.github.io/cbe67701-uncertainty-quantification/10.03-Gaussian-Process-Regression.html#10.3-**Using-scikit-learn-for-Gaussian-Process-Regression**)", "section": "10.3 **Using scikit-learn for Gaussian Process Regression**" } }, "source": [ "# 10.3 **Using scikit-learn for Gaussian Process Regression**\n", "\n", "Created by Nilay Kumar \n", "\n", "The following resources were used for preparing this notebook:\n", "1. https://www.youtube.com/channel/UCcAtD_VYwcYwVbTdvArsm7w\n", "2. Dr. Juan Camilo Orduz, An Introduction to Gaussian Process Regression, https://juanitorduz.github.io/gaussian_process_reg/\n", "3. Hilarie Sit, Quick Start to Gaussian Process Regression, https://towardsdatascience.com/quick-start-to-gaussian-process-regression-36d838810319\n", "\n", "\n" ] }, { "cell_type": "markdown", "metadata": { "colab_type": "text", "id": "DrDrC1MQJtmJ", "nbpages": { "level": 2, "link": "[10.3.1 **Objectives**](https://ndcbe.github.io/cbe67701-uncertainty-quantification/10.03-Gaussian-Process-Regression.html#10.3.1-**Objectives**)", "section": "10.3.1 **Objectives**" } }, "source": [ "## 10.3.1 **Objectives**\n", "\n", "1. A mathematical understanding of how gaussian process regression model is built. The set of equations also highlight how Bayesian Linear Regression is just a special case of Gaussian Process Regression.\n", "2. Using scikit lear to fit a GPR model to data points generated from the mathematical function $y = sin(4\\pi x) + sin(7\\pi x)$" ] }, { "cell_type": "markdown", "metadata": { "colab_type": "text", "id": "eJVkg2exj0uz", "nbpages": { "level": 2, "link": "[10.3.2 **Mathematical overview**](https://ndcbe.github.io/cbe67701-uncertainty-quantification/10.03-Gaussian-Process-Regression.html#10.3.2-**Mathematical-overview**)", "section": "10.3.2 **Mathematical overview**" } }, "source": [ "## 10.3.2 **Mathematical overview**" ] }, { "cell_type": "markdown", "metadata": { "colab_type": "text", "id": "ImWoTdLtj_sp", "nbpages": { "level": 2, "link": "[10.3.2 **Mathematical overview**](https://ndcbe.github.io/cbe67701-uncertainty-quantification/10.03-Gaussian-Process-Regression.html#10.3.2-**Mathematical-overview**)", "section": "10.3.2 **Mathematical overview**" } }, "source": [ "**1. Definition of Bayesian Linear Regression Models**\n", "\n", "Given a dataset $D$,\n", "\n", "$D = [(x_{1},y_{1}), (x_{2},y_{2}),.......,{x_{n},y_{n}}], x_{i} \\in R^{d}, y_{i} \\in R$ \n", "\n", "One can simply describe as bayesian linear regression model on the dataset as \n", "\n", "$Y_{i} = w^{T} x + \\epsilon _{i}$\n", "\n", "where, $w$ is a prior and can be approximated as $ w ~ N(0, \\nu I)$ and $\\epsilon$ is the noise defined using a gaussian with mean o and variance $\\sigma^2$" ] }, { "cell_type": "markdown", "metadata": { "colab_type": "text", "id": "DcBOtiXMnI2E", "nbpages": { "level": 2, "link": "[10.3.2 **Mathematical overview**](https://ndcbe.github.io/cbe67701-uncertainty-quantification/10.03-Gaussian-Process-Regression.html#10.3.2-**Mathematical-overview**)", "section": "10.3.2 **Mathematical overview**" } }, "source": [ "**2. $z = x^{T} w$ is a Gaussian Process!