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.
Bounds on the geodesic distances on the stiefel manifold for a family of riemannian metrics
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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.