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Finite space Kantorovich problem with an MCMC of table moves

02/24/2020

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by Giovanni Pistone, et al.

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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 nonegative-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 an Monte Carlo Markov Chain solution algorithm.

Giovanni Pistone
9 publications
Fabio Rapallo
9 publications
Maria Piera Rogantin
2 publications

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