AISTATS 2023poster11 citations
Bures-Wasserstein Barycenters and Low-Rank Matrix Recovery
Tyler Maunu, Thibaut Le Gouic, Philippe Rigollet
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.
BibTeX
@InProceedings{pmlr-v206-maunu23a,
title = {Bures-Wasserstein Barycenters and Low-Rank Matrix Recovery},
author = {Maunu, Tyler and Le Gouic, Thibaut and Rigollet, Philippe},
booktitle = {Proceedings of The 26th International Conference on Artificial Intelligence and Statistics},
pages = {8183--8210},
year = {2023},
editor = {Ruiz, Francisco and Dy, Jennifer and van de Meent, Jan-Willem},
volume = {206},
series = {Proceedings of Machine Learning Research},
month = {25--27 Apr},
publisher = {PMLR},
pdf = {https://proceedings.mlr.press/v206/maunu23a/maunu23a.pdf},
url = {https://proceedings.mlr.press/v206/maunu23a.html},
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.}
}