{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Gaussian processes\n", "\n", "## Introduction\n", "\n", "In supervised learning, we often use parametric models $p(\\mathbf{y} \\lvert \\mathbf{X},\\boldsymbol\\theta)$ to explain data and infer optimal values of parameter $\\boldsymbol\\theta$ via [maximum likelihood](https://en.wikipedia.org/wiki/Maximum_likelihood_estimation) or [maximum a posteriori](https://de.wikipedia.org/wiki/Maximum_a_posteriori) estimation. If needed we can also infer a full [posterior distribution](https://en.wikipedia.org/wiki/Posterior_probability) $p(\\boldsymbol\\theta \\lvert \\mathbf{X},\\mathbf{y})$ instead of a point estimate $\\boldsymbol{\\hat\\theta}$. With increasing data complexity, models with a higher number of parameters are usually needed to explain data reasonably well. Methods that use models with a fixed number of parameters are called parametric methods. \n", "\n", "In non-parametric methods, on the other hand, the number of parameters depend on the dataset size. For example, in [Nadaraya-Watson kernel regression](https://en.wikipedia.org/wiki/Kernel_regression), a weight $w_i$ is assigned to each observed target $y_i$ and for predicting the target value at a new point $\\mathbf{x}$ a weighted average is computed: \n", "\n", "$$f(\\mathbf{x}) = \\sum_{i=1}^{N}w_i(\\mathbf{x})y_i$$\n", "\n", "$$w_i(\\mathbf{x}) = \\frac{\\kappa(\\mathbf{x}, \\mathbf{x}_{i})}{\\sum_{i'=1}^{N}\\kappa(\\mathbf{x}, \\mathbf{x}_{i'})}$$\n", "\n", "Observations that are closer to $\\mathbf{x}$ have a higher weight than observations that are further away. Weights are computed from $\\mathbf{x}$ and observed $\\mathbf{x}_i$ with a kernel $\\kappa$. A special case is k-nearest neighbors (KNN) where the $k$ closest observations have a weight $1/k$, and all others have weight $0$. Non-parametric methods often need to process all training data for prediction and are therefore slower at inference time than parametric methods. On the other hand, training is usually faster as non-parametric models only need to remember training data. \n", "\n", "Another example of non-parametric methods are [Gaussian processes](https://en.wikipedia.org/wiki/Gaussian_process) (GPs). Instead of inferring a distribution over the parameters of a parametric function Gaussian processes can be used to infer a distribution over functions directly. A Gaussian process defines a prior over functions. After having observed some function values it can be converted into a posterior over functions. Inference of continuous function values in this context is known as GP regression but GPs can also be used for classification. \n", "\n", "A Gaussian process is a [random process](https://en.wikipedia.org/wiki/Stochastic_process) where any point $\\mathbf{x} \\in \\mathbb{R}^d$ is assigned a random variable $f(\\mathbf{x})$ and where the joint distribution of a finite number of these variables $p(f(\\mathbf{x}_1),...,f(\\mathbf{x}_N))$ is itself Gaussian:\n", "\n", "$$p(\\mathbf{f} \\lvert \\mathbf{X}) = \\mathcal{N}(\\mathbf{f} \\lvert \\boldsymbol\\mu, \\mathbf{K})\\tag{1}\\label{eq1}$$\n", "\n", "In Equation $(1)$, $\\mathbf{f} = (f(\\mathbf{x}_1),...,f(\\mathbf{x}_N))$, $\\boldsymbol\\mu = (m(\\mathbf{x}_1),...,m(\\mathbf{x}_N))$ and $K_{ij} = \\kappa(\\mathbf{x}_i,\\mathbf{x}_j)$. $m$ is the mean function and it is common to use $m(\\mathbf{x}) = 0$ as GPs are flexible enough to model the mean arbitrarily well. $\\kappa$ is a positive definite *kernel function* or *covariance function*. Thus, a Gaussian process is a distribution over functions whose shape (smoothness, ...) is defined by $\\mathbf{K}$. If points $\\mathbf{x}_i$ and $\\mathbf{x}_j$ are