Finite space Kantorovich problem with an MCMC of table moves

2020/02/24 by Pistone, Giovanni, Rapallo, Fabio, Rogantin, Maria Piera
#62R01 65C05 62H17 62H05 #Computation (stat.CO) #FOS: Computer and information sciences #Methodology (stat.ME)

paper · doi:10.48550/arxiv.2002.10335

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.

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