文章基本信息

标题：Rank penalized estimators for high-dimensional matrices
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作者：Olga Klopp
期刊名称：Electronic Journal of Statistics
印刷版ISSN：1935-7524
出版年度：2011
卷号：5
页码：1161-1183
DOI：10.1214/11-EJS637
语种：English
出版社：Institute of Mathematical Statistics
摘要：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.