tmg-hmc

Exact Hamiltonian Monte Carlo sampling for truncated multivariate Gaussians with quadratic constraints

This package implements the exact HMC algorithm from Pakman and Paninski (2014) for sampling from truncated multivariate Gaussian distributions.

How It Works

The algorithm uses Hamiltonian Monte Carlo with:

  1. Analytic Hamiltonian Dynamics: Particles follow deterministic Hamiltonian trajectories that are analytically computable.

  2. Exact Bounces: When a trajectory hits a constraint boundary, the algorithm computes the exact bounce time by solving the quartic equation for the hit time analytically.

  3. Perfect Acceptance Probability: Unlike standard HMC, there is no integration error in solving the Hamiltonian dynamics, so the acceptance probability is always 1.

See Pakman & Paninski (2014) for mathematical details.

Features

  • Flexible constraints - Supports linear and quadratic inequality constraints

  • Efficient - Uses optimized compiled C++ hit time calculation for efficient sampling

  • GPU acceleration - Optional PyTorch backend for large-scale problems

  • Well-tested - Comprehensive test suite ensuring correctness

Installation

From PyPI:

pip install tmg-hmc

With optional GPU support:

pip install tmg-hmc[gpu]

From source:

git clone https://github.com/erik-a-bensen/tmg_hmc.git
cd tmg_hmc
pip install .

Requirements: Python 3.10+, numpy, scipy. PyTorch is optional for GPU support.

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