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.
More precisely, introduce for alli∈[2 rdy], Ai =A+ 2Cε√r QiW ⊤ −r,whereQ i ∈ P dy r , andC≥1is a universal constant previously defined in Lemma 4.1
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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.