Intersecting singularities for multi-structured estimation

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Emile Richard, Francis BACH, Jean-Philippe Vert ;
Proceedings of the 30th International Conference on Machine Learning, PMLR 28(3):1157-1165, 2013.

Abstract

We address the problem of designing a convex nonsmooth regularizer encouraging multiple structural effects simultaneously. Focusing on the inference of sparse and low-rank matrices we suggest a new complexity index and a convex penalty approximating it. The new penalty term can be written as the trace norm of a linear function of the matrix. By analyzing theoretical properties of this family of regularizers we come up with oracle inequalities and compressed sensing results ensuring the quality of our