Finite space Kantorovich problem with an MCMC of table moves
Methodology
2021-01-14 v3 Computation
Abstract
In Optimal Transport (OT) on a finite metric space, one defines a distance on the probability simplex that extends the distance on the ground space. The distance is the value of a Linear Programming (LP) problem on the set of non-negative-valued 2-way tables with assigned probability functions as margins. We apply to this case the methodology of moves from Algebraic Statistics (AS) and use it to derive a Monte Carlo Markov Chain (MCMC) solution algorithm.
Keywords
Cite
@article{arxiv.2002.10335,
title = {Finite space Kantorovich problem with an MCMC of table moves},
author = {Giovanni Pistone and Fabio Rapallo and Maria Piera Rogantin},
journal= {arXiv preprint arXiv:2002.10335},
year = {2021}
}
Comments
25 pages; a proof has been added and some notational issues have been fixed