{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Basic Gaussian process regression (GPR)\n", "In this notebook, we will go over the basics of Gaussian process regression and get familiar with the [GPSat Model API](../GPSat.models.rst) to get/set parameters, train our model and make predictions on new data points." ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "2023-08-02 18:06:25.326820: I tensorflow/core/platform/cpu_feature_guard.cc:182] This TensorFlow binary is optimized to use available CPU instructions in performance-critical operations.\n", "To enable the following instructions: SSE4.1 SSE4.2, in other operations, rebuild TensorFlow with the appropriate compiler flags.\n" ] } ], "source": [ "import numpy as np\n", "import scipy\n", "import matplotlib.pyplot as plt\n", "from GPSat.models.sklearn_models import sklearnGPRModel" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Consider data generated from a simple cosine function\n", "\n", "\\begin{align}\n", "\\tag{1}\n", "y = \\cos(X) + \\epsilon,\n", "\\end{align}\n", "\n", "where $X = (x_1, \\ldots, x_N)$ is a set of randomly generated points within the interval $[-L, L]$, and $\\epsilon$ is a measurement error, which we take to be an i.i.d. zero-mean Gaussian noise with standard deviation $0.05$.\n", "\n", "Our goal is to use a Gaussian process model to filter out the noise $\\epsilon$ and recover the function $f(x) = \\cos(x)$ from the training data $(X, y)$." ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 2, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Set random seed\n", "np.random.seed(0)\n", "\n", "# Generate data\n", "N = 30\n", "L = 5\n", "noise_std = 0.05\n", "\n", "X_grid = np.linspace(-L, L, 100)\n", "X = np.random.uniform(-L, L, (N,))\n", "f = lambda x: np.cos(x)\n", "epsilon = noise_std * np.random.randn(N)\n", "\n", "y = f(X) + epsilon\n", "f_truth = f(X_grid) # Ground truth\n", "\n", "# Plot\n", "plt.plot(X_grid, f_truth, 'k', zorder=1, label='Ground truth')\n", "plt.scatter(X, y, color='C3', alpha=0.6, zorder=2, label='Noisy observations')\n", "plt.legend()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Gaussian processes\n", "\n", "Intuitively, a zero-mean Gaussian process (GP) can be understood as a Gaussian distribution on an *arbitrary collection of inputs*.\n", "\n", "More specifically, it is a random function $f : \\mathbb{R} \\rightarrow \\mathbb{R}$ such that for an arbitrary collection of inputs $X = (x_1, \\ldots, x_N)$, the random variable $f(X)$ is a multivariate Gaussian\n", "\n", "\\begin{align*}\n", "f(X) \\sim \\mathcal{N}(0, K_{XX}),\n", "\\end{align*}\n", "\n", "for some $N \\times N$ covariance matrix $K_{XX}$. Importantly, this covariance matrix can be computed using a **kernel function** $k : \\mathbb{R} \\times \\mathbb{R} \\rightarrow \\mathbb{R}$ as\n", "\n", "\\begin{align*}\n", "[K_{XX}]_{ij} = k(x_i, x_j), \\quad \\forall i,j = 1, \\ldots, N,\n", "\\end{align*}\n", "\n", "and this completely characterises the zero-mean GP. i.e. the properties of a GP are completely determined by the kernel!\n", "\n", "Below, we set up a GP with the so-called radial basis function (RBF) kernel, given as\n", "\n", "\\begin{align*}\n", "\\tag{RBF}\n", "k_{\\text{RBF}}(x, x') = \\sigma^2 \\exp\\left(-\\frac{|x-x'|^2}{2\\ell^2}\\right),\n", "\\end{align*}\n", "\n", "using ``sklearnGPRModel``, a GPSat GP regression model based on the ``scikit-learn`` GPR module." ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "'__init__': 0.040 seconds\n" ] } ], "source": [ "gpr = sklearnGPRModel(coords=X, obs=y, kernel='RBF', verbose=False)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In the expression for the kernel (RBF) above, we see that it is controlled by two parameters $\\sigma^2$ and $\\ell$, which are referred to as the *kernel variance* and the *lengthscale* hyperparameters respectively (in machine learning lingo, we refer to parameters that define the models as *hyperparameters*).\n", "\n", "Every ``GPSat`` model comes equipped with a getter/setter method for all (hyper)-parameters in the model. A list of all parameters is stored in the ``param_names`` property." ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "['lengthscales', 'kernel_variance', 'likelihood_variance']\n" ] } ], "source": [ "print(gpr.param_names)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can retrieve their values using the ``get_*()`` method, where ``*`` is to be substituted with the parameter name." ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Lengthscale: [1.], Kernel variance: 1.0\n" ] } ], "source": [ "ls = gpr.get_lengthscales()\n", "kv = gpr.get_kernel_variance()\n", "\n", "print(f\"Lengthscale: {ls}, Kernel variance: {kv}\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Suppose we want to set the kernel variance to 1.5. We can achieve this using the ``set_*()`` method." ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "New kernel variance: 1.5\n" ] } ], "source": [ "gpr.set_kernel_variance(1.5)\n", "kv = gpr.get_kernel_variance()\n", "print(f\"New kernel variance: {kv:.1f}\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## The likelihood\n", "In ``param_names`` above, we also saw a parameter ``likelihood_variance``. This is not a hyperparameter of the GP kernel, but is instead a parameter of the so-called *likelihood*.\n", "\n", "In general, the likelihood describes the probability of an observation $y$ given the ground truth field $f(X)$, i.e., the conditional distribution $p(y | f(X))$. In our case, since the observations are assumed to only differ from the ground truth by some measurement error, the likelihood is understood as modelling precisely this measurement error.\n", "\n", "From (1), we see that the likelihood is given by\n", "\n", "\\begin{align*}\n", "p(y | f(X)) \\sim \\mathcal{N}(f(X), \\alpha^2 I),\n", "\\end{align*}\n", "\n", "with $\\alpha = 0.05$ and $f(x) = \\cos(x)$. Here, the parameter $\\alpha^2$ is referred to as the *likelihood variance*.\n", "\n", "We can get the default value for the likelihood variance using the ``get_*`` method:" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Likelihood variance: 1.0\n" ] } ], "source": [ "print(f\"Likelihood variance: {gpr.get_likelihood_variance()}\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "and set the correct value by using the ``set_*`` method." ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "New likelihood variance: 0.0025\n" ] } ], "source": [ "alpha = 0.05\n", "gpr.set_likelihood_variance(alpha**2)\n", "print(f\"New likelihood variance: {gpr.get_likelihood_variance():.4f}\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Alternatively, we could have also initialised the GPR model by specifying the ``likelihood_variance`` and ``kernel_variance`` arguments with their respective values." ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "'__init__': 0.048 seconds\n", "Lengthscale: [1.], Kernel variance: 1.5, Likelihood variance: 0.0025\n" ] } ], "source": [ "# This initialises a GP model with the desired values\n", "gpr = sklearnGPRModel(coords=X, obs=y, kernel='RBF', likelihood_variance=alpha**2, kernel_variance=1.5, verbose=False)\n", "\n", "ls = gpr.get_lengthscales()\n", "kv = gpr.get_kernel_variance()\n", "lv = gpr.get_likelihood_variance()\n", "\n", "print(f\"Lengthscale: {ls}, Kernel variance: {kv:.1f}, Likelihood variance: {lv:.4f}\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Prediction\n", "From just these information, we can now infer what our ground truth function $f$ should be, given the data pair $(X, y)$.\n", "\n", "Mathematically this is achieved by the simple, yet powerful **Bayes' rule** to update our belief on the function $f$ given our data $(X, y)$. Informally, this reads:\n", "\n", "\\begin{align}\n", "\\tag{2}\n", "\\underbrace{p(f \\,|\\, X, y)}_{\\text{posterior}} \\propto \\underbrace{p(y \\,|\\, f(X))}_{\\text{likelihood}} \\,\\, \\underbrace{p(f)}_{\\text{prior}}.\n", "\\end{align}\n", "\n", "In GP regression, one can understand the GP as modelling a prior distribution on the function $f$. Thus, the term $p(f)$ corresponds to our GP model. The posterior distribution $p(f | X, y)$ thus gives our prediction of the field $f$ given the data.\n", "\n", "In ``GPSat`` models, this is computed using the ``predict()`` method. This takes as inputs a set of $N_*$ prediction points, which must be an array of size $(N_*, D)$, where $D$ is the input dimension (in our case, just 1)." ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "'predict': 0.010 seconds\n" ] }, { "data": { "text/plain": [ "" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Make predictions on a uniform grid\n", "pred_dict = gpr.predict(X_grid.reshape(-1, 1))\n", "\n", "# Extract the mean and variance from the results dictionary\n", "f_mean = pred_dict['f*']\n", "f_var = pred_dict['f*_var']\n", "f_std = np.sqrt(f_var)\n", "\n", "# Plot results\n", "plt.plot(X_grid, f_truth, 'k', zorder=0, label='Ground truth')\n", "plt.plot(X_grid, f_mean, color='C0', zorder=1, label='GP Prediction')\n", "plt.fill_between(X_grid, f_mean-1.96*f_std, f_mean+1.96*f_std, color='C0', alpha=0.3)\n", "plt.scatter(X, y, color='C3', alpha=0.6, zorder=2, label='Noisy observations')\n", "plt.legend()\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In the plot above, we have plotted the prediction in blue, where the shaded region indicates a 90% credible interval, where we believe the ground truth lies.\n", "\n", "To assess the quality of this prediction, we can look at two metrics:\n", "\n", "(1) the mean squared error $\\frac{1}{N_*} \\sum_{n=1}^{N^*} (f_{truth}(x_n') - f_{mean}(x_n'))^2$ between the predictive mean and the ground truth, and\n", "\n", "(2) the mean log-likelihood $\\frac{1}{N_*} \\sum_{n=1}^{N^*} \\log \\mathcal{N}(f_{truth}(x_n') \\,|\\, f_{mean}(x_n'), f_{std}(x_n')^2)$ of the ground truth given the predictive mean and standard deviation.