Home > Research > Publications & Outputs > Efficient computation of the volume of a polyto...

Electronic data

  • AISTATS_Efficient Computation

    Final published version, 588 KB, PDF document

    Available under license: CC BY: Creative Commons Attribution 4.0 International License

Keywords

View graph of relations

Efficient computation of the volume of a polytope in high-dimensions using Piecewise Deterministic Markov Processes

Research output: Contribution to Journal/MagazineConference articlepeer-review

Published
<mark>Journal publication date</mark>28/03/2022
<mark>Journal</mark>Proceedings of Machine Learning Research
Volume151
Number of pages15
Pages (from-to)10146-10160
Publication StatusPublished
<mark>Original language</mark>English

Abstract

Computing the volume of a polytope in high dimensions is computationally challenging but has wide applications. Current state-of-the-art algorithms to compute such volumes rely on efficient sampling of a Gaussian distribution restricted to the polytope, using e.g. Hamiltonian Monte Carlo. We present a new sampling strategy that uses a Piecewise Deterministic Markov Process. Like Hamiltonian Monte Carlo, this new method involves simulating trajectories of a non-reversible process and inherits similar good mixing properties. However, importantly, the process can be simulated more easily due to its piecewise linear trajectories - and this leads to a reduction of the computational cost by a factor of the dimension of the space. Our experiments indicate that our method is numerically robust and is one order of magnitude faster (or better) than existing methods using Hamiltonian Monte Carlo. On a single core processor, we report computational time of a few minutes up to dimension 500.