{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Monte Carlo Integration: standard sampling, importance sampling, rejection sampling" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Florent Leclercq,
\n", "Imperial Centre for Inference and Cosmology, Imperial College London,
\n", "florent.leclercq@polytechnique.org" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "from scipy.integrate import quad\n", "from scipy.stats import norm\n", "from matplotlib import pyplot as plt\n", "from math import sin, pi\n", "np.random.seed(123456)\n", "%matplotlib inline\n", "plt.rcParams.update({'lines.linewidth': 2})" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "Nsamp=200" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## The target pdf" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "def target_pdf(x):\n", " return sin(x)*sin(x)\n", "target_pdf=np.vectorize(target_pdf)" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "a=0.\n", "b=pi\n", "x_arr=np.linspace(a,b,100)\n", "f_arr=target_pdf(x_arr)" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.figure(figsize=(10,6))\n", "plt.xlim(a,b)\n", "plt.ylim(0,1.05)\n", "plt.plot(x_arr,f_arr)\n", "plt.title(\"Target pdf\")\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "1.5707963267948966" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "trueI=quad(target_pdf,a,b)[0]\n", "trueI" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Standard Monte Carlo integration" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We directly draw samples from the target pdf." ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [], "source": [ "randoms=np.random.uniform(a,b,Nsamp)\n", "samples=target_pdf(randoms)" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.figure(figsize=(10,6))\n", "plt.xlim(a,b)\n", "plt.ylim(0,1.05)\n", "plt.plot(x_arr,f_arr)\n", "markerline, stemlines, baseline = plt.stem(randoms,samples,linefmt='-k',markerfmt='k.')\n", "baseline.set_visible(False)\n", "plt.title(\"Standard Monte Carlo integration\")\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "1.660402945484072" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ "StandardMonteCarloI=np.sum(samples)*(b-a)/Nsamp\n", "StandardMonteCarloI" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Importance sampling" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We draw samples from a proposal pdf, designed to be as close as possible to the target pdf. We then assign each sample a weight proportional to its likelihood divided by its prior probability." ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [], "source": [ "proposal=norm(loc=(b-a)/2,scale=0.5)\n", "proposal_pdf=proposal.pdf" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.figure(figsize=(10,6))\n", "plt.xlim(a,b)\n", "plt.ylim(0,1.05)\n", "plt.plot(x_arr,f_arr,label=\"target\")\n", "plt.plot(x_arr,proposal_pdf(x_arr),label=\"proposal\")\n", "plt.title(\"Importance sampling: target pdf and proposal pdf\")\n", "plt.legend(loc='best')\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [], "source": [ "samples=proposal.rvs(size=Nsamp)\n", "weights=target_pdf(samples)/proposal_pdf(samples)" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "f, (ax1, ax2) = plt.subplots(2, 1, sharex=True, figsize=(10,12))\n", "ax1.set_xlim(a,b)\n", "ax1.set_ylim(0,1.05)\n", "ax1.plot(x_arr,f_arr,label=\"target\")\n", "ax1.plot(x_arr,proposal_pdf(x_arr),label=\"proposal\")\n", "markerline, stemlines, baseline = ax1.stem(samples,proposal_pdf(samples),linefmt='-k',markerfmt='k.')\n", "baseline.set_visible(False)\n", "ax1.legend(loc='best')\n", "ax1.set_title(\"Importance sampling: samples and weights\")\n", "markerline, stemlines, baseline = ax2.stem(samples,weights,linefmt='-k',markerfmt='k.')