considered to be similar by the kernel the function values at these points, $f(\\mathbf{x}_i)$ and $f(\\mathbf{x}_j)$, can be expected to be similar too. \n", "\n", "A GP prior $p(\\mathbf{f} \\lvert \\mathbf{X})$ can be converted into a GP posterior $p(\\mathbf{f} \\lvert \\mathbf{X},\\mathbf{y})$ after having observed some data $\\mathbf{y}$. The posterior can then be used to make predictions $\\mathbf{f}_*$ given new input $\\mathbf{X}_*$:\n", "\n", "\n", "\\begin{align*}\n", "p(\\mathbf{f}_* \\lvert \\mathbf{X}_*,\\mathbf{X},\\mathbf{y}) \n", "&= \\int{p(\\mathbf{f}_* \\lvert \\mathbf{X}_*,\\mathbf{f})p(\\mathbf{f} \\lvert \\mathbf{X},\\mathbf{y})}\\ d\\mathbf{f} \\\\ \n", "&= \\mathcal{N}(\\mathbf{f}_* \\lvert \\boldsymbol{\\mu}_*, \\boldsymbol{\\Sigma}_*)\\tag{2}\\label{eq2}\n", "\\end{align*}\n", "\n", "\n", "Equation $(2)$ is the posterior predictive distribution which is also a Gaussian with mean $\\boldsymbol{\\mu}_*$ and $\\boldsymbol{\\Sigma}_*$. By definition of the GP, the joint distribution of observed data $\\mathbf{y}$ and predictions $\\mathbf{f}_*$ is\n", "\n", "$$\n", "\\begin{pmatrix}\\mathbf{y} \\\\ \\mathbf{f}_*\\end{pmatrix} \\sim \\mathcal{N}\n", "\\left(\\boldsymbol{0},\n", "\\begin{pmatrix}\\mathbf{K}_y & \\mathbf{K}_* \\\\ \\mathbf{K}_*^T & \\mathbf{K}_{**}\\end{pmatrix}\n", "\\right)\\tag{3}\\label{eq3}\n", "$$\n", "\n", "With $N$ training data and $N_*$ new input data, $\\mathbf{K}_y = \\kappa(\\mathbf{X},\\mathbf{X}) + \\sigma_y^2\\mathbf{I} = \\mathbf{K} + \\sigma_y^2\\mathbf{I}$ is $N \\times N$, $\\mathbf{K}_* = \\kappa(\\mathbf{X},\\mathbf{X}_*)$ is $N \\times N_*$ and $\\mathbf{K}_{**} = \\kappa(\\mathbf{X}_*,\\mathbf{X}_*)$ is $N_* \\times N_*$. $\\sigma_y^2$ is the noise term in the diagonal of $\\mathbf{K_y}$. It is set to zero if training targets are noise-free and to a value greater than zero if observations are noisy. The mean is set to $\\boldsymbol{0}$ for notational simplicity. The sufficient statistics of the posterior predictive distribution, $\\boldsymbol{\\mu}_*$ and $\\boldsymbol{\\Sigma}_*$, can be computed with[1][3]\n", "\n", "\n", "\\begin{align*}\n", "\\boldsymbol{\\mu_*} &= \\mathbf{K}_*^T \\mathbf{K}_y^{-1} \\mathbf{y}\\tag{4}\\label{eq4} \\\\\n", "\\boldsymbol{\\Sigma_*} &= \\mathbf{K}_{**} - \\mathbf{K}_*^T \\mathbf{K}_y^{-1} \\mathbf{K}_*\\tag{5}\\label{eq5}\n", "\\end{align*}\n", "\n", "\n", "This is the minimum we need to know for implementing Gaussian processes and applying them to regression problems. For further details, please consult the literature in the [References](#References) section. The next section shows how to implement GPs with plain NumPy from scratch, later sections demonstrate how to use GP implementations from [scikit-learn](http://scikit-learn.org/stable/) and [GPy](http://sheffieldml.github.io/GPy/)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Implementation with NumPy" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here, we will use the squared exponential kernel, also known as Gaussian kernel or RBF kernel:\n", "\n", "$$\n", "\\kappa(\\mathbf{x}_i,\\mathbf{x}_j) = \\sigma_f^2 \\exp(-\\frac{1}{2l^2}\n", " (\\mathbf{x}_i - \\mathbf{x}_j)^T\n", " (\\mathbf{x}_i - \\mathbf{x}_j))\\tag{6}\n", "$$\n", "\n", "The length parameter $l$ controls the smoothness of the function and $\\sigma_f$ the vertical variation. For simplicity, we use the same length parameter $l$ for all input dimensions (isotropic kernel). " ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "\n", "def kernel(X1, X2, l=1.0, sigma_f=1.0):\n", " '''\n", " Isotropic squared exponential kernel. Computes \n", " a covariance matrix from points in X1 and X2.