\n", "\n", "The former only assess the quality of the mean, however the latter also assess the quality of the predictive uncertainty. For the log-likelihood loss, a higher value indicates better performance." ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Mean squared error: 0.0026\n", "Mean log likelihood: 1.4578\n" ] } ], "source": [ "print(f\"Mean squared error: {np.mean((f_truth - f_mean)**2):.4f}\")\n", "print(f\"Mean log likelihood: {scipy.stats.norm.logpdf(f_truth, f_mean, f_std).mean():.4f}\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Training\n", "To further improve our predictions, we can think of finding a value for the hyperparameters $\\Theta = (\\sigma^2, \\ell, \\alpha^2)$ that fit the data \"better\". This is called the *training* process.\n", "\n", "To define what a \"better\" model means, we can compare them using a certain metric. A perferred such metric in Bayesian modelling is the so-called *marginal likelihood*, defined as:\n", "\n", "\\begin{align}\n", "\\tag{3}\n", "p(y | \\Theta) = \\int p(y | f(X), \\Theta) \\,p(f(X) | \\Theta) \\,df(X).\n", "\\end{align}\n", "\n", "Thus, we can find an optimal set of parameters by maximising (3) with respect to $\\Theta$. Equivalently, we can also maximise their log-transformed counterpart, which is more typically used.\n", "\n", "In ``GPSat`` models, we can compute the log-transformed version of the metric (3) by simply calling the ``get_objective_function_value()`` method." ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "'get_objective_function_value': 0.000 seconds\n", "log marginal likelihood = 16.6180\n" ] } ], "source": [ "print(f\"log marginal likelihood = {gpr.get_objective_function_value():.4f}\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now, let's optimise this loss function, which can be achieved in ``GPSat`` model by calling the ``optimise_parameters()`` method." ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "'optimise_parameters': 0.026 seconds\n", "Optimise success: True\n", "------------------------------\n", "'get_parameters': 0.000 seconds\n", "Values of model hyperparameters after training:\n", "lengthscales : 1.5648\n", "kernel_variance : 0.5168\n", "likelihood_variance : 0.0025\n", "------------------------------\n", "'get_objective_function_value': 0.000 seconds\n", "log marginal likelihood (after training) = 21.4700\n" ] } ], "source": [ "# Optimise model\n", "opt_success = gpr.optimise_parameters()\n", "\n", "# Print outputs\n", "print(f\"Optimise success: {opt_success}\")\n", "print(\"-\"*30)\n", "param_dict = gpr.get_parameters(*gpr.param_names)\n", "print(\"Values of model hyperparameters after training:\")\n", "for k, v in param_dict.items():\n", " print(f\"{k} : {v:.4f}\")\n", "print(\"-\"*30)\n", "print(f\"log marginal likelihood (after training) = {gpr.get_objective_function_value():.4f}\")\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We see that after training, the values of the lengthscale and kernel variance hyperparameters have changed. In addition, the log marginal likelihood value has increased.\n", "\n", "**Note:** For scikit-learn models, the likelihood variance is assumed constant and does not get optimised. If you want to optimise the likelihood variance, use e.g. ``GPSat.models.gpflow_models.GPflowGPRModel`` instead.\n", "\n", "Now let's see the updated predictions." ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "'predict': 0.002 seconds\n" ] }, { "data": { "text/plain": [ "" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Predict again\n", "pred_dict = gpr.predict(X_grid[:,None])\n", "\n", "# Extract mean, variance and standard deviation\n", "f_mean = pred_dict['f*']\n", "f_var = pred_dict['f*_var']\n", "f_std = np.sqrt(f_var)\n", "\n", "# Plot predictions\n", "plt.plot(X_grid, f_truth, 'k', zorder=0, label='Ground truth')\n", "plt.plot(X_grid, f_mean, color='C0', zorder=1, label='GP Prediction')\n", "plt.fill_between(X_grid, f_mean-1.96*f_std, f_mean+1.96*f_std, color='C0', alpha=0.3)\n", "plt.scatter(X, y, color='C3', alpha=0.6, zorder=2, label='Noisy observations')\n", "plt.legend()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We see that the uncertainty bounds are now tighter around the ground truth after training, although the mean prediction is a little bit more off than before.\n", "\n", "This is reflected in the metrics:" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Mean squared error: 0.0037\n", "Mean log likelihood: 1.8717\n" ] } ], "source": [ "print(f\"Mean squared error: {np.mean((f_truth - f_mean)**2):.4f}\")\n", "print(f\"Mean log likelihood: {scipy.stats.norm.logpdf(f_truth, f_mean, f_std).mean():.4f}\")" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 3.8.17 ('gpsat2')", "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": "3.8.17" }, "orig_nbformat": 4, "vscode": { "interpreter": { "hash": "42c89ee418f45ab16d4cd7d85b9f5fd46783f67990f590db7ef8d9e48f3f848d" } } }, "nbformat": 4, "nbformat_minor": 2 }