# 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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