\n", " \n", " Args:\n", " X1: Array of m points (m x d).\n", " X2: Array of n points (n x d).\n", "\n", " Returns:\n", " Covariance matrix (m x n).\n", " '''\n", " sqdist = np.sum(X1**2, 1).reshape(-1, 1) + np.sum(X2**2, 1) - 2 * np.dot(X1, X2.T)\n", " return sigma_f**2 * np.exp(-0.5 / l**2 * sqdist)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "There are many other kernels that can be used for Gaussian processes. See \$3\$ for a detailed reference or the scikit-learn documentation for [some examples](http://scikit-learn.org/stable/modules/gaussian_process.html#gp-kernels)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Prior\n", "\n", "Let's first define a prior over functions with mean zero and a covariance matrix computed with kernel parameters $l=1$ and $\\sigma_f=1$. To draw random functions from that GP we draw random samples from the corresponding multivariate normal. The following example draws three random samples and plots it together with the zero mean and the 95% confidence interval (computed from the diagonal of the covariance matrix)." ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "%matplotlib inline\n", "\n", "from gaussian_processes_util import plot_gp\n", "\n", "# Finite number of points\n", "X = np.arange(-5, 5, 0.2).reshape(-1, 1)\n", "\n", "# Mean and covariance of the prior\n", "mu = np.zeros(X.shape)\n", "cov = kernel(X, X)\n", "\n", "# Draw three samples from the prior\n", "samples = np.random.multivariate_normal(mu.ravel(), cov, 3)\n", "\n", "# Plot GP mean, confidence interval and samples \n", "plot_gp(mu, cov, X, samples=samples)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The plot_gp function is defined [here](gaussian_processes_util.py).\n", "\n", "### Prediction from noise-free training data\n", "\n", "To compute the sufficient statistics i.e. mean and covariance of the posterior predictive distribution we implement Equations $(4)$ and $(5)$" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "from numpy.linalg import inv\n", "\n", "def posterior_predictive(X_s, X_train, Y_train, l=1.0, sigma_f=1.0, sigma_y=1e-8):\n", " '''\n", " Computes the suffifient statistics of the GP posterior predictive distribution \n", " from m training data X_train and Y_train and n new inputs X_s.\n", " \n", " Args:\n", " X_s: New input locations (n x d).\n", " X_train: Training locations (m x d).\n", " Y_train: Training targets (m x 1).\n", " l: Kernel length parameter.\n", " sigma_f: Kernel vertical variation parameter.\n", " sigma_y: Noise parameter.\n", " \n", " Returns:\n", " Posterior mean vector (n x d) and covariance matrix (n x n).\n", " '''\n", " K = kernel(X_train, X_train, l, sigma_f) + sigma_y**2 * np.eye(len(X_train))\n", " K_s = kernel(X_train, X_s, l, sigma_f)\n", " K_ss = kernel(X_s, X_s, l, sigma_f) + 1e-8 * np.eye(len(X_s))\n", " K_inv = inv(K)\n", " \n", " # Equation (4)\n", " mu_s = K_s.T.dot(K_inv).dot(Y_train)\n", "\n", " # Equation (5)\n", " cov_s = K_ss - K_s.T.dot(K_inv).dot(K_s)\n", " \n", " return mu_s, cov_s" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "and apply them to noise-free training data X_train and Y_train. The following example draws three samples from the posterior predictive and plots them along with the mean, confidence interval and training data. In a noise-free model, variance at the training points is zero and all random functions drawn from the posterior go through the trainig points. " ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Noise free training data\n", "X_train = np.array([-4, -3, -2, -1, 1]).reshape(-1, 1)\n", "Y_train = np.sin(X_train)\n", "\n", "# Compute mean and covariance of the posterior predictive distribution\n", "mu_s, cov_s = posterior_predictive(X, X_train, Y_train)\n", "\n", "samples = np.random.multivariate_normal(mu_s.ravel(), cov_s, 3)\n", "plot_gp(mu_s, cov_s, X, X_train=X_train, Y_train=Y_train, samples=samples)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Prediction from noisy training data\n", "\n", "If some noise is included in the model, training points are only approximated and the variance at the training points is non-zero." ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "noise = 0.4\n", "\n", "# Noisy training data\n", "X_train = np.arange(-3, 4, 1).reshape(-1, 1)\n", "Y_train = np.sin(X_train) + noise * np.random.randn(*X_train.shape)\n", "\n", "# Compute mean and covariance of the posterior predictive distribution\n", "mu_s, cov_s = posterior_predictive(X, X_train, Y_train, sigma_y=noise)\n", "\n", "samples = np.random.multivariate_normal(mu_s.ravel(), cov_s, 3)\n", "plot_gp(mu_s, cov_s, X, X_train=X_train, Y_train=Y_train, samples=samples)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Effect of kernel parameters and noise parameter\n", "\n", "The following example shows the effect of kernel parameters $l$ and $\\sigma_f$ as well as the noise parameter $\\sigma_y$. Higher $l$ values lead to smoother functions and therefore to coarser approximations of the training data. Lower $l$ values make functions more wiggly with wide confidence intervals between training data points. $\\sigma_f$ controls the vertical variation of functions drawn from the GP. This can be seen by the wide confidence intervals outside the training data region in the right figure of the second row. $\\sigma_y$ represents the amount of noise in the training data. Higher $\\sigma_y$ values make more coarse approximations which avoids overfitting to noisy data." ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import matplotlib.pyplot as plt\n", "\n", "params = [\n", " (0.3, 1.0, 0.2),\n", " (3.0, 1.0, 0.2),\n", " (1.0, 0.3, 0.2),\n", " (1.0, 3.0, 0.2),\n", " (1.0, 1.0, 0.05),\n", " (1.0, 1.0, 1.5),\n", "]\n", "\n", "plt.figure(figsize=(12, 5))\n", "\n", "for i, (l, sigma_f, sigma_y) in enumerate(params):\n", " mu_s, cov_s = posterior_predictive(X, X_train, Y_train, l=l, \n", " sigma_f=sigma_f, \n", " sigma_y=sigma_y)\n", " plt.subplot(3, 2, i + 1)\n", " plt.subplots_adjust(top=2)\n", " plt.title(f'l = {l}, sigma_f = {sigma_f}, sigma_y = {sigma_y}')\n", " plot_gp(mu_s, cov_s, X, X_train=X_train, Y_train=Y_train)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Optimal values for these parameters can be estimated by maximizing the marginal log-likelihood which is given by[1][3]\n", "\n", "$$\n", "\\log p(\\mathbf{y} \\lvert \\mathbf{X}) = \n", "\\log \\mathcal{N}(\\mathbf{y} \\lvert \\boldsymbol{0},\\mathbf{K}_y) =\n", "-\\frac{1}{2} \\mathbf{y}^T \\mathbf{K}_y^{-1} \\mathbf{y} \n", "-\\frac{1}{2} \\log \\begin{vmatrix}\\mathbf{K}_y\\end{vmatrix} \n", "-\\frac{N}{2} \\log(2\\pi) \\tag{7}\n", "$$\n", "\n", "In the following we will minimize the negative marginal log-likelihood w.r.t. parameters $l$ and $\\sigma_f$, $\\sigma_y$ is set to the known noise level of the data. If the noise level is unknown, $\\sigma_y$ can be estimated as well along with the other parameters. " ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from numpy.linalg import cholesky\n", "from scipy.optimize import minimize\n", "\n", "def nll_fn(X_train, Y_train, noise):\n", " '''\n", " Returns a function that computes the negative log-likelihood\n", " for training data X_train and Y_train and given noise level.\n", " \n", " Args:\n", " X_train: training locations (m x d).\n", " Y_train: training targets (m x 1).\n", " noise: known noise level of Y_train.\n", " \n", " Returns:\n", " Minimization objective.