Derives instance-specific lower bounds on sample complexity for rank-adaptive matrix estimation and proposes a least-squares plus universal singular-value-thresholding algorithm whose finite-sample error nearly matches those bounds.
Tight oracle inequalities for low-rank matrix recovery from a minimal number of noisy random measurements.IEEE Transactions on Information Theory, 57(4):2342–2359
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Nonconvex low-rank matrix estimation procedures are shown to be equivalent to locally strongly convex formulations via a benign regularizer that does not change the algorithm's update rule.
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Near-optimal Rank Adaptive Inference of High Dimensional Matrices
Derives instance-specific lower bounds on sample complexity for rank-adaptive matrix estimation and proposes a least-squares plus universal singular-value-thresholding algorithm whose finite-sample error nearly matches those bounds.
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Convexity in Disguise: A Theoretical Framework for Nonconvex Low-Rank Matrix Estimation
Nonconvex low-rank matrix estimation procedures are shown to be equivalent to locally strongly convex formulations via a benign regularizer that does not change the algorithm's update rule.