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Beyond Procrustes: Balancing-Free Gradient Descent for Asymmetric Low-Rank Matrix Sensing
Low-rank matrix estimation plays a central role in various applications across science and engineering.
Nonconvex Matrix Factorization from Rank-One Measurements
We consider the problem of recovering low-rank matrices from random rank-one measurements, which spans numerous applications including covariance sketching, phase retrieval, quantum state tomography, and learning shallow polynomial neural networks, among others.
Nonconvex Low-Rank Matrix Recovery with Arbitrary Outliers via Median-Truncated Gradient Descent
Recent work has demonstrated the effectiveness of gradient descent for directly recovering the factors of low-rank matrices from random linear measurements in a globally convergent manner when initialized properly.
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