{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Twisted Gaussian (banana) toy LogPDF" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This distribution (described [here](http://pints.readthedocs.io/en/latest/toy/twisted_gaussian_logpdf.html)) has a curved \"banana\" shape. The problem can be more more or less difficult by changing the \"bananicity\" parameter `b`." ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "data": { "image/png": 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2CSzv+wCl1CXAJTA4vP7gXVriYNn5yyW++tVbcR45Sm9EEFRDcuUeU/kGs+kN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\nnDDxMj7zseFtoYQWROqLSOcKHN9jaxBi2clg10yMTZ/TznzouMNWlG0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"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.TwistedGaussianLogPDF(dimension=2)\n", "\n", "# Contour plot of pdf\n", "levels = np.linspace(-50, -1, 20)\n", "x = np.linspace(-50, 50, 250)\n", "y = np.linspace(-100, 20, 250)\n", "X, Y = np.meshgrid(x, y)\n", "Z = [[log_pdf([i, j]) for i in x] for j in y]\n", "plt.contour(X, Y, Z, levels = levels)\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": 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PHrRyCqtIV9Yv4NUiipQMt2i8PJxElQ7VqtXIla+trTE6OsrAwAAHDhxg69at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\nL3HmzJl2h73i6USwgi0uLvLGG28QxzFhQmtdwLAQtvtgA5mKAoQMUcD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IfPQt6+4Qkd0i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\nMcY0OEsExhjT4P4PAiKSUVn+ZH4AAAAASUVORK5CYII=\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "direct = log_pdf.sample(15000)\n", "\n", "plt.contour(X, Y, Z, levels=levels, colors='k', alpha=0.2)\n", "plt.scatter(direct[:, 0], direct[:, 1], alpha=0.2)\n", "plt.xlim(-50, 50)\n", "plt.ylim(-100, 20)\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, 2))\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": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "image/png": 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9ZX9/P52dnezdu5dNmzbR1tbGpUuXOHv2LOl0mmAwSE1NDfX19TQ1NeHz+cpx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\nNTnq9e1RrhH8b8CXLMv6JyHEh+5//BTwQWDP/bdB4M/v/ym9gWVZDA0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"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[:, 1], alpha=0.2)\n", "plt.xlim(-50, 50)\n", "plt.ylim(-100, 20)\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": [ "1.69270294721\n", "8.72282979447e-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": 8, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Running...\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "pints/_mcmc/_hamiltonian.py:284: RuntimeWarning: invalid value encountered in subtract\n", " self._momentum -= self._scaled_epsilon * self._gradient\n", "pints/toy/_twisted_gaussian_banana.py:67: RuntimeWarning: invalid value encountered in double_scalars\n", " y[1] += self._b * ((x[0] ** 2) - self._V)\n", "pints/toy/_twisted_gaussian_banana.py:78: RuntimeWarning: invalid value encountered in double_scalars\n", " -x[0] / (50 * V) - 4 * b * x[0] * (b * (x[0]**2 - V) + x[1])\n", "pints/toy/_twisted_gaussian_banana.py:80: RuntimeWarning: invalid value encountered in double_scalars\n", " dy_first = -b * (x[0]**2 - V) - x[1]\n", "pints/_mcmc/_hamiltonian.py:290: RuntimeWarning: invalid value encountered in subtract\n", " self._momentum -= self._scaled_epsilon * self._gradient * 0.5\n", "pints/_mcmc/_hamiltonian.py:302: RuntimeWarning: overflow encountered in square\n", " proposed_K = np.sum(self._momentum**2 / 2)\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Done!\n", "76.1477311635\n", "8.72282979447e-05\n" ] } ], "source": [ "# Create an adaptive covariance MCMC routine\n", "x0 = np.random.uniform(-25, 25, size=(3, 2))\n", "sigma0 = [5, 5]\n", "mcmc = pints.MCMCController(log_pdf, 3, x0, method=pints.HamiltonianMCMC, sigma0=sigma0)\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", "chains1 = [chain[1000:] for chain in chains]\n", "stacked = np.vstack(chains1)\n", "\n", "print(log_pdf.kl_divergence(stacked))\n", "print(log_pdf.kl_divergence(direct))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Visualising the path of a single HMC chain, we see that it moves naturally along contours although does occassionally suffer from divergent iterations (red dots) in the neck of the banana due to the varying posterior curvature throughout the domain." ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [ { "data": { "image/png": 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lFhYWkCTJ6DLm9XqJxWLki2UGlRjBoIdGo4HH48Ht/uCCFQ6HDIuFarVKNpul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\nTkSuQmCC\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[0][:, 0], chains[0][:, 1], alpha=0.5)\n", "plt.scatter(chains[0][divergent_transitions, 0], chains[0][divergent_transitions, 1], color='red')\n", "plt.xlim(-50, 50)\n", "plt.ylim(-100, 20)\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 }