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.
Hankel matrix rank minimization with applications to system identification and realization.SIAM Journal on Matrix Analysis and Applications, 34(3):946–977, 2013
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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.