Rank penalized estimators for high-dimensional matrices
Klopp, Olga (2011), Rank penalized estimators for high-dimensional matrices, Electronic Journal of Statistics, 5, p. 1161-1183. http://dx.doi.org/10.1214/11-EJS637
TypeArticle accepté pour publication ou publié
External document linkhttp://hal.archives-ouvertes.fr/hal-00583884/fr/
Journal nameElectronic Journal of Statistics
Institute of Mathematical Statistics
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Abstract (EN)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 $A_0$ corrupted by noise. We propose a new rank penalized estimator of $A_0$. 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 problem of matrix completion when our estimator has a particularly simple form: it is obtained by hard thresholding of the singular values of a matrix constructed from the observations.
Subjects / Keywordslow rank matrix estimation; matrix completion; recovery of the rank; statistical learning
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