Open Access
2011 Rank penalized estimators for high-dimensional matrices
Olga Klopp
Electron. J. Statist. 5: 1161-1183 (2011). DOI: 10.1214/11-EJS637


In this paper we consider the trace regression model. Assume that we observe a small set of entries or linear combinations of entries of an unknown matrix A0 corrupted by noise. We propose a new rank penalized estimator of A0. For this estimator we establish general oracle inequality for the prediction error both in probability and in expectation. We also prove upper bounds for the rank of our estimator. Then, we apply our general results to the problems of matrix completion and matrix regression. In these cases our estimator has a particularly simple form: it is obtained by hard thresholding of the singular values of a matrix constructed from the observations.


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Olga Klopp. "Rank penalized estimators for high-dimensional matrices." Electron. J. Statist. 5 1161 - 1183, 2011.


Published: 2011
First available in Project Euclid: 6 October 2011

zbMATH: 1274.62489
MathSciNet: MR2842903
Digital Object Identifier: 10.1214/11-EJS637

Primary: 60B20 , 60G15 , 62H12 , 62J99

Keywords: low rank matrix estimation , Matrix completion , recovery of the rank , Statistical learning

Rights: Copyright © 2011 The Institute of Mathematical Statistics and the Bernoulli Society

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