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.
Lemma A.4.There exists a universal constantc≈0.17such thatb≥e −1−log(2) 3 − 1 2 −c q k 2
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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.