Le transport optimal entropique correspond à l'estimateur du maximum de vraisemblance en déconvolution

Philippe Rigollet; Jonathan Weed

doi:10.1016/j.crma.2018.10.010

Le transport optimal entropique correspond à l'estimateur du maximum de vraisemblance en déconvolution

Translated title of the contribution: Entropic optimal transport is maximum-likelihood deconvolution

Philippe Rigollet, Jonathan Weed

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We give a statistical interpretation of entropic optimal transport by showing that performing maximum-likelihood estimation for Gaussian deconvolution corresponds to calculating a projection with respect to the entropic optimal transport distance. This structural result gives theoretical support for the wide adoption of these tools in the machine learning community.

Translated title of the contribution	Entropic optimal transport is maximum-likelihood deconvolution
Original language	French
Pages (from-to)	1228-1235
Number of pages	8
Journal	Comptes Rendus Mathematique
Volume	356
Issue number	11-12
DOIs	https://doi.org/10.1016/j.crma.2018.10.010
State	Published - Nov 1 2018

ASJC Scopus subject areas

Mathematics(all)

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10.1016/j.crma.2018.10.010

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title = "Le transport optimal entropique correspond {\`a} l'estimateur du maximum de vraisemblance en d{\'e}convolution",

abstract = "We give a statistical interpretation of entropic optimal transport by showing that performing maximum-likelihood estimation for Gaussian deconvolution corresponds to calculating a projection with respect to the entropic optimal transport distance. This structural result gives theoretical support for the wide adoption of these tools in the machine learning community.",

author = "Philippe Rigollet and Jonathan Weed",

note = "Funding Information: This work was supported by the National Science Foundation [ DGE-1122374 to J.W.; DMS-1712596 , TRIPODS-1740751 to P.R.], the Office of Naval Research [ N00014-17-1-2147 to P.R.], the Chan Zuckerberg Initiative DAF, a donor advised fund of the Silicon Valley Community Foundation [ 2018-182642 to P.R.]; and the MIT Skoltech Program [MIT Skoltech Seed Fund to P.R.]. Publisher Copyright: {\textcopyright} 2018 Acad{\'e}mie des sciences",

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doi = "10.1016/j.crma.2018.10.010",

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AU - Weed, Jonathan

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Y1 - 2018/11/1

N2 - We give a statistical interpretation of entropic optimal transport by showing that performing maximum-likelihood estimation for Gaussian deconvolution corresponds to calculating a projection with respect to the entropic optimal transport distance. This structural result gives theoretical support for the wide adoption of these tools in the machine learning community.

AB - We give a statistical interpretation of entropic optimal transport by showing that performing maximum-likelihood estimation for Gaussian deconvolution corresponds to calculating a projection with respect to the entropic optimal transport distance. This structural result gives theoretical support for the wide adoption of these tools in the machine learning community.

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Le transport optimal entropique correspond à l'estimateur du maximum de vraisemblance en déconvolution

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