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.
Dimension reduction and coefficient estimation in multivariate linear regression.Journal of the Royal Statistical Society: Series B (Statistical Methodology), 69(3):329–346
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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.