{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# A Quick Tutorial\n", "\n", "In this example, we sample a truncated Gaussian distribution centered at the origin and restricted to a simplex. To reduce the amount of required code, we rely on hopsy.setup() to heuristically set sensible defaults for us.\n", "The simplex inequality is given as\n", "$$\n", " Ax = \\begin{pmatrix}\n", " 1 & 1 & \\cdots & 1 \\\\\n", " -1 & 0 & \\cdots & 0 \\\\\n", " 0 & -1 & \\cdots & 0 \\\\\n", " \\vdots & \\vdots & \\cdots & \\vdots \\\\\n", " 0 & 0 & \\cdots & -1\n", " \\end{pmatrix} \\begin{pmatrix}\n", " x_1 \\\\\n", " \\vdots \\\\\n", " x_n\n", " \\end{pmatrix} \\leq \\begin{pmatrix}\n", " 1 \\\\\n", " 0 \\\\\n", " \\vdots \\\\\n", " 0\n", " \\end{pmatrix} = b,\n", "$$\n", "with $A \\in \\mathbb{R}^{m \\times n}$, $x \\in \\mathbb{R}^n$ and $b \\in \\mathbb{R}^m$.\n", "Since the Gaussian distribution is included in ``hopsy`` as a model, \n", "we do not have to worry further about it for the following example." ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "ExecuteTime": { "end_time": "2024-04-28T15:42:10.987720Z", "start_time": "2024-04-28T15:42:10.894672Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Set parameter Username\n", "Academic license - for non-commercial use only - expires 2025-03-22\n", "Acceptance rates (per chain): 1.0 1.0 1.0 1.0\n", "Ess (for all chains): [[19990.02206217 19463.9249551 18939.15180953]]\n", "Ess per chain (100+ is usually good enough): [[4997.50551554 4865.98123877 4734.78795238]]\n" ] }, { "data": { "image/png": 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import hopsy\n", "import matplotlib.pyplot as plt\n", "import numpy as np\n", "\n", "# set up the polytope inequality for a 3-dimensional simplex\n", "A, b = [[1, 1, 1], [-1, 0, 0], [0, -1, 0], [0, 0, -1]], [1, 0, 0, 0]\n", "\n", "# create a 3-dimensional gaussian model centered at the origin\n", "model = hopsy.Gaussian(mean=[0.5, 0.25, 0], covariance=0.01*np.identity(3))\n", "\n", "# set up the problem\n", "problem = hopsy.Problem(A, b, model)\n", "\n", "# hopsy.setup creates markov chains with a herustic selection of proposal algorithm and tunes the acceptance rate of the chains, if the chains have the step size parameter.\n", "# For the case of a Gaussian on the polytope, the TruncatedGaussianProposal is the best algorithm and it is automatically selected.\n", "random_seed = 511\n", "n_chains = 4 # Not required, will use number of available cpu cores otherwise\n", "chains, rngs = hopsy.setup(problem, random_seed=random_seed, n_chains=n_chains)\n", "# Below we run hopsy.setup again but overwrite the default proposal selection and use markov chain tuning\n", "\n", "# and now for the fun!\n", "n_samples = 5000\n", "accrate, states = hopsy.sample(chains, rngs, n_samples=n_samples, thinning=10)\n", "\n", "# when doing mcmc, assessing convergence is very important!\n", "rhat = hopsy.rhat(states, series=10)\n", "\n", "print('Acceptance rates (per chain):', *accrate)\n", "\n", "ess = hopsy.ess(states)\n", "print('Ess (for all chains):', hopsy.ess(states))\n", "print('Ess per chain (100+ is usually good enough):', ess/len(chains))\n", "\n", "fig, ax = plt.subplots(1, 1, figsize=(12,7))\n", "plt.suptitle(\"Convergence diagnostic\", fontsize=18)\n", "\n", "ax.plot(range(10, n_samples+10, 10), rhat)\n", "# The convergence threshold depends on how strict the sample quality is evaluated. Typical values are 1.1, 1.05, 1.02 and 1.01.\n", "ax.plot([0, n_samples], [1.05, 1.05], linestyle='dashed', color='gray',\n", " label='Convergence threshold')\n", "\n", "ax.set_xlabel(r\"$n_{samples}$\", fontsize=14)\n", "ax.set_ylabel(r\"$\\hat{R}$\", fontsize=14)\n", "ax.legend(fontsize=14)\n", "\n", "\n", "n_dims = 3\n", "n_cols = 3\n", "n_rows = 1\n", "plt.figure(figsize=(n_cols * 4, n_rows * 4))\n", "plt.subplot(n_rows, n_cols, 1)\n", "plt.suptitle(\"Marginal densities\", fontsize=18)\n", "\n", "for dim in range(n_dims):\n", " plt.subplot(n_rows, n_cols, dim + 1)\n", " plt.title(f\"dimension {dim}\", fontsize=14)\n", " chain_index = 0 \n", " _, bins, _ = plt.hist(\n", " states[chain_index,:,dim],\n", " bins=50,\n", " density=True,\n", " label=f\"chain {chain_index}\" if dim == 0 else None,\n", " alpha=0.75,\n", " color=\"C0\")\n", " for chain_index in range(1, n_chains):\n", " _ = plt.hist(\n", " states[chain_index,:,dim],\n", " bins=bins,\n", " alpha=0.5,\n", " density=True,\n", " label=f\"chain {chain_index}\" if dim == 0 else None,\n", " color=f\"C{chain_index}\",\n", " )\n", "\n", " plt.ylabel('density', fontsize=12)\n", " plt.xlabel('value', fontsize=12)\n", "\n", "plt.figlegend(fontsize=12, loc='lower right')\n", "plt.tight_layout()\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": "3.12.4" } }, "nbformat": 4, "nbformat_minor": 4 }