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A Consistent Extension of Discrete Optimal Transport Maps for Machine Learning Applications

Abstract : Optimal transport maps define a one-to-one correspondence between probability distributions, and as such have grown popular for machine learning applications. However, these maps are generally defined on empirical observations and cannot be generalized to new samples while preserving asymptotic properties. We extend a novel method to learn a consistent estimator of a continuous optimal transport map from two empirical distributions. The consequences of this work are two-fold: first, it enables to extend the transport plan to new observations without computing again the discrete optimal transport map; second, it provides statistical guarantees to machine learning applications of optimal transport. We illustrate the strength of this approach by deriving a consistent framework for transport-based counterfactual explanations in fairness.
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Preprints, Working Papers, ...
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https://hal.archives-ouvertes.fr/hal-03142788
Contributor : Alberto Gonzalez-Sanz <>
Submitted on : Tuesday, February 16, 2021 - 12:04:03 PM
Last modification on : Friday, February 19, 2021 - 1:24:01 PM

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  • HAL Id : hal-03142788, version 1

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Lucas de Lara, Alberto González-Sanz, Jean-Michel Loubes. A Consistent Extension of Discrete Optimal Transport Maps for Machine Learning Applications. 2021. ⟨hal-03142788⟩

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