Sampling with Riemannian Hamiltonian Monte Carlo in a Constrained SpaceDownload PDF

Published: 31 Oct 2022, 18:00, Last Modified: 14 Oct 2022, 01:16NeurIPS 2022 AcceptReaders: Everyone
Keywords: Sampling, Hamiltonian Monte Carlo
TL;DR: We demonstrate for the first time that ill-conditioned, non-smooth, constrained distributions in very high dimension, can be sampled efficiently in practice, outperforming existing packages by orders of magnitude.
Abstract: We demonstrate for the first time that ill-conditioned, non-smooth, constrained distributions in very high dimension, upwards of 100,000, can be sampled efficiently \emph{in practice}. Our algorithm incorporates constraints into the Riemannian version of Hamiltonian Monte Carlo and maintains sparsity. This allows us to achieve a mixing rate independent of smoothness and condition numbers. On benchmark data sets in systems biology and linear programming, our algorithm outperforms existing packages by orders of magnitude. In particular, we achieve a 1,000-fold speed-up for sampling from the largest published human metabolic network (RECON3D). Our package has been incorporated into a popular Bioinformatics library.
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