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Stochastic Billiards for Sampling from the Boundary of a Convex Set

Stochastic Billiards for Sampling from the Boundary of a Convex Set Stochastic billiards can be used for approximate sampling from the boundary of a bounded convex set through the Markov Chain Monte Carlo paradigm. This paper studies how many steps of the underlying Markov chain are required to get samples (approximately) from the uniform distribution on the boundary of the set, for sets with an upper bound on the curvature of the boundary. Our main theorem implies a polynomial-time algorithm for sampling from the boundary of such sets. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Mathematics of Operations Research INFORMS

Stochastic Billiards for Sampling from the Boundary of a Convex Set

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Stochastic Billiards for Sampling from the Boundary of a Convex Set

Dieker, A. B.; Vempala, Santosh S.
Mathematics of Operations Research , Volume 40 (4): 14 – Oct 12, 2015

Abstract

Stochastic billiards can be used for approximate sampling from the boundary of a bounded convex set through the Markov Chain Monte Carlo paradigm. This paper studies how many steps of the underlying Markov chain are required to get samples (approximately) from the uniform distribution on the boundary of the set, for sets with an upper bound on the curvature of the boundary. Our main theorem implies a polynomial-time algorithm for sampling from the boundary of such sets.

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Publisher
INFORMS
Copyright
Copyright © INFORMS
Subject
Research Article
ISSN
0364-765X
eISSN
1526-5471
DOI
10.1287/moor.2014.0701
Publisher site
See Article on Publisher Site

Abstract

Stochastic billiards can be used for approximate sampling from the boundary of a bounded convex set through the Markov Chain Monte Carlo paradigm. This paper studies how many steps of the underlying Markov chain are required to get samples (approximately) from the uniform distribution on the boundary of the set, for sets with an upper bound on the curvature of the boundary. Our main theorem implies a polynomial-time algorithm for sampling from the boundary of such sets.

Journal

Mathematics of Operations Research – INFORMS

Published: Oct 12, 2015

Keywords: Keywords : Markov Chain Monte Carlo ; rapid mixing ; sampling ; stochastic billiard

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