{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Neal's funnel\n", "\n", "This notebook introduces a toy distribution introduced by Radford Neal and is the $d+1$ dimensional,\n", "\n", "$p(\\boldsymbol{x},\\nu) = \\left[\\prod_{i=1}^{d} \\mathcal{N}(x_i|0,e^{\\nu / 2})\\right] \\mathcal{N}(\\nu|0,3),$\n", "\n", "which has shown to cause problems for samplers owing to its \"funnel\" shaped geometry in the marginals $(x_i,\\nu)$,\n", "\n", "$p(x_i,\\nu) = \\mathcal{N}(x_i|0,e^{\\nu / 2})\\mathcal{N}(\\nu|0,3),$\n", "\n", "which we now plot." ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAZsAAAELCAYAAAAP/iu7AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nErv/B5B+wk3BeahkAAAAAElFTkSuQmCC\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import pints\n", "import pints.toy\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "\n", "# Create log pdf\n", "log_pdf = pints.toy.NealsFunnelLogPDF()\n", "\n", "# Plot marginal density\n", "levels = np.linspace(-7, -1, 20)\n", "x = np.linspace(-10, 10, 100)\n", "y = np.linspace(-10, 10, 100)\n", "X, Y = np.meshgrid(x, y)\n", "Z = [[log_pdf.marginal_log_pdf(i, j) for i in x] for j in y]\n", "plt.contour(X, Y, Z, levels = levels)\n", "plt.xlabel('x_i')\n", "plt.ylabel('nu')\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can also sample independently from this toy LogPDF, and add that to the visualisation:" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAY0AAAD8CAYAAACLrvgBAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nOI7j5MaThuM4jpOb/wM8AjpRcdyLrQAAAABJRU5ErkJggg==\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "direct = log_pdf.sample(1500)\n", "\n", "plt.contour(X, Y, Z, levels=levels, colors='k', alpha=0.2)\n", "plt.scatter(direct[:, 0], direct[:, 9], alpha=0.2)\n", "plt.xlim(-10, 10)\n", "plt.ylim(-10, 10)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We now try to sample from the distribution with MCMC:" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Running...\n", "Done!\n" ] } ], "source": [ "# Create an adaptive covariance MCMC routine\n", "x0 = np.random.uniform(-25, 25, size=(3, 10))\n", "mcmc = pints.MCMCController(log_pdf, 3, x0, method=pints.AdaptiveCovarianceMCMC)\n", "\n", "# Stop after 10000 iterations\n", "mcmc.set_max_iterations(3000)\n", "\n", "# Disable logging\n", "mcmc.set_log_to_screen(False)\n", "\n", "# Run!\n", "print('Running...')\n", "chains = mcmc.run()\n", "print('Done!')\n", "\n", "# Discard warm-up\n", "chains = [chain[1000:] for chain in chains]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The adaptive covariance fails to get into the funnel region." ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAY0AAAD8CAYAAACLrvgBAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nzw93vQAAAABJRU5ErkJggg==\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "stacked = np.vstack(chains)\n", "plt.contour(X, Y, Z, levels=levels, colors='k', alpha=0.2)\n", "plt.scatter(stacked[:, 0], stacked[:, 9], alpha=0.2)\n", "plt.xlim(-10, 10)\n", "plt.ylim(-10, 10)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now check how close the result is to the expected result, using the [Kullback-Leibler divergence](https://en.wikipedia.org/wiki/Kullback–Leibler_divergence), and compare this to the result from sampling directly." ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "1.66259443754\n", "8.35418859013e-05\n" ] } ], "source": [ "print(log_pdf.kl_divergence(stacked))\n", "print(log_pdf.kl_divergence(direct))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Hamiltonian Monte Carlo fares much better on this curved density." ] }, { "cell_type": "code", "execution_count": 28, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Running...\n", "Done!\n" ] } ], "source": [ "# Create an adaptive covariance MCMC routine\n", "x0 = np.random.uniform(0, 10, size=(3, 10))\n", "sigma0 = np.repeat(0.25, 10)\n", "mcmc = pints.MCMCController(log_pdf, 3, x0, method=pints.HamiltonianMCMC, sigma0=sigma0)\n", "\n", "# Stop after 10000 iterations\n", "mcmc.set_max_iterations(500)\n", "\n", "# Disable logging\n", "mcmc.set_log_to_screen(False)\n", "\n", "# Run!\n", "print('Running...')\n", "chains = mcmc.run()\n", "print('Done!')\n", "\n", "stacked = np.vstack(chains)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Hamiltonian Monte Carlo does better than adaptive but still not great." ] }, { "cell_type": "code", "execution_count": 29, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "0.451968021049\n", "8.35418859013e-05\n" ] } ], "source": [ "print(log_pdf.kl_divergence(stacked))\n", "print(log_pdf.kl_divergence(direct))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Visualising the path of one of the chains the sampler struggles to explore both the neck and the outside region efficiently." ] }, { "cell_type": "code", "execution_count": 30, "metadata": {}, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAY0AAAD8CAYAAACLrvgBAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\no9FoDow2GhqNRqM5MNpoaDQajebA/P+X/rh2qldaiAAAAABJRU5ErkJggg==\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "divergent_transitions = mcmc.samplers()[0].divergent_iterations()\n", "plt.contour(X, Y, Z, levels=levels, colors='k', alpha=0.2)\n", "plt.plot(chains[2][:, 1], chains[2][:, 9], alpha=0.5)\n", "plt.scatter(chains[0][divergent_transitions, 0], chains[0][divergent_transitions, 1], color='red')\n", "plt.xlim(-10, 10)\n", "plt.ylim(-10, 10)\n", "plt.show()" ] } ], "metadata": { "kernelspec": { "display_name": "Python 2", "language": "python", "name": "python2" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 2 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython2", "version": "2.7.14" } }, "nbformat": 4, "nbformat_minor": 2 }