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, where f is L-smooth and m-strongly-convex, within accuracy \varepsilon after } \widetilde O(\kappa d^2 \ell^2 \log (1 / \varepsilon)) steps for a well-rounded polytope, ignoring logarithmic factors where \kappa is the condition number of the negative log-density, d is the dimension, \ell is an upper bound on the number of reflections, and \varepsilon 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  .
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 \pi(x) \propto e^{-f(x), where f is L-smooth and m-strongly-convex, within accuracy \varepsilon after } \widetilde O(\kappa d^2 \ell^2 \log (1 / \varepsilon)) steps for a well-rounded convex body where \kappa = L / m is the condition number of the negative log-density, d is the dimension, \ell is an upper bound on the number of reflections, and \varepsilon 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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polytope
body
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it mixes in
the walk mixes to a log-concave target distribution \pi(x) \propto e^{-f(x)
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polytope, ignoring logarithmic factors where \kappa
convex body where \kappa = L / m
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efficient
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Experiments
The experiments
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and introduces practical truncated sampling in thousands of dimensions