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Article Dans Une Revue ACM Transactions on Mathematical Software Année : 2023

Truncated Log-concave Sampling for Convex Bodies with Reflective Hamiltonian Monte Carlo

Résumé

We introduce Reflective Hamiltonian Monte Carlo (ReHMC), an HMC-based algorithm to sample from a log-concave distribution restricted to a convex body. The random walk is based on incorporating reflections to the Hamiltonian dynamics such that the support of the target density is the convex body. We develop an efficient open source implementation of ReHMC and perform an experimental study on various high-dimensional datasets. The experiments suggest that ReHMC outperforms Hit-and-Run and Coordinate-Hit-and-Run regarding the time it needs to produce an independent sample, introducing practical truncated sampling in thousands of dimensions.
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Dates et versions

hal-04222039 , version 1 (28-09-2023)

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Apostolos Chalkis, Vissarion Fisikopoulos, Marios Papachristou, Elias Tsigaridas. Truncated Log-concave Sampling for Convex Bodies with Reflective Hamiltonian Monte Carlo. ACM Transactions on Mathematical Software, 2023, 49 (2), pp.1-25. ⟨10.1145/3589505⟩. ⟨hal-04222039⟩
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