{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Constrained Sampling\n", "\n", "The importance of using specialized proposal distributions for constrained sample problems can be illustrated \n", "with a simple example.\n", "Consider a box $[0, 1e5]^d$ for some dimension $d$ and assume the sampler starts close to the origin. \n", "In this case, a classical isotropical Gaussian proposal distribution will have approximately $\\frac{2^d - 1}{2^d}$ of \n", "its density located outside the constrained region.\n", "Thus, the probability to generate a proposal which lies inside the constrained region is geometrically\n", "distributed and has probability $2^{-d}$.\n", "It is easy to see, that this probability will vanish very quickly, hence, leaving the Markov chain stuck for \n", "a long time.\n", "More precisely, it will remain stuck for $2^d$ moves in expectation.\n", "In contrast, the Hit-and-Run algorithm will never generate samples outside the constrained region.\n", "The effect of this can be seen by monitoring the proposed states of a Gaussian and a Hit-and-Run algorithm\n", "for the same problem as dimension increases." ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import hopsy\n", "import numpy as np\n", "import matplotlib.pyplot as plt" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Set parameter Username\n", "Academic license - for non-commercial use only - expires 2023-11-30\n" ] } ], "source": [ "dims = np.array(range(1, 14))\n", "Problem = lambda dim: hopsy.add_box_constraints(\n", " hopsy.Problem(-np.identity(dim), [0]*dim), 0, 1e3)\n", "\n", "proposals = [\n", " hopsy.GaussianHitAndRunProposal,\n", " hopsy.GaussianProposal,\n", "]\n", "\n", "accrates = np.zeros((len(dims), len(proposals)))\n", "\n", "n = 1000\n", "\n", "for i, dim in enumerate(dims):\n", " for k, Proposal in enumerate(proposals):\n", " problem = Problem(dim)\n", " proposal = Proposal(problem, starting_point=[.001]*dim)\n", " rng = hopsy.RandomNumberGenerator(seed=42)\n", " accrate = 0\n", "\n", " for _ in range(n):\n", " state = proposal.propose(rng)\n", " accrate += 1 if (problem.A @ state <= problem.b).all() else 0\n", "\n", " accrates[i, k] = 1.*accrate / n\n" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "analytical = 1./2**dims\n", "\n", "plt.figure(dpi=300)\n", "plt.plot(dims, accrates, label=['Hit-and-Run', 'Gaussian'])\n", "plt.plot(dims, analytical, linestyle='dashed', color='gray')\n", "\n", "plt.xlabel(r'dimension $d$')\n", "plt.ylabel(r'acceptance rate $\\alpha$')\n", "\n", "plt.legend()\n", "\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "dims = np.array(range(1, 14))\n", "Problem = lambda dim: hopsy.add_box_constraints(\n", " hopsy.Problem(-np.identity(dim), [0]*dim, hopsy.Gaussian(mean=[0]*dim)), 0, 1e3)\n", "\n", "proposals = [\n", " hopsy.GaussianHitAndRunProposal,\n", " hopsy.GaussianProposal,\n", "]\n", "\n", "accrates = np.zeros((len(dims), len(proposals)))\n", "\n", "for i, dim in enumerate(dims):\n", " for k, Proposal in enumerate(proposals):\n", " problem = Problem(dim)\n", " mc = hopsy.MarkovChain(problem, Proposal, starting_point=[.001]*dim)\n", " rng = hopsy.RandomNumberGenerator(seed=42)\n", "\n", " accrate, _ = hopsy.sample(mc, rng, 10*2**dim)\n", "\n", " accrates[i, k] = accrate[0]\n" ] }, { "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": [ "analytical = 1./2**dims\n", "\n", "plt.figure(dpi=300)\n", "plt.plot(dims, accrates, label=['Hit-and-Run', 'Gaussian'])\n", "plt.plot(dims, analytical, linestyle='dashed', color='gray')\n", "\n", "plt.xlabel(r'dimension $d$')\n", "plt.ylabel(r'acceptance rate $\\alpha$')\n", "\n", "plt.legend()\n", "\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "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": "3.10.6" } }, "nbformat": 4, "nbformat_minor": 4 }