{ "cells": [ { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "%matplotlib inline\n", "\n", "from matplotlib.ticker import MultipleLocator, MaxNLocator, FormatStrFormatter, AutoMinorLocator\n", "from matplotlib import rcParams\n", "from matplotlib import rc_context\n", "\n", "# Seed\n", "np.random.seed(1)\n", "\n", "# Print precision\n", "np.set_printoptions(precision=3)\n", "\n", "# Text box properties\n", "text_bbox = dict(boxstyle='round',\n", " facecolor=(1., 1., 1., 1.),\n", " edgecolor='k',\n", " pad=0.5)\n", "\n", "# Colours\n", "colours = [plt.cm.tab10(i) for i in range(10)]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Gaussian process library [GPy](https://sheffieldml.github.io/GPy/) used in this notebook:" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "import GPy as gpy" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Gaussian processes" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Sampling a GP" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "A Gaussian process (GP) is an infinite-dimensional Gaussian distribution. A great Jupyter notebook by [Andreas Damianou](http://adamian.github.io/talks/Brown2016.html) (2016) gives an intuitive, step-by-step explanation of this idea.\n", "\n", "In this notebook we only consider input dimension $d=1$. The the RBF kernel (Eq. 6.2) then takes the form:\n", "$$\n", "k_{\\mathrm{RBF}}(x,x') = \\eta^2 e^{-\\frac{(x-x')^2}{2\\ell^2}}\n", "$$\n", "\n", "Below are samples from the RBF kernel:" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "def createSamples(kernel):\n", " # Input space between 0 and 1\n", " numX = 1000\n", " X = np.linspace(0., 5., numX)\n", " # X must be a 2D array\n", " X = np.atleast_2d(X).T\n", "\n", " # Mean\n", " mu = np.zeros(numX)\n", " # Covariance\n", " C = kernel.K(X, X)\n", " # 5 random samples from GP\n", " samples = np.random.multivariate_normal(mu, C, 5)\n", " \n", " return X, samples\n", "\n", "# RBF kernel\n", "kernel = gpy.kern.RBF(input_dim=1, variance=1.0, lengthscale=1.0)\n", "X, samples = createSamples(kernel)\n", "\n", "fig, ax = plt.subplots(1, 1)\n", "\n", "for sample in samples:\n", " ax.plot(X, sample)\n", "\n", "ax.set_xlabel(r'$x$')\n", "ax.set_ylabel(r'$y$')\n", "\n", "fig.tight_layout()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Below we can see the effect of changing the parameters of the kernel:" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Changing kernel parameters (Figure 6.1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Below are five samples each, for kernels with different parameters. The **GP mean** (here always 0) and **confidence intervals** (shaded blue areas) give the mean and the spread of these samples. The shaded blue areas give the $\\mathbf{1\\sigma}$ confidence intervals for the GP, i.e. we would expect the samples to lie within these areas about 68% of the time." ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "image/png": 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# Fix seed to 1 here in order to reproduce plot exactly as it appears in the thesis\n", "np.random.seed(1)\n", "\n", "variances = [1., 1., 1., 1.]\n", "lengthscales = [2., 1., 0.5, 0.2]\n", "\n", "fig, axs = plt.subplots(2, 2, sharex=True,\n", " figsize=(5.5, 4.),\n", " gridspec_kw={'hspace': 0})\n", "\n", "for ax, sigma2, l in zip(np.ravel(axs), variances, lengthscales):\n", " kernel = gpy.kern.RBF(input_dim=1, variance=sigma2, lengthscale=l)\n", " X, samples = createSamples(kernel)\n", " \n", " for i, sample in enumerate(samples):\n", " ax.plot(X, sample, c=colours[i], lw=1.)\n", " \n", " ax.fill_between(X.ravel(), -1.*np.sqrt(sigma2), 1.*np.sqrt(sigma2), alpha=0.2)\n", " \n", " ax.text(0.86, 0.9,\n", " fr'$\\ell={l}$',\n", " bbox=text_bbox,\n", " ha='center', va='center',\n", " transform=ax.transAxes)\n", " \n", " ax.set_ylabel(r'$y$')\n", " \n", " ax.set_xlim([0., 5.])\n", " ax.yaxis.set_major_locator(MultipleLocator(1.))