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Abstract
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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.
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Keywords
Markov basis, biased sampling, fiber sampling
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Mathematical Subject Classification
Primary: 62-08, 62R01
Secondary: 52B20
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Milestones
Received: 18 July 2023
Revised: 20 February 2024
Accepted: 27 March 2024
Published: 17 May 2024
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