On the potential benefits of entropic regularization for smoothing Wasserstein estimators
hal.structure.identifier | Université de Bordeaux [UB] | |
hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
dc.contributor.author | BIGOT, Jérémie | |
hal.structure.identifier | Université de Bordeaux [UB] | |
hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
dc.contributor.author | FREULON, Paul | |
hal.structure.identifier | Statistics In System biology and Translational Medicine [SISTM] | |
hal.structure.identifier | Vaccine Research Institute [Créteil, France] [VRI] | |
hal.structure.identifier | Bordeaux population health [BPH] | |
dc.contributor.author | HEJBLUM, Boris P. | |
hal.structure.identifier | Université de Bordeaux [UB] | |
hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
dc.contributor.author | LECLAIRE, Arthur | |
dc.date.accessioned | 2024-04-04T02:36:58Z | |
dc.date.available | 2024-04-04T02:36:58Z | |
dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/190767 | |
dc.description.abstractEn | This paper is focused on the study of entropic regularization in optimal transport as a smoothing method for Wasserstein estimators, through the prism of the classical tradeoff between approximation and estimation errors in statistics. Wasserstein estimators are defined as solutions of variational problems whose objective function involves the use of an optimal transport cost between probability measures. Such estimators can be regularized by replacing the optimal transport cost by its regularized version using an entropy penalty on the transport plan. The use of such a regularization has a potentially significant smoothing effect on the resulting estimators. In this work, we investigate its potential benefits on the approximation and estimation properties of regularized Wasserstein estimators. Our main contribution is to discuss how entropic regularization may reach, at a lowest computational cost, statistical performances that are comparable to those of un-regularized Wasserstein estimators in statistical learning problems involving distributional data analysis. To this end, we present new theoretical results on the convergence of regularized Wasserstein estimators. We also study their numerical performances using simulated and real data in the supervised learning problem of proportions estimation in mixture models using optimal transport. | |
dc.language.iso | en | |
dc.title.en | On the potential benefits of entropic regularization for smoothing Wasserstein estimators | |
dc.type | Document de travail - Pré-publication | |
dc.subject.hal | Statistiques [stat]/Machine Learning [stat.ML] | |
dc.identifier.arxiv | 2210.06934 | |
bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
bordeaux.institution | Université de Bordeaux | |
bordeaux.institution | Bordeaux INP | |
bordeaux.institution | CNRS | |
hal.identifier | hal-03908229 | |
hal.version | 1 | |
hal.origin.link | https://hal.archives-ouvertes.fr//hal-03908229v1 | |
bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.au=BIGOT,%20J%C3%A9r%C3%A9mie&FREULON,%20Paul&HEJBLUM,%20Boris%20P.&LECLAIRE,%20Arthur&rft.genre=preprint |
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