Papers › Truncated Log-concave Sampling with Reflective Hamiltonian Monte Carlo
Truncated Log-concave Sampling with Reflective Hamiltonian Monte Carlo
Apostolos Chalkis, Vissarion Fisikopoulos, Marios Papachristou, Elias Tsigaridas
We introduce Reflective Hamiltonian Monte Carlo (ReHMC), an HMC-based algorithm, to sample from a log-concave distribution restricted to a convex body. We prove that, starting from a warm start, the walk mixes to a log-concave target distribution π(x) ∝e⁻ᶠ⁽ˣ⁾, where f is L-smooth and m-strongly-convex, within accuracy ε after O(κd² ℓ² log(1 / ε)) steps for a well-rounded convex body where κ= L / m is the condition number of the negative log-density, d is the dimension, ℓ is an upper bound on the number of reflections, and ε is the accuracy parameter. We also developed an efficient open source implementation of ReHMC and we performed an experimental study on various high-dimensional data-sets. The experiments suggest that ReHMC outperfroms Hit-and-Run and Coordinate-Hit-and-Run regarding the time it needs to produce an independent sample and introduces practical truncated sampling in thousands of dimensions.
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