Download this article
 Download this article For screen
For printing
Recent Issues
Volume 15, Issue 1
Volume 14, Issue 2
Volume 14, Issue 1
Volume 13, Issue 1
Volume 12, Issue 2
Volume 12, Issue 1
Volume 11, Issue 2
Volume 11, Issue 1
The Journal
About the journal
Ethics and policies
Peer-review process
 
Submission guidelines
Submission form
Editorial board
 
Subscriptions
 
ISSN 2693-3004 (online)
ISSN 2693-2997 (print)
Author Index
To Appear
 
Other MSP Journals
This article is available for purchase or by subscription. See below.
Sampling lattice points in a polytope: a Bayesian biased algorithm with random updates

Miles Bakenhus and Sonja Petrović

Vol. 15 (2024), No. 1, 61–83
Abstract

The set of nonnegative integer lattice points in a polytope, also known as the fiber of a linear map, makes an appearance in several applications including optimization and statistics. We address the problem of sampling from this set using three ingredients: an easy-to-compute lattice basis of the constraint matrix, a biased sampling algorithm with a Bayesian framework, and a stepwise selection method. The bias embedded in our algorithm updates sampler parameters to improve fiber discovery rate at each step chosen from previously discovered elements. We showcase the performance of the algorithm on several examples, including fibers that are out of reach for the state-of-the-art Markov bases samplers.

PDF Access Denied

We have not been able to recognize your IP address 44.220.251.236 as that of a subscriber to this journal.
Online access to the content of recent issues is by subscription, or purchase of single articles.

Please contact your institution's librarian suggesting a subscription, for example by using our journal-recom­mendation form. Or, visit our subscription page for instructions on purchasing a subscription.

You may also contact us at contact@msp.org
or by using our contact form.

Or, you may purchase this single article for USD 40.00:

Keywords
Markov basis, biased sampling, fiber sampling
Mathematical Subject Classification
Primary: 62-08, 62R01
Secondary: 52B20
Milestones
Received: 18 July 2023
Revised: 20 February 2024
Accepted: 27 March 2024
Published: 17 May 2024
Authors
Miles Bakenhus
Department of Applied Mathematics
Illinois Institute of Technology
Chicago, IL
United States
Sonja Petrović
Department of Applied Mathematics
Illinois Institute of Technology
Chicago, IL
United States