Truncated Log-concave Sampling with Reflective Hamiltonian Monte Carlo

Abstract

We introduce Reflective Hamiltonian Monte Carlo (ReHMC), an HMC-based algorithm, to sample from a log-concave distribution restricted to a convex polytope. We prove that, starting from a warm start, it mixes in O(κd 2 2 log(1/ε)) steps for a well-rounded polytope, ignoring logarithmic factors where κ is the condition number of the negative log-density, d is the dimension, is an upper bound on the number of reflections, and ε is the accuracy parameter. We also developed an open source implementation of ReHMC and we performed an experimental study on various high-dimensional data-sets. Experiments suggest that ReHMC outperfroms Hit-and-Run and Coordinate-Hit-and-Run regarding the time it needs to produce an independent sample.

CHRRT: boosting coordinate hit-and-run with rounding by thinning

“…Concerning the question of how the computational requirements of CHRRT scale with effective model dimension, our numerical results reveal a quadratic and linear correlation for simplices and GEMs, respectively. Benchmarking new UPCS algorithms and comparing their performances with those of leading algorithms, such as CHRRT, is important to advance the field and a topic of active research (Chalkis et al, 2021b). Recognizing the substantial impact of thinning on the performance of CHRRT, we advise performing comparisons with tuned thinning, and to report the used thinning constant, which will help their reproduction.…”