**\n", "\n", "$\n", " \\begin{pmatrix}\n", " z_{x_{1}} \\\\\n", " z_{x_{2}} \\\\\n", " \\vdots \\\\\n", " z_{x_{n}} \n", " \\end{pmatrix} = $ $\n", " \\begin{pmatrix}\n", " x_{1}^T w \\\\\n", " x_{2}^Tw \\\\\n", " \\vdots \\\\\n", " x_{n}^Tw \n", " \\end{pmatrix} = $$\n", " \\begin{pmatrix}\n", " \\cdots & x_{1}^T & \\cdots \\\\\n", " \\cdots & x_{2}^T & \\cdots \\\\\n", " \\vdots \\\\\n", " \\cdots & x_{n}^T & \\cdots \n", " \\end{pmatrix} w $ $= Aw$ \n", "\n", " A is the design matrix of a linear regression. Since w, the prior for \n", " the bayesian regression model is normally distributed. Hence, by $Affine$ $property$ of multivariate gaussian $Aw$ is also a Gausiisn.\n", "\n", " **Mean and Covariance of $z = x^{T} w$**\n", "\n", " $\\mu (z) = E(z_{z}) = E(x^{T} w)= x^{T} E(w) = 0$\n", "\n", " $K(z,z') = cov(z_{x},z_{x}') = E(z_{x}z_{x}') - E(z_{x})E(z_{x}') = x^{T}E(ww^{T})x'^{T} = \\nu x^{T}x'^{T}$ \n" ] }, { "cell_type": "markdown", "metadata": { "colab_type": "text", "id": "oUHrhL5CuhXI", "nbpages": { "level": 2, "link": "[10.3.2 **Mathematical overview**](https://ndcbe.github.io/cbe67701-uncertainty-quantification/10.03-Gaussian-Process-Regression.html#10.3.2-**Mathematical-overview**)", "section": "10.3.2 **Mathematical overview**" } }, "source": [ "**3. Estimationg conditional distribution for inference using a Gaussian Process Model**\n", "\n", "A gaussian process model can be defined as\n", "\n", "$Y_{i} = Z_{x_{i}} + \\epsilon _{i}$ , where\n", "\n", "$Z = N(\\mu, K)$, $\\epsilon = N(0, \\sigma ^2)$\n", "\n", "Hence, $Y = N(\\mu, K + \\sigma ^2 I)$\n", "\n", "Let $a = (1,\\cdots \\cdots, l)$ and $a = (l+1,\\cdots \\cdots, n)$ be the indices for the variables in training and test dataset\n", "\n", "$ Y = \n", " \\begin{pmatrix}\n", " Y_{a} \\\\\n", " Y_{b} \\\\ \n", " \\end{pmatrix} , $\n", " $ Y_{a} = \n", " \\begin{pmatrix}\n", " Y_{1} \\\\\n", " \\vdots \\\\\n", " Y_{l} \\\\ \n", " \\end{pmatrix} , $ \n", " $ Y_{b} = \n", " \\begin{pmatrix}\n", " Y_{l+1} \\\\\n", " \\vdots \\\\\n", " Y_{n} \\\\ \n", " \\end{pmatrix} $\n", "\n", "\n", " $ C = \n", " \\begin{pmatrix}\n", " C_{aa} && C_{ab} \\\\\n", " C_{ba} && C_{bb}\\\\ \n", " \\end{pmatrix} , $ \n", " $C_{ab} = K_{ab}$, $C_{aa} = K_{aa} + \\sigma ^2 I$\n", "\n", " Here K is the kernel function used to define the covariance matrix.With little efforts, it can be easily shown that the conditional distribution $P(Y_{a} | Y_{b} = y_{b})$ is normally distributed.\n", "\n", " $P(Y_{a} | Y_{b} = y_{b}) = N(n,D)$, where\n", "\n", " $m = \\mu _{a} + C_{ab}C_{bb}^{-1}(y_{b} - \\mu _{b})$\n", "\n", " $D = C_{aa} + C_{ab}C_{bb}^{-1}C_{ba} $\n", "\n" ] }, { "cell_type": "markdown", "metadata": { "colab_type": "text", "id": "APwnZg5szzK9", "nbpages": { "level": 2, "link": "[10.3.2 **Mathematical overview**](https://ndcbe.github.io/cbe67701-uncertainty-quantification/10.03-Gaussian-Process-Regression.html#10.3.2-**Mathematical-overview**)", "section": "10.3.2 **Mathematical overview**" } }, "source": [ "**4. Summary for Gausian Process Regression**\n", "\n", "$Input: (x_{1},\\cdots,x_{l},x_{l+1},\\cdots,x_{n})$\n", "\n", "$Response:(y_{1},\\cdots,y_{l},y_{l+1},\\cdots,y_{n})$\n", "\n", "$GP: \\hat{Z} = (Z_{x_{1}}, \\cdots, Z_{x_{n}})$\n", "\n", "**Model**\n", "\n", "$Y_{i} = Z_{x_{i}} + \\epsilon _{i}$ , where\n", "\n", "$Z_{x} = GP(\\mu, K)$, $\\epsilon = N(0, \\sigma ^2 I)$\n", "\n", "**Inference**\n", "\n", "$P(y_{a}|y_{b}) = N(y_{a}|m,D)$" ] }, { "cell_type": "markdown", "metadata": { "colab_type": "text", "id": "3or_IiDKXztW", "nbpages": { "level": 2, "link": "[10.3.3 **Import