Année
2011
Abstract
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.
KLOPP, O. (2011). Rank penalized estimators for high-dimensional matrices. The Electronic Journal of Statistics, 5, pp. 1161-1183.