Computing Kantorovich distance with a MCMC of moves
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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 a set of real-valued 2-way tables with assigned margins. We apply to this case the methodology of moves which is usually applied in Algebraic Statistics to contingency tables.
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