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

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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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

Information

Received: 1 March 2020; Published: 2021
First available in Project Euclid: 22 January 2021

Digital Object Identifier: 10.1214/21-EJS1804

Subjects:
Secondary: 62H17 62H05

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Vol.15 • No. 1 • 2021
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