On the Pythagorean Structure of the Optimal Transport for Separable Cost Functions
@inproceedings{Auricchio2021OnTP,
title={On the Pythagorean Structure of the Optimal Transport for Separable Cost Functions},
author={Gennaro Auricchio},
year={2021}
}In this paper, we study the optimal transport problem induced by separable cost functions. In this framework, transportation can be expressed as the composition of two lower-dimensional movements. Through this reformulation, we prove that the random variable inducing the optimal transportation plan enjoys a conditional independence property. We conclude the paper by focusing on some significant settings. In particular, we study the problem in the Euclidean space endowed with the squared…
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