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arXiv · 2210.14671

Bures-Wasserstein Barycenters and Low-Rank Matrix Recovery

Tyler Maunu·Thibaut Le Gouic·Philippe Rigollet
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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.

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Tyler Maunu, Thibaut Le Gouic, Philippe Rigollet. 2022-10-26. Bures-Wasserstein Barycenters and Low-Rank Matrix Recovery. https://arxiv.org/abs/2210.14671

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