\n", " '''\n", " def step(theta):\n", " K = kernel(X_train, X_train, l=theta[0], sigma_f=theta[1]) + \\\n", " noise**2 * np.eye(len(X_train))\n", " # Compute determinant via Cholesky decomposition\n", " return np.sum(np.log(np.diagonal(cholesky(K)))) + \\\n", " 0.5 * Y_train.T.dot(inv(K).dot(Y_train)) + \\\n", " 0.5 * len(X_train) * np.log(2*np.pi)\n", " return step\n", "\n", "# Minimize the negative log-likelihood w.r.t. parameters l and sigma_f.\n", "# We should actually run the minimization several times with different\n", "# initializations to avoid local minima but this is skipped here for\n", "# simplicity.\n", "res = minimize(nll_fn(X_train, Y_train, noise), [1, 1], \n", " bounds=((1e-5, None), (1e-5, None)),\n", " method='L-BFGS-B')\n", "\n", "# Store the optimization results in global variables so that we can\n", "# compare it later with the results from other implementations.\n", "l_opt, sigma_f_opt = res.x\n", "l_opt, sigma_f_opt\n", "\n", "# Compute the prosterior predictive statistics with optimized kernel parameters and plot the results\n", "mu_s, cov_s = posterior_predictive(X, X_train, Y_train, l=l_opt, sigma_f=sigma_f_opt, sigma_y=noise)\n", "plot_gp(mu_s, cov_s, X, X_train=X_train, Y_train=Y_train)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "With optimized kernel parameters, training data are reasonably covered by the 95% confidence interval and the mean of the posterior predictive is a good approximation.\n", "\n", "### Higher dimensions\n", "\n", "The above implementation can also be used for higher input data dimensions. Here, a GP is used to fit noisy samples from a sine wave originating at $\\boldsymbol{0}$ and expanding in the x-y plane. The following plots show the noisy samples and the posterior predictive mean before and after kernel parameter optimization." ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from gaussian_processes_util import plot_gp_2D\n", "\n", "noise_2D = 0.1\n", "\n", "rx, ry = np.arange(-5, 5, 0.3), np.arange(-5, 5, 0.3)\n", "gx, gy = np.meshgrid(rx, rx)\n", "\n", "X_2D = np.c_[gx.ravel(), gy.ravel()]\n", "\n", "X_2D_train = np.random.uniform(-4, 4, (100, 2))\n", "Y_2D_train = np.sin(0.5 * np.linalg.norm(X_2D_train, axis=1)) + \\\n", " noise_2D * np.random.randn(len(X_2D_train))\n", "\n", "plt.figure(figsize=(14,7))\n", "\n", "mu_s, _ = posterior_predictive(X_2D, X_2D_train, Y_2D_train, sigma_y=noise_2D)\n", "plot_gp_2D(gx, gy, mu_s, X_2D_train, Y_2D_train, \n", " f'Before parameter optimization: l={1.00} sigma_f={1.00}', 1)\n", "\n", "res = minimize(nll_fn(X_2D_train, Y_2D_train, noise_2D), [1, 1], \n", " bounds=((1e-5, None), (1e-5, None)),\n", " method='L-BFGS-B')\n", "\n", "mu_s, _ = posterior_predictive(X_2D, X_2D_train, Y_2D_train, *res.x, sigma_y=noise_2D)\n", "plot_gp_2D(gx, gy, mu_s, X_2D_train, Y_2D_train,\n", " f'After parameter optimization: l={res.x[0]:.2f} sigma_f={res.x[1]:.2f}', 2)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Note how the true sine wave is approximated much better after parameter optimization.\n", "\n", "## Libraries that implement GPs\n", "\n", "This section shows two examples of libraries that provide implementations of GPs. I'll provide only a minimal setup here, just enough for reproducing the above results. For further details please consult the documentation of these libraries.\n", "\n", "### Scikit-learn\n", "\n", "Scikit-learn provides a GaussianProcessRegressor for implementing [GP regression models](http://scikit-learn.org/stable/modules/gaussian_process.html#gaussian-process-regression-gpr). It can be configured with [pre-defined kernels and user-defined kernels](http://scikit-learn.org/stable/modules/gaussian_process.html#gp-kernels). Kernels can also be composed. The squared exponential kernel is the RBF kernel in scikit-learn. The RBF kernel only has a length_scale parameter which corresponds to the $l$ parameter above. To have a $\\sigma_f$ parameter as well, we have to compose the RBF kernel with a ConstantKernel." ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from sklearn.gaussian_process import GaussianProcessRegressor\n", "from sklearn.gaussian_process.kernels import ConstantKernel, RBF\n", "\n", "rbf = ConstantKernel(1.0) * RBF(length_scale=1.0)\n", "gpr = GaussianProcessRegressor(kernel=rbf, alpha=noise**2)\n", "\n", "# Reuse training data from previous 1D example\n", "gpr.fit(X_train, Y_train)\n", "\n", "# Compute posterior predictive mean and covariance\n", "mu_s, cov_s = gpr.predict(X, return_cov=True)\n", "\n", "# Obtain optimized kernel parameters\n", "l = gpr.kernel_.k2.get_params()['length_scale']\n", "sigma_f = np.sqrt(gpr.kernel_.k1.get_params()['constant_value'])\n", "\n", "# Compare with previous results\n", "assert(np.isclose(l_opt, l))\n", "assert(np.isclose(sigma_f_opt, sigma_f))\n", "\n", "# Plot the results\n", "plot_gp(mu_s, cov_s, X, X_train=X_train, Y_train=Y_train)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### GPy\n", "\n", "[GPy](http://sheffieldml.github.io/GPy/) is a Gaussian processes framework from the Sheffield machine learning group. It provides a GPRegression class for implementing GP regression models. By default, GPRegression also estimates the noise parameter $\\sigma_y$ from data, so we have to fix() this parameter to be able to reproduce the above results." ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "\n", "

\n", "Model: GP regression
\n", "Objective: 7.59157756278024
\n", "Number of Parameters: 3
\n", "Number of Optimization Parameters: 2
" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import GPy\n", "\n", "rbf = GPy.kern.RBF(input_dim=1, variance=1.0, lengthscale=1.0)\n", "gpr = GPy.models.GPRegression(X_train, Y_train, rbf)\n", "\n", "# Fix the noise variance to known value \n", "gpr.Gaussian_noise.variance = noise**2\n", "gpr.Gaussian_noise.variance.fix()\n", "\n", "# Run optimization\n", "gpr.optimize();\n", "\n", "# Display optimized parameter values\n", "display(gpr)" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ " /Users/martin/.venv/bs/lib/python3.6/site-packages/matplotlib/figure.py:2022: UserWarning:This figure includes Axes that are not compatible with tight_layout, so results might be incorrect.\n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Obtain optimized kernel parameters\n", "l = gpr.rbf.lengthscale.values[0]\n", "sigma_f = np.sqrt(gpr.rbf.variance.values[0])\n", "\n", "# Compare with previous results\n", "assert(np.isclose(l_opt, l))\n", "assert(np.isclose(sigma_f_opt, sigma_f))\n", "\n", "# Plot the results with the built-in plot function\n", "gpr.plot();" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Thanks for reading up to here :-) In another article, I'll show how Gaussian processes can be used for black-box optimization." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## References\n", "\n", "\$1\$ Kevin P. Murphy. [Machine Learning, A Probabilistic Perspective](https://mitpress.mit.edu/books/machine-learning-0), Chapters 4, 14 and 15. \n", "\$2\$ Christopher M. Bishop. [Pattern Recognition and Machine Learning](http://www.springer.com/de/book/9780387310732), Chapter 6. \n", "\$3\$ Carl Edward Rasmussen and Christopher K. I. Williams. [Gaussian Processes for Machine Learning](http://www.gaussianprocess.org/gpml/). " ] } ], "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": "3.6.6" } }, "nbformat": 4, "nbformat_minor": 2 }