Large-Scale Optimal Transport and Mapping Estimation

Abstract : This paper presents a novel two-step approach for the fundamental problem of learning an optimal map from one distribution to another. First, we learn an optimal transport (OT) plan, which can be thought as a one-to-many map between the two distributions. To that end, we propose a stochastic dual approach of regularized OT, and show empirically that it scales better than a recent related approach when the amount of samples is very large. Second, we estimate a \textit{Monge map} as a deep neural network learned by approximating the barycentric projection of the previously-obtained OT plan. This parameterization allows generalization of the mapping outside the support of the input measure. We prove two theoretical stability results of regularized OT which show that our estimations converge to the OT plan and Monge map between the underlying continuous measures. We showcase our proposed approach on two applications: domain adaptation and generative modeling.
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https://hal.inria.fr/hal-01956354
Contributor : Nicolas Courty <>
Submitted on : Saturday, December 15, 2018 - 3:26:20 PM
Last modification on : Friday, September 13, 2019 - 9:50:02 AM

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  • HAL Id : hal-01956354, version 1
  • ARXIV : 1711.02283

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Vivien Seguy, Bharath Bhushan Damodaran, Remi Flamary, Nicolas Courty, Antoine Rolet, et al.. Large-Scale Optimal Transport and Mapping Estimation. ICLR 2018 - International Conference on Learning Representations, Apr 2018, Vancouver, Canada. pp.1-15. ⟨hal-01956354⟩

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