Statistical Optimal Transport via Factored Couplings

Aden Forrow, Jan-Christian Hütter, Mor Nitzan, Philippe Rigollet, Geoffrey Schiebinger, Jonathan Weed
Proceedings of the Twenty-Second International Conference on Artificial Intelligence and Statistics, PMLR 89:2454-2465, 2019.

Abstract

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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v89-forrow19a, title = {Statistical Optimal Transport via Factored Couplings}, author = {Forrow, Aden and H\"{u}tter, Jan-Christian and Nitzan, Mor and Rigollet, Philippe and Schiebinger, Geoffrey and Weed, Jonathan}, booktitle = {Proceedings of the Twenty-Second International Conference on Artificial Intelligence and Statistics}, pages = {2454--2465}, year = {2019}, editor = {Chaudhuri, Kamalika and Sugiyama, Masashi}, volume = {89}, series = {Proceedings of Machine Learning Research}, month = {16--18 Apr}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v89/forrow19a/forrow19a.pdf}, url = {https://proceedings.mlr.press/v89/forrow19a.html}, abstract = {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.} }
Endnote
%0 Conference Paper %T Statistical Optimal Transport via Factored Couplings %A Aden Forrow %A Jan-Christian Hütter %A Mor Nitzan %A Philippe Rigollet %A Geoffrey Schiebinger %A Jonathan Weed %B Proceedings of the Twenty-Second International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2019 %E Kamalika Chaudhuri %E Masashi Sugiyama %F pmlr-v89-forrow19a %I PMLR %P 2454--2465 %U https://proceedings.mlr.press/v89/forrow19a.html %V 89 %X 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.
APA
Forrow, A., Hütter, J., Nitzan, M., Rigollet, P., Schiebinger, G. & Weed, J.. (2019). Statistical Optimal Transport via Factored Couplings. Proceedings of the Twenty-Second International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 89:2454-2465 Available from https://proceedings.mlr.press/v89/forrow19a.html.

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