libraries**](https://ndcbe.github.io/cbe67701-uncertainty-quantification/10.03-Gaussian-Process-Regression.html#10.3.3-**Import-libraries**)", "section": "10.3.3 **Import libraries**" } }, "source": [ "## 10.3.3 **Import libraries**\n" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "colab": {}, "colab_type": "code", "id": "-TmqGOWgXuYG", "nbpages": { "level": 2, "link": "[10.3.3 **Import libraries**](https://ndcbe.github.io/cbe67701-uncertainty-quantification/10.03-Gaussian-Process-Regression.html#10.3.3-**Import-libraries**)", "section": "10.3.3 **Import libraries**" } }, "outputs": [], "source": [ "import pandas as pd\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "import seaborn as sns; sns.set()" ] }, { "cell_type": "markdown", "metadata": { "colab_type": "text", "id": "FHN4aDwFOJuc", "nbpages": { "level": 2, "link": "[10.3.4 **Generate training data**](https://ndcbe.github.io/cbe67701-uncertainty-quantification/10.03-Gaussian-Process-Regression.html#10.3.4-**Generate-training-data**)", "section": "10.3.4 **Generate training data**" } }, "source": [ "## 10.3.4 **Generate training data**\n", "$y = sin(4\\pi x) + sin(7\\pi x)$" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "colab": {}, "colab_type": "code", "id": "z1SDXgLXQgsC", "nbpages": { "level": 2, "link": "[10.3.4 **Generate training data**](https://ndcbe.github.io/cbe67701-uncertainty-quantification/10.03-Gaussian-Process-Regression.html#10.3.4-**Generate-training-data**)", "section": "10.3.4 **Generate training data**" } }, "outputs": [], "source": [ "\"\"\"\n", "This section of code generates training data for fitting the Gaussian Process Regression model\n", "\n", "Variables declared:\n", "x_end: The length till which x's need to be sampled\n", "num_train: It denotes the number of training points that needs to be extracted within the define interval\n", "sigma_noise: It is the standard deviation of the normal distribution from which random numbers are sampled\n", "\n", "\"\"\"\n", "\n", "# sampling points along x\n", "x_end = 2\n", "num_train = 200\n", "x = np.linspace(start=0, stop=x_end, num=num_train)\n", "\n", "# Defining function f(x) = sin(4*pi*x) + sin(7*pi*x)\n", "def f(x):\n", " f = np.sin((4*np.pi)*x) + np.sin((7*np.pi)*x)\n", " return(f)\n", "\n", "# Stroring the functional evaluations at x sampled\n", "f_x = f(x)\n", "\n", "# Adding noise to the functional evaluations\n", "sigma_noise = 0.4\n", "error_train = np.random.normal(loc=0, scale=sigma_noise, size=num_train)\n", "y_train = f_x + error_train\n" ] }, { "cell_type": "markdown", "metadata": { "colab_type": "text", "id": "mxGDPxyrWC8r", "nbpages": { "level": 2, "link": "[10.3.5 **Visualizing the training data**](https://ndcbe.github.io/cbe67701-uncertainty-quantification/10.03-Gaussian-Process-Regression.html#10.3.5-**Visualizing-the-training-data**)", "section": "10.3.5 **Visualizing the training data**" } }, "source": [ "## 10.3.5 **Visualizing the training data**" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 318 }, "colab_type": "code", "id": "Aw5QEtaGYCEe", "nbpages": { "level": 2, "link": "[10.3.5 **Visualizing the training data**](https://ndcbe.github.io/cbe67701-uncertainty-quantification/10.03-Gaussian-Process-Regression.html#10.3.5-**Visualizing-the-training-data**)", "section": "10.3.5 **Visualizing the training data**" }, "outputId": "fa6cf11a-4501-491e-a089-980ed322529c" }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "

" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots()\n", "# Plot data points with added noise\n", "sns.scatterplot(x=x, y=y_train, label='training data', ax=ax);\n", "# Plot function.\n", "sns.lineplot(x=x, y=f_x, color='red', label='f(x)', ax=ax);\n", "ax.set(title='Training data for GPR model')\n", "ax.legend(loc='upper right');\n", "ax.set(xlabel='x', ylabel='y')\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": { "colab_type": "text", "id": "sgOP59m5YRJE", "nbpages": { "level": 2, "link": "[10.3.6 **Define test data**](https://ndcbe.github.io/cbe67701-uncertainty-quantification/10.03-Gaussian-Process-Regression.html#10.3.6-**Define-test-data**)", "section": "10.3.6 **Define test data**" } }, "source": [ "## 10.3.6 **Define test data**" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "colab": {}, "colab_type": "code", "id": "0Md3DvGFXKbE", "nbpages": { "level": 2, "link": "[10.3.6 **Define test data**](https://ndcbe.github.io/cbe67701-uncertainty-quantification/10.03-Gaussian-Process-Regression.html#10.3.6-**Define-test-data**)", "section": "10.3.6 **Define test data**" } }, "outputs": [], "source": [ "num_test = num_train + 300\n", "x_test = np.linspace(start=0, stop=(x_end + 1), num=num_test)" ] }, { "cell_type": "markdown", "metadata": { "colab_type": "text", "id": "NssFP2g1Xx3s", "nbpages": { "level": 2, "link": "[10.3.7 **scikit-learn example**](https://ndcbe.github.io/cbe67701-uncertainty-quantification/10.03-Gaussian-Process-Regression.html#10.3.7-**scikit-learn-example**)", "section": "10.3.7 **scikit-learn example**" } }, "source": [ "## 10.3.7 **scikit-learn example**" ] }, { "cell_type": "markdown", "metadata": { "colab_type": "text", "id": "7sze29ROX9bO", "nbpages": { "level": 3, "link": "[10.3.7.1 Step 1: Loading libraries for defining kernel and gaussian process regression model](https://ndcbe.github.io/cbe67701-uncertainty-quantification/10.03-Gaussian-Process-Regression.html#10.3.7.1-Step-1:-Loading-libraries-for-defining-kernel-and-gaussian-process-regression-model)", "section": "10.3.7.1 Step 1: Loading libraries for defining kernel and gaussian process regression model" } }, "source": [ "### 10.3.7.1 Step 1: Loading libraries for defining kernel and gaussian process regression model" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "colab": {}, "colab_type": "code", "id": "UqHJjSxDYW57", "nbpages": { "level": 3, "link": "[10.3.7.1 Step 1: Loading libraries for defining kernel and gaussian process regression model](https://ndcbe.github.io/cbe67701-uncertainty-quantification/10.03-Gaussian-Process-Regression.html#10.3.7.1-Step-1:-Loading-libraries-for-defining-kernel-and-gaussian-process-regression-model)", "section": "10.3.7.1 Step 1: Loading libraries for defining kernel and gaussian process regression model" } }, "outputs": [], "source": [ "from sklearn.gaussian_process import GaussianProcessRegressor\n", "from sklearn.gaussian_process.kernels import ConstantKernel, RBF\n" ] }, { "cell_type": "markdown", "metadata": { "colab_type": "text", "id": "aUV-ECSvYNzC", "nbpages": { "level": 3, "link": "[10.3.7.2 Step 2: Reshaping the data according to the dimensionality of the problem](https://ndcbe.github.io/cbe67701-uncertainty-quantification/10.03-Gaussian-Process-Regression.html#10.3.7.2-Step-2:-Reshaping-the-data-according-to-the-dimensionality-of-the-problem)", "section": "10.3.7.2 Step 2: Reshaping the data according