hdtg: An R package for high-dimensional truncated normal simulation

TL;DR

The hdtg R package offers efficient, rejection-free algorithms for high-dimensional multivariate truncated normal distribution simulation, outperforming existing methods in terms of speed and effectiveness.

Contribution

Introduction of the hdtg package implementing harmonic-HMC and Zigzag-HMC algorithms for high-dimensional MTN simulation, providing a general and efficient computational tool.

Findings

Zigzag-HMC and harmonic-HMC achieve 100 effective samples within 3,600 seconds for dimensions 100 to 1,600.

Both algorithms outperform the minimax tilting accept-reject sampler (MET) in high-dimensional scenarios.

Guidance provided on selecting appropriate methods based on correlation structures.

Abstract

Simulating from the multivariate truncated normal distribution (MTN) is required in various statistical applications yet remains challenging in high dimensions. Currently available algorithms and their implementations often fail when the number of parameters exceeds a few hundred. To provide a general computational tool to efficiently sample from high-dimensional MTNs, we introduce the hdtg package that implements two state-of-the-art simulation algorithms: harmonic Hamiltonian Monte Carlo (harmonic-HMC) and zigzag Hamiltonian Monte Carlo (Zigzag-HMC). Both algorithms exploit analytical solutions of the Hamiltonian dynamics under a quadratic potential energy with hard boundary constraints, leading to rejection-free methods. We compare their efficiencies against another state-of-the-art algorithm for MTN simulation, the minimax tilting accept-reject sampler (MET). The run-time of these three approaches heavily depends on the underlying multivariate normal correlation structure. Zigzag-HMC and harmonic-HMC both achieve 100 effective samples within 3,600 seconds across all tests with dimension ranging from 100 to 1,600, while MET has difficulty in several high-dimensional examples. We provide guidance on how to choose an appropriate method for a given situation and illustrate the usage of hdtg.