Optimal singular value shrinkage for operator norm loss: Extending to non-square matrices

William Leeb

doi:10.1016/j.spl.2022.109472

Optimal singular value shrinkage for operator norm loss: Extending to non-square matrices

William Leeb

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We correct a formula of Gavish and Donoho for singular value shrinkage with operator norm loss for non-square matrices. We also observe that in the classical regime, optimal shrinkage for any Schatten loss converges to the best linear predictor.

Original language	English (US)
Article number	109472
Journal	Statistics and Probability Letters
Volume	186
DOIs	https://doi.org/10.1016/j.spl.2022.109472
State	Published - Jul 2022

Bibliographical note

Funding Information:
I thank Edgar Dobriban for helpful feedback on an earlier version of this manuscript. I acknowledge support from the NSF, United States of America BIGDATA program IIS 1837992 and BSF, Israel award 2018230 .

Publisher Copyright:
© 2022 Elsevier B.V.

Keywords

Best linear predictor
Linear prediction
Operator norm loss
Schatten loss
Singular value shrinkage

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KW - Operator norm loss

KW - Schatten loss

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Optimal singular value shrinkage for operator norm loss: Extending to non-square matrices

Abstract

Bibliographical note

Keywords

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