to the dimensionality of the problem" } }, "source": [ "### 10.3.7.2 Step 2: Reshaping the data according to the dimensionality of the problem\n", "\n" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "colab": {}, "colab_type": "code", "id": "Idu3ExLPYmAX", "nbpages": { "level": 3, "link": "[10.3.7.2 Step 2: Reshaping the data according to the dimensionality of the problem](https://ndcbe.github.io/cbe67701-uncertainty-quantification/10.03-Gaussian-Process-Regression.html#10.3.7.2-Step-2:-Reshaping-the-data-according-to-the-dimensionality-of-the-problem)", "section": "10.3.7.2 Step 2: Reshaping the data according to the dimensionality of the problem" } }, "outputs": [], "source": [ "\"\"\"\n", "This section of the code rfeshapes the training data so as to be used by scikit-learns's\n", "Gaussion Process Regressor object\n", "\n", "Variables:\n", "d: dimensionality of the problem (1 in this case)\n", "\"\"\"\n", "d = 1; \n", "# Reshaping training dataset\n", "X_train = x.reshape(num_train, d)\n", "# Reshaping test dataset\n", "X_test = x_test.reshape(num_test,d)" ] }, { "cell_type": "markdown", "metadata": { "colab_type": "text", "id": "XN3z_mPCaOar", "nbpages": { "level": 3, "link": "[10.3.7.3 Step 3: Defining the kernel and GPR model](https://ndcbe.github.io/cbe67701-uncertainty-quantification/10.03-Gaussian-Process-Regression.html#10.3.7.3-Step-3:-Defining-the-kernel-and-GPR-model)", "section": "10.3.7.3 Step 3: Defining the kernel and GPR model" } }, "source": [ "### 10.3.7.3 Step 3: Defining the kernel and GPR model" ] }, { "cell_type": "markdown", "metadata": { "colab_type": "text", "id": "nIyW4CN14Ctl", "nbpages": { "level": 3, "link": "[10.3.7.3 Step 3: Defining the kernel and GPR model](https://ndcbe.github.io/cbe67701-uncertainty-quantification/10.03-Gaussian-Process-Regression.html#10.3.7.3-Step-3:-Defining-the-kernel-and-GPR-model)", "section": "10.3.7.3 Step 3: Defining the kernel and GPR model" } }, "source": [ "For this example problem we choose a squared exponential kernel function defined by\n", "\n", "$K(x_{p},x_{q}) = \\sigma _{f}exp(-\\frac{1}{2l^{2}} ||x_{p} - x_{q} ||^2)$\n", "\n", "where $\\sigma _{f}$ and $l$ are the hyperparameters of the kernel function." ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "colab": {}, "colab_type": "code", "id": "CovnVKTSaTWh", "nbpages": { "level": 3, "link": "[10.3.7.3 Step 3: Defining the kernel and GPR model](https://ndcbe.github.io/cbe67701-uncertainty-quantification/10.03-Gaussian-Process-Regression.html#10.3.7.3-Step-3:-Defining-the-kernel-and-GPR-model)", "section": "10.3.7.3 Step 3: Defining the kernel and GPR model" } }, "outputs": [], "source": [ "\"\"\"\n", "The part of code is used to describe the type of kernel used and the gaussian process regression model\n", "\n", "1. Definition of kernel:\n", "\n", "kernel = ConstantKernel(constant_value=sigma_f, constant_value_bounds=(1e-2, 1e2)) \\\n", " * RBF(length_scale=l, length_scale_bounds=(1e-2, 1e2))\n", "\n", "a. RBF kenel has been used for this problem.