• Corpus ID: 234742153

On the Pythagorean Structure of the Optimal Transport for Separable Cost Functions

  title={On the Pythagorean Structure of the Optimal Transport for Separable Cost Functions},
  author={Gennaro Auricchio},
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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