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arXiv · 2104.07097

Novel Matrix Hit and Run for Sampling Polytopes and Its GPU Implementation

Mario Vazquez Corte·Luis V. Montiel
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Abstract

We propose and analyze a new Markov Chain Monte Carlo algorithm that generates a uniform sample over full and non-full dimensional polytopes. This algorithm, termed "Matrix Hit and Run" (MHAR), is a modification of the Hit and Run framework. For the regime $n^{1+\frac{1}{3}} \ll m$, MHAR has a lower asymptotic cost per sample in terms of soft-O notation ($\SO$) than do existing sampling algorithms after a \textit{warm start}. MHAR is designed to take advantage of matrix multiplication routines that require less computational and memory resources. Our tests show this implementation to be substantially faster than the \textit{hitandrun} R package, especially for higher dimensions. Finally, we provide a python library based on Pytorch and a Colab notebook with the implementation ready for deployment in architectures with GPU or just CPU.

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BibTeXRIS

Mario Vazquez Corte, Luis V. Montiel. 2021-04-14. Novel Matrix Hit and Run for Sampling Polytopes and Its GPU Implementation. https://arxiv.org/abs/2104.07097

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