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 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
Text
Forrow et al. "Statistical Optimal Transport via Factored Couplings." Artificial Intelligence and Statistics, 2019.Markdown
[Forrow et al. "Statistical Optimal Transport via Factored Couplings." Artificial Intelligence and Statistics, 2019.](https://mlanthology.org/aistats/2019/forrow2019aistats-statistical/)BibTeX
@inproceedings{forrow2019aistats-statistical,
title = {{Statistical Optimal Transport via Factored Couplings}},
author = {Forrow, Aden and Hütter, Jan-Christian and Nitzan, Mor and Rigollet, Philippe and Schiebinger, Geoffrey and Weed, Jonathan},
booktitle = {Artificial Intelligence and Statistics},
year = {2019},
pages = {2454-2465},
volume = {89},
url = {https://mlanthology.org/aistats/2019/forrow2019aistats-statistical/}
}