Finite space Kantorovich problem with an MCMC of table moves

24 Feb 2020 · Giovanni Pistone, Fabio Rapallo, Maria Piera Rogantin ·

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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Finite space Kantorovich problem with an MCMC of table moves

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