论文标题
Bures-Wasserstein Barycenters和低级矩阵恢复
Bures-Wasserstein Barycenters and Low-Rank Matrix Recovery
论文作者
论文摘要
我们回顾了使用最佳运输工具从排名一预测中恢复低级别正半数矩阵的问题。更具体地说，我们表明，此问题的变异表述等同于计算垃圾塞林重中心。反过来，这种新的观点可以开发新的几何一阶方法，具有强大的收敛性，可以保证Bures-Wasserstein距离。模拟数据的实验证明了我们新方法比现有方法的优势。
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.