\n", "b. Hyperparameter definitions:\n", " (i) sigma_f: defines the amplitude of the kernel function\n", " (ii) l: the locality parameter; used to define how far each point is able to interacts\n", "c. The hyperparameter are best chosen so as to minimise the marginal log likelihood\n", "\n", "2. Definition of gp model\n", "\n", "gp = GaussianProcessRegressor(kernel=kernel, alpha=sigma_n**2, n_restarts_optimizer=10, )\n", "\n", "a. Parameter definitions\n", " (i) sigma_n: It is the value added to the diagonal elements of defined kernel matrix. Larger values mean a \n", " larger value of noise in the data\n", " (ii) The number of restarts of the optimizer for finding the kernel’s parameters which maximize the \n", " log-marginal likelihood\n", "\n", "3. Output of the code is the gp model and the predictions on the test data\n", "\n", "\"\"\"\n", "\n", "# Initial values of l, sigma_f and sigma_n needs to be defined.\n", "# Other inputs are the training and test datasets that need to be input\n", "\n", "def gpPrediction( l, sigma_f, sigma_n , X_train, y_train, X_test):\n", " # Kernel definition \n", " kernel = ConstantKernel(constant_value=sigma_f, constant_value_bounds=(1e-2, 1e2)) \\\n", " * RBF(length_scale=l, length_scale_bounds=(1e-2, 1e2))\n", " # GP model \n", " gp = GaussianProcessRegressor(kernel=kernel, alpha=sigma_n**2, n_restarts_optimizer=10, )\n", " # Fitting in the gp model\n", " gp.fit(X_train, y_train)\n", " # Make the prediction on test set.\n", " y_pred = gp.predict(X_test)\n", " return y_pred, gp;" ] }, { "cell_type": "markdown", "metadata": { "colab_type": "text", "id": "yl6Sd5TKeWTK", "nbpages": { "level": 3, "link": "[10.3.7.4 Step 4: Calling in the defined GP model for making predictions on the test dataset](https://ndcbe.github.io/cbe67701-uncertainty-quantification/10.03-Gaussian-Process-Regression.html#10.3.7.4-Step-4:-Calling-in-the-defined-GP-model-for-making-predictions-on-the-test-dataset)", "section": "10.3.7.4 Step 4: Calling in the defined GP model for making predictions on the test dataset" } }, "source": [ "### 10.3.7.4 Step 4: Calling in the defined GP model for making predictions on the test dataset" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "colab": {}, "colab_type": "code", "id": "myA4p2l9eoUq", "nbpages": { "level": 3, "link": "[10.3.7.4 Step 4: Calling in the defined GP model for making predictions on the test dataset](https://ndcbe.github.io/cbe67701-uncertainty-quantification/10.03-Gaussian-Process-Regression.html#10.3.7.4-Step-4:-Calling-in-the-defined-GP-model-for-making-predictions-on-the-test-dataset)", "section": "10.3.7.4 Step 4: Calling in the defined GP model for making predictions on the test dataset" } }, "outputs": [], "source": [ "\"\"\"\n", "l_init and sigma_f init are the initial values of the hyperparameters l and sigma_f of the kernel function\n", "\n", "\"\"\"\n", "\n", "l_init = 1\n", "sigma_f_init = 3\n", "sigma_n = 1\n", "\n", "y_pred, gp = gpPrediction( l_init, sigma_f_init, sigma_n , X_train, y_train, X_test)" ] }, { "cell_type": "markdown", "metadata": { "colab_type": "text", "id": "5MBqWUw7gDsD", "nbpages": { "level": 3, "link": "[10.3.7.5 Step 5: Estimating credible intervals](https://ndcbe.github.io/cbe67701-uncertainty-quantification/10.03-Gaussian-Process-Regression.html#10.3.7.5-Step-5:-Estimating-credible-intervals)", "section": "10.3.7.5 Step 5: Estimating credible intervals" } }, "source": [ "### 10.3.7.5 Step 5: Estimating credible intervals" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "colab": {}, "colab_type": "code", "id": "1nV9FOqBgJRd", "nbpages": { "level": 3, "link": "[10.3.7.5 Step 5: Estimating credible intervals](https://ndcbe.github.io/cbe67701-uncertainty-quantification/10.03-Gaussian-Process-Regression.html#10.3.7.5-Step-5:-Estimating-credible-intervals)", "section": "10.3.7.5 