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Approximation du transport optimal entre distributions empiriques par flux de normalisation

Abstract : Normalization flows are generic and powerful tools for probabilistic modeling and density estimation. In this paper, we show that this class of models can also be used to approximate the solution of an optimal transport problem between any empirical distributions. Specifically, the optimal transport plan is approximated by an invertible network whose training is based on the relaxation of the Monge formulation. This approach has the advantage of allowing a discretization of this transport plan into a composition of functions associated with each layer of the network, providing intermediate transports between two measures.
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https://hal.archives-ouvertes.fr/hal-03704666
Contributor : Nicolas Dobigeon Connect in order to contact the contributor
Submitted on : Saturday, June 25, 2022 - 1:34:24 PM
Last modification on : Wednesday, September 7, 2022 - 8:14:05 AM
Long-term archiving on: : Monday, September 26, 2022 - 6:57:03 PM

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  • HAL Id : hal-03704666, version 1

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Florentin Coeurdoux, Nicolas Dobigeon, Pierre Chainais. Approximation du transport optimal entre distributions empiriques par flux de normalisation. XXVIIIème Colloque Francophone de Traitement du Signal et des Images (GRETSI 2022), Sep 2022, Nancy, France. ⟨hal-03704666⟩

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