\n", "\n", "# x-axis label for bottom subplot only\n", "for ax in axs[-1,:]:\n", " ax.set_xlabel(r'$x$')\n", "\n", "# y-axis labels for right column on right\n", "for ax in axs[:,1]:\n", " ax.yaxis.tick_right()\n", " ax.yaxis.set_label_position(\"right\")\n", "\n", "for i in range(axs.shape[1]):\n", " fig.align_ylabels(axs[i,0])\n", "\n", "fig.tight_layout()\n", "fig.savefig('prior.pdf')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Decreasing $\\ell$ makes the samples oscillate more rapidly. If, for example, we were to increase $\\eta^2$ by a factor of 100, we would obtain samples that have a typical magnitude about 10x larger." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# GPs for regression" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ " ## Changing kernel parameters" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "It is possible to constrain a GP at a number of inputs $x$, and perform the same sampling. The confidence intervals will now tell us about the spread of possible functions that pass through these points. Shown below are samples (faint colours), the GP mean (solid blue line), and the $\\mathbf{2\\sigma}$ confidence intervals (shaded blue areas), each for the a different set of kernel parameters. Here the confidence intervals are telling us the expected distribution of possible functions that pass through the points." ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "X_train = np.array([0., 0.5, 2., 3.5, 6.]).reshape(-1, 1)\n", "Y_train = np.sin(X_train)\n", "\n", "fig, axs = plt.subplots(2, 2, figsize=(7., 5.))\n", "for ax, sigma2, l in zip(np.ravel(axs), variances, lengthscales):\n", " kernel = gpy.kern.RBF(input_dim=1, variance=sigma2, lengthscale=l)\n", " GPModel = gpy.models.GPRegression(X_train, Y_train, kernel)\n", " # We assume here that data are noiseless --> fix Gaussian noise (\"nugget\") to 0\n", " GPModel.Gaussian_noise.variance.fix(0.)\n", " \n", " # We make use of the inbuilt plot function for GPy models to quickly plot\n", " GPModel.plot(plot_limits=[-2, 8.], ax=ax)\n", " \n", " # Plot samples from \"posterior\"\n", " numSamples = 5\n", " XSample = np.linspace(-2., 8., 1000).reshape(-1, 1)\n", " posteriorSamples = GPModel.posterior_samples_f(XSample, full_cov=True, size=numSamples)\n", " for i in range(numSamples):\n", " ax.plot(XSample, posteriorSamples[:,:,i], alpha=0.2)\n", " \n", " ax.set_title(fr'$\\eta^2 = {sigma2}, \\ell = {l}$')\n", " ax.set_xlabel(r'$x$')\n", " ax.set_ylabel(r'$y$')\n", "\n", "fig.tight_layout()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Optimising kernel parameters (Figure 6.2)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Below we optimise kernel parameters by maximising the likelihood." ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ " /home/matt/anaconda3/envs/gp/lib/python3.7/site-packages/paramz/transformations.py:111: RuntimeWarning:divide by zero encountered in log\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "eta^2 = 0.602, l = 1.063\n" ] }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "GPModel.Gaussian_noise.variance.fix(0.)\n", "# Multiple restarts to optimization - likelihood surface often has multiple local maxima\n", "GPModel.optimize_restarts(verbose=False)\n", "\n", "# Obtain optimized kernel parameters\n", "l = GPModel.rbf.lengthscale.values[0]\n", "sigma2 = np.sqrt(GPModel.rbf.variance.values[0])\n", "print(f'eta^2 = {sigma2:.3f}, l = {l:.3f}')\n", "\n", "fig, ax = plt.subplots(1, 1, figsize=(3.4, 2.5))\n", "\n", "# Plot original sine function\n", "X_sin = np.linspace(-2., 8., 1000)\n", "Y_sin = np.sin(X_sin)\n", "trueHandle = ax.plot(X_sin, Y_sin, 'k--', label='True')[0]\n", "\n", "# Plot data/training points\n", "dataHandle = ax.plot(X_train, Y_train, 'kx', ms=5., label='Data')[0]\n", "\n", "# Plot GP mean and 2-sigma confidence intervals\n", "GPmean, GPcov = GPModel.predict_noiseless(np.atleast_2d(X_sin).T)\n", "lower = GPmean - 2.*np.sqrt(GPcov)\n", "higher = GPmean + 2.