Step 5: Estimating credible intervals" } }, "outputs": [], "source": [ "# Generate samples from posterior distribution. \n", "y_hat_samples = gp.sample_y(X_test, n_samples=num_test)\n", "# Compute the mean of the sample. \n", "y_hat = np.apply_over_axes(func=np.mean, a=y_hat_samples, axes=1).squeeze()\n", "# Compute the standard deviation of the sample. \n", "y_hat_sd = np.apply_over_axes(func=np.std, a=y_hat_samples, axes=1).squeeze()" ] }, { "cell_type": "markdown", "metadata": { "colab_type": "text", "id": "icTAVluGgzOi", "nbpages": { "level": 3, "link": "[10.3.7.6 Step 6: Visualizating results](https://ndcbe.github.io/cbe67701-uncertainty-quantification/10.03-Gaussian-Process-Regression.html#10.3.7.6-Step-6:-Visualizating-results)", "section": "10.3.7.6 Step 6: Visualizating results" } }, "source": [ "### 10.3.7.6 Step 6: Visualizating results" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 535 }, "colab_type": "code", "id": "HhbbWMTMg3-w", "nbpages": { "level": 3, "link": "[10.3.7.6 Step 6: Visualizating results](https://ndcbe.github.io/cbe67701-uncertainty-quantification/10.03-Gaussian-Process-Regression.html#10.3.7.6-Step-6:-Visualizating-results)", "section": "10.3.7.6 Step 6: Visualizating results" }, "outputId": "954d93e8-17e0-4fbc-8661-993076a31f0f" }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "\"\"\"\n", "This portion of the code is used to visualize the preductions made by gp model on the test datase. \n", "Cridible intervals for the predictions has also been plotted and indicated through the tranparent green corridor\n", "\"\"\"\n", "\n", "fig, ax = plt.subplots(figsize=(15, 8))\n", "# Plotting the training data.\n", "sns.scatterplot(x=x, y=y_train, label='training data', ax=ax);\n", "# Plot the functional evaluation\n", "sns.lineplot(x=x_test, y=f(x_test), color='red', label='f(x)', ax=ax)\n", "# Plot corridor. \n", "ax.fill_between(x=x_test, y1=(y_hat - 2*y_hat_sd), y2=(y_hat + 2*y_hat_sd), color='green',alpha=0.3, label='Credible Interval')\n", "# Plot prediction. \n", "sns.lineplot(x=x_test, y=y_pred, color='green', label='pred')\n", "\n", "# Labeling axes\n", "ax.set(title='Gaussian Process Regression')\n", "ax.legend(loc='lower left');\n", "ax.set(xlabel='x', ylabel='')\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "nbpages": { "level": 3, "link": "[10.3.7.6 Step 6: Visualizating results](https://ndcbe.github.io/cbe67701-uncertainty-quantification/10.03-Gaussian-Process-Regression.html#10.3.7.6-Step-6:-Visualizating-results)", "section": "10.3.7.6 Step 6: Visualizating results" } }, "outputs": [], "source": [] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "< [10.2 A simple example of Bayesian quadrature](https://ndcbe.github.io/cbe67701-uncertainty-quantification/10.02-Bayesian-quadrature.html) | [Contents](toc.html) | [11.0 Predictive Models Informed by Simulation, Measurement, and Surrogates](https://ndcbe.github.io/cbe67701-uncertainty-quantification/11.00-Predictive-Models-Informed-by-Simulation-Measurement-and-Surrogates.html)

\"Open

\"Download\"" ] } ], "metadata": { "colab": { "collapsed_sections": [], "name": "10.03-Gaussian_Process_Regression.ipynb", "provenance": [], "toc_visible": true }, "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": "3.7.3" } }, "nbformat": 4, "nbformat_minor": 1 }