Bures-Wasserstein Barycenters and Low-Rank Matrix Recovery
Abstract
We revisit the problem of recovering a low-rank positive semidefinite matrix from rank-one projections using tools from optimal transport. More specifically, we show that a variational formulation of this problem is equivalent to computing a Wasserstein barycenter. In turn, this new perspective enables the development of new geometric first-order methods with strong convergence guarantees in Bures-Wasserstein distance. Experiments on simulated data demonstrate the advantages of our new methodology over existing methods.
Cite
Text
Maunu et al. "Bures-Wasserstein Barycenters and Low-Rank Matrix Recovery." Artificial Intelligence and Statistics, 2023.Markdown
[Maunu et al. "Bures-Wasserstein Barycenters and Low-Rank Matrix Recovery." Artificial Intelligence and Statistics, 2023.](https://mlanthology.org/aistats/2023/maunu2023aistats-bureswasserstein/)BibTeX
@inproceedings{maunu2023aistats-bureswasserstein,
title = {{Bures-Wasserstein Barycenters and Low-Rank Matrix Recovery}},
author = {Maunu, Tyler and Le Gouic, Thibaut and Rigollet, Philippe},
booktitle = {Artificial Intelligence and Statistics},
year = {2023},
pages = {8183-8210},
volume = {206},
url = {https://mlanthology.org/aistats/2023/maunu2023aistats-bureswasserstein/}
}