*np.sqrt(GPcov)\n", "\n", "meanHandle = ax.plot(X_sin, GPmean, c=colours[0], ls='-')[0]\n", "sigmaHandle = ax.fill_between(X_sin, lower.T[0], higher.T[0],\n", " color=colours[0], alpha=0.2, lw=0.)\n", "\n", "ax.set_xlim([-2, 8.])\n", "ax.set_ylim([-1.5, 1.5])\n", "\n", "ax.set_xlabel(r'$x$')\n", "ax.set_ylabel(r'$y$')\n", "\n", "ax.xaxis.set_major_formatter(FormatStrFormatter('%g')) # No unnecessary trailing decimals\n", "ax.yaxis.set_major_formatter(FormatStrFormatter('%g'))\n", "\n", "ax.legend([trueHandle, dataHandle, (sigmaHandle, meanHandle)],\n", " ['True', 'Data', 'GP'],\n", " loc=(0.61, 0.7))\n", "\n", "fig.tight_layout()\n", "fig.savefig('GP_regression.pdf')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Sampling the optimised GP" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As in all previous figures, we can draw samples from this newly-optimised GP." ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "X = np.linspace(-2., 8., 100).reshape(-1, 1)\n", "posteriorSamples = GPModel.posterior_samples_f(X, full_cov=True, size=5)\n", "\n", "fig, ax = plt.subplots(1, 1)\n", "\n", "for i in range(posteriorSamples.shape[2]):\n", " ax.plot(X, posteriorSamples[:,:,i])\n", "ax.plot(X_train, Y_train, 'kx', ms=5.)\n", "\n", "ax.set_xlabel(r'$x$')\n", "ax.set_ylabel(r'$y$')\n", "ax.set_title('Random samples from GP posterior')\n", "fig.tight_layout()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Using a non-zero \"nugget\" component in the kernel" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The case with a non-zero \"nugget\" / Gaussian noise for each data point (we use here the 1D equivalent of kernel given in Eq. 6.4 of the thesis, and explained in Sec. 6.2.1):" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Optimization restart 1/10, f = 3.5070571835468294\n", "Optimization restart 2/10, f = 3.5070571835483175\n", "Optimization restart 3/10, f = 3.507057184169997\n", "Optimization restart 4/10, f = 3.6420185908785725\n", "Optimization restart 5/10, f = 3.5070571835463586\n", "Optimization restart 6/10, f = 3.5070571835476483\n", "Optimization restart 7/10, f = 3.64201859085395\n", "Optimization restart 8/10, f = 3.642018590854088\n", "Optimization restart 9/10, f = 3.507057183568184\n", "Optimization restart 10/10, f = 3.5070571835462276\n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# Fix Gaussian noise variance (\"nugget\") to 0.01 --> sigma_n of 0.1\n", "GPModel.Gaussian_noise.variance.fix(0.01)\n", "\n", "# Multiple restarts to optimization - likelihood surface often has multiple local maxima\n", "GPModel.optimize_restarts()\n", "\n", "# Optimized kernel parameters\n", "l = GPModel.rbf.lengthscale.values[0]\n", "sigma2 = np.sqrt(GPModel.rbf.variance.values[0])\n", "\n", "# Plot\n", "fig, ax = plt.subplots(1, 1)\n", "\n", "GPModel.plot(plot_limits=[-2, 8.], ax=ax)\n", "ax.plot(X_sin, Y_sin, 'k--', label='True function')\n", "\n", "# Plot samples from \"posterior\"\n", "numSamples = 5\n", "XSample = np.linspace(-2., 8., 1000).reshape(-1, 1)\n", "posteriorSamples = GPModel.posterior_samples_f(XSample, full_cov=True, size=numSamples)\n", "for i in range(numSamples):\n", " ax.plot(XSample, posteriorSamples[:,:,i], alpha=0.2)\n", "\n", "ax.set_xlabel(r'$x$')\n", "ax.set_ylabel(r'$y$')\n", "ax.legend(loc=(0.55, 0.7))\n", "ax.set_title(fr'$\\eta^2 = {sigma2:.3f}, \\ell = {l:.3f}$')\n", "\n", "fig.tight_layout()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "At each training point, the $2\\sigma$ confidence intervals shrink to a minimum of $2\\sigma_{n}$, here $0.2$. (In the zero-nugget case they shrink to 0.)" ] } ], "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": "3.7.8" }, "toc": { "base_numbering": 1, "nav_menu": {}, "number_sections": true, "sideBar": true, "skip_h1_title": false, "title_cell": "Table of Contents", "title_sidebar": "Contents", "toc_cell": false, "toc_position": { "height": "calc(100% - 180px)", "left": "10px", "top": "150px", "width": "325.391px" }, "toc_section_display": true, "toc_window_display": true } }, "nbformat": 4, "nbformat_minor": 4 }