Bures-Wasserstein Barycenters and Low-Rank Matrix Recovery

Tyler Maunu, Thibaut Le Gouic, Philippe Rigollet
Proceedings of The 26th International Conference on Artificial Intelligence and Statistics, PMLR 206:8183-8210, 2023.

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 this Paper

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.} }
Endnote
%0 Conference Paper %T Bures-Wasserstein Barycenters and Low-Rank Matrix Recovery %A Tyler Maunu %A Thibaut Le Gouic %A Philippe Rigollet %B Proceedings of The 26th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2023 %E Francisco Ruiz %E Jennifer Dy %E Jan-Willem van de Meent %F pmlr-v206-maunu23a %I PMLR %P 8183--8210 %U https://proceedings.mlr.press/v206/maunu23a.html %V 206 %X 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.
APA
Maunu, T., Le Gouic, T. & Rigollet, P.. (2023). Bures-Wasserstein Barycenters and Low-Rank Matrix Recovery. Proceedings of The 26th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 206:8183-8210 Available from https://proceedings.mlr.press/v206/maunu23a.html.

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