\n", "baseline.set_visible(False)\n", "ax2.plot(x_arr,f_arr/proposal_pdf(x_arr),color='C2',label=\"target/proposal\")\n", "ax2.set_ylim([0,weights.max()+0.5])\n", "ax2.legend(loc='best')\n", "f.subplots_adjust(hspace=0)\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "1.5100957559182684" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" } ], "source": [ "ImportanceI=np.average(samples,weights=weights)\n", "ImportanceI" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Importance resampling" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "A problem with importance sampling is the situation in which all but one of the weights are close to zero. To avoid with situation, we can do **importance resampling**. We draw Nresamp new samples from the current sample set with probabilities proportional to their weights. We replace the current samples with this new set, and the the current weights by 1/Nresamp (drawing according to the importance weight replaces likelihoods by frequencies)." ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [], "source": [ "Nresamp=100\n", "normalizedweights=weights/np.sum(weights)\n", "resamples=np.random.choice(samples, size=Nresamp, replace=True, p=normalizedweights)\n", "reweights=1./Nresamp*np.ones(Nresamp)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Weights are then updated given their likelihood, as in the previous importance sampling step." ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [], "source": [ "reweights*=target_pdf(resamples)/(1./Nresamp)" ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.figure(figsize=(10,6))\n", "plt.xlim(a,b)\n", "plt.ylim(0,1.05)\n", "plt.plot(x_arr,f_arr)\n", "markerline, stemlines, baseline = plt.stem(resamples,reweights,linefmt='-k',markerfmt='k.')\n", "baseline.set_visible(False)\n", "plt.title(\"Importance resampling\")\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "1.531675529534044" ] }, "execution_count": 18, "metadata": {}, "output_type": "execute_result" } ], "source": [ "ImportanceReI=np.average(resamples,weights=reweights)\n", "ImportanceReI" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Iterating this procedure yields the **Sequential Importance Resampling** (SIR) algorithm, which is a simple \"*particle filter*\" or \"*Sequential Monte Carlo*\" algorithm." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Rejection sampling" ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [], "source": [ "upperbound=1\n", "xs=np.random.uniform(a,b,Nsamp)\n", "ys=np.random.uniform(0,upperbound,Nsamp)" ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.figure(figsize=(10,6))\n", "plt.xlim(a-0.1,b+0.1)\n", "plt.ylim(0,1.05)\n", "plt.plot(x_arr,f_arr)\n", "plt.scatter(xs,ys,s=15,marker='o',color='black')\n", "plt.fill_between(x_arr,np.zeros_like(x_arr),upperbound*np.ones_like(x_arr),color='grey',alpha=0.25)\n", "plt.plot([a,b],[upperbound,upperbound],color='black')\n", "plt.plot([a,a],[0,upperbound],color='black')\n", "plt.plot([b,b],[0,upperbound],color='black')\n", "plt.title(\"Rejection sampling\")\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [], "source": [ "accepted=np.where(ys<=target_pdf(xs))\n", "rejected=np.where(ys>target_pdf(xs))\n", "accepted_randoms=xs[accepted]\n", "accepted_samples=ys[accepted]\n", "rejected_randoms=xs[rejected]\n", "rejected_samples=ys[rejected]" ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.figure(figsize=(10,6))\n", "plt.xlim(a-0.1,b+0.1)\n", "plt.ylim(0,1.05)\n", "plt.plot(x_arr,f_arr)\n", "plt.scatter(accepted_randoms,accepted_samples,s=15,marker='o',color='green')\n", "plt.scatter(rejected_randoms,rejected_samples,s=15,marker='o',color='red')\n", "plt.fill_between(x_arr,np.zeros_like(x_arr),f_arr,color='green',alpha=0.25)\n", "plt.fill_between(x_arr,upperbound*np.ones_like(x_arr),f_arr,color='red',alpha=0.25)\n", "plt.plot([a,b],[upperbound,upperbound],color='black')\n", "plt.plot([a,a],[0,upperbound],color='black')\n", "plt.plot([b,b],[0,upperbound],color='black')\n", "plt.title(\"Rejection sampling\")\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.465" ] }, "execution_count": 23, "metadata": {}, "output_type": "execute_result" } ], "source": [ "fraction=float(len(accepted_samples))/Nsamp\n", "fraction" ] }, { "cell_type": "code", "execution_count": 24, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "1.460840583919254" ] }, "execution_count": 24, "metadata": {}, "output_type": "execute_result" } ], "source": [ "fraction=float(len(accepted_samples))/Nsamp\n", "RejectionI=fraction*upperbound*(b-a)\n", "RejectionI" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "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": "3.8.10" } }, "nbformat": 4, "nbformat_minor": 4 }