Statistical optimal transport via factored couplings
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forrow19a.pdf
Description
Published version
Size
1.81 MB
Format
Adobe PDF
Checksum (MD5)
241da08cfa513adb173970589c859357
Author(s)
Forrow, A
Hütter, JC
Nitzan, M
Rigollet, P
Schiebinger, G
Weed, J
Date Issued
2019
Journal
AISTATS 2019 - 22nd International Conference on Artificial Intelligence and Statistics
Citation
Forrow, A, Hütter, JC, Nitzan, M, Rigollet, P, Schiebinger, G et al. 2019. "Statistical optimal transport via factored couplings." AISTATS 2019 - 22nd International Conference on Artificial Intelligence and Statistics, 89.
Version
Final published version
Abstract
© 2019 by the author(s). We propose a new method to estimate Wasserstein distances and optimal transport plans between two probability distributions from samples in high dimension. Unlike plug-in rules that simply replace the true distributions by their empirical counterparts, our method promotes couplings with low transport 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 high-dimensional data for various tasks, including domain adaptation in single-cell RNA sequencing data. These findings are supported by a theoretical analysis that indicates that the transport rank is key in overcoming the curse of dimensionality inherent to data-driven optimal transport.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Statistics and Data Science Center (Massachusetts Institute of Technology)
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Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
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DOI of Published Version
http://proceedings.mlr.press/v89/forrow19a.html
