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Statistical optimal transport via factored couplings

Abstract:

We propose a new method to estimate Wasserstein distances and optimal transport plans between two probability distributions from samples in high dimension. Unlike plugin rules that simply replace the true distributions by their empirical counterparts, our method promotes couplings with low trans- port rank, a new structural assumption that is similar to the nonnegative rank of a matrix. Regularizing based on this assumption leads to drastic improvements on highdimensional data for various tas...

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Publication status:
Published
Peer review status:
Peer reviewed
Version:
Publisher's Version

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Institution:
University of Oxford
Division:
MPLS Division
Department:
Mathematical Institute
Hütter, JC More by this author
Rigollet, P More by this author
Schiebinger, G More by this author
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Publisher:
Proceedings of Machine Learning Research Publisher's website
Volume:
89
Pages:
2454-2465
Publication date:
2019-04-11
Acceptance date:
2018-12-24
ISSN:
2640-3498
Pubs id:
pubs:958941
URN:
uri:15e3e28d-86d1-4589-82a3-c6a5f9a35f62
UUID:
uuid:15e3e28d-86d1-4589-82a3-c6a5f9a35f62
Local pid:
pubs:958941

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