{ "cells": [ { "cell_type": "markdown", "id": "4d73e2fc", "metadata": {}, "source": [ "# Product Constraint Examples\n", "\n", "This notebook demonstrates **product constraints**, a feature unique to exact HMC that allows sampling from regions defined by products of linear and quadratic constraints.\n", "\n", "A product constraint has the form:\n", "\n", "$$\\prod_{i=1}^k \\left( \\mathbf{x}^\\top A_i \\mathbf{x} + \\mathbf{f}_i^\\top \\mathbf{x} + c_i \\right) \\geq 0$$\n", "\n", "Each factor is itself a linear or quadratic constraint. The product is satisfied when an **even number** of the individual factors are negative (or all are non-negative). This allows sampling from non-convex regions that cannot be expressed as a single quadratic constraint. HMC handles them naturally by computing the exact hit times for each factor and composing them into a product constraint.\n", "\n", "Product constraints are added via `add_product_constraint`, which takes a list of parameter dictionaries, one per factor.\n", "\n", "## Setup\n", "\n", "Install notebook dependencies if needed:\n", "```bash\n", "pip install tmg_hmc[examples]\n", "```" ] }, { "cell_type": "code", "execution_count": 1, "id": "d8c8e1cb", "metadata": {}, "outputs": [], "source": [ "from tmg_hmc import TMGSampler\n", "import matplotlib.pyplot as plt\n", "import numpy as np\n", "\n", "# Set seed for reproducibility\n", "np.random.seed(42)" ] }, { "cell_type": "markdown", "id": "8486bc42", "metadata": {}, "source": [ "## Star Constraint\n", "\n", "We sample from $\\mathcal{N}(\\mathbf{0}, \\Sigma)$ constrained to the region defined by:\n", "\n", "$$(x_1 x_2 + 1)(-x_1 x_2 + 1) \\geq 0$$\n", "\n", "i.e. $x_1 x_2 \\in [-1, 1]$, which carves out a star-shaped region bounded by the hyperbolas $x_1 x_2 = 1$ and $x_1 x_2 = -1$.\n", "\n", "Each factor is a simple quadratic constraint with no linear term ($\\mathbf{f} = 0$, $\\boldsymbol{\\mu} = \\mathbf{0}$):\n", "\n", "**Factor 1:** $x_1 x_2 + 1 \\geq 0$, specified with:\n", "$$A_1 = \\begin{pmatrix} 0 & 0.5 \\\\ 0.5 & 0 \\end{pmatrix}, \\quad c_1 = 1$$\n", "\n", "**Factor 2:** $-x_1 x_2 + 1 \\geq 0$, specified with:\n", "$$A_2 = \\begin{pmatrix} 0 & -0.5 \\\\ -0.5 & 0 \\end{pmatrix}, \\quad c_2 = 1$$\n", "\n", "Since $\\boldsymbol{\\mu} = \\mathbf{0}$ and $S = \\Sigma^{1/2}$, both factors become `SimpleQuadraticConstraint`s in the transformed space (the non-identity covariance of $\\Sigma$ does not introduce linear terms since $\\boldsymbol{\\mu} = \\mathbf{0}$). To further illustrate the effect of the truncations, we plot the untruncated mean and 1 and 2 $\\sigma$ ellipsoids of the untruncated Gaussian in red." ] }, { "cell_type": "code", "execution_count": 2, "id": "52d745b0", "metadata": {}, "outputs": [], "source": [ "mu = np.array([0.0, 0.0]).reshape(-1, 1)\n", "sigma = 3 * np.array([[1.0, -0.6], [-0.6, 1.0]])\n", "sampler = TMGSampler(mu, sigma, gpu=False)\n", "\n", "# Define the product constraint (x1*x2 + 1)(-x1*x2 + 1) >= 0\n", "# This is satisfied when x1*x2 is in [-1, 1], carving out a star-shaped region\n", "# Each factor is a SimpleQuadraticConstraint: x^T A x + c >= 0\n", "parameters = [\n", " # Factor 1: x1*x2 + 1 >= 0 => A = [[0, 0.5], [0.5, 0]], c = 1\n", " {\"A\": np.array([[0, 0.5], [0.5, 0]]), \"c\": 1.0},\n", " # Factor 2: -x1*x2 + 1 >= 0 => A = [[0, -0.5], [-0.5, 0]], c = 1\n", " {\"A\": np.array([[0, -0.5], [-0.5, 0]]), \"c\": 1.0},\n", "]\n", "sampler.add_product_constraint(parameters=parameters)\n", "\n", "# Initial point must satisfy the product constraint: x1*x2 = 0 which is in [-1, 1]\n", "x0 = np.array([-1, 0]).reshape(-1, 1)\n", "samples = sampler.sample(x0, 1000, 100)" ] }, { "cell_type": "code", "execution_count": 3, "id": "7d301953", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Compute 1-sigma and 2-sigma ellipses of the untruncated distribution\n", "theta = np.linspace(0, 2 * np.pi, 100)\n", "scale = np.linalg.cholesky(sigma)\n", "ellipse = np.array(\n", " [scale @ np.array([np.cos(t), np.sin(t)]).reshape(-1, 1) + mu for t in theta]\n", ")\n", "ellipse2 = np.array(\n", " [2 * scale @ np.array([np.cos(t), np.sin(t)]).reshape(-1, 1) + mu for t in theta]\n", ")\n", "\n", "fig, ax = plt.subplots()\n", "ax.scatter(samples[:, 0], samples[:, 1], alpha=0.5)\n", "ax.scatter(x0[0], x0[1], color=\"k\", marker=\"x\", label=\"Start point\")\n", "\n", "# Plot the constraint boundary: hyperbolas x1*x2 = 1 and x1*x2 = -1\n", "x = np.linspace(0, 5, 101)[1:]\n", "ax.plot(x, 1.0 / x, color=\"black\", linestyle=\"--\", label=\"Constraint Boundary\")\n", "ax.plot(x, -1.0 / x, color=\"black\", linestyle=\"--\")\n", "ax.plot(-x, 1.0 / x, color=\"black\", linestyle=\"--\")\n", "ax.plot(-x, -1.0 / x, color=\"black\", linestyle=\"--\")\n", "\n", "# Plot untruncated mean and covariance ellipses for reference\n", "ax.scatter(mu[0], mu[1], color=\"red\", label=\"Untruncated Mean\")\n", "ax.plot(\n", " ellipse[:, 0],\n", " ellipse[:, 1],\n", " color=\"red\",\n", " linestyle=\"--\",\n", " label=r\"1$\\sigma$ Ellipse\",\n", ")\n", "ax.plot(\n", " ellipse2[:, 0],\n", " ellipse2[:, 1],\n", " color=\"red\",\n", " linestyle=\":\",\n", " label=r\"2$\\sigma$ Ellipse\",\n", ")\n", "ax.legend()\n", "ax.set_xlim(-5, 5)\n", "ax.set_ylim(-5, 5)\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": null, "id": "d8aa3b2f", "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "tmg", "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": "3.10.19" } }, "nbformat": 4, "nbformat_minor": 5 }