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.
Citation
Giovanni Pistone. Fabio Rapallo. Maria Piera Rogantin. "Finite space Kantorovich problem with an MCMC of table moves." Electron. J. Statist. 15 (1) 880 - 907, 2021. https://doi.org/10.1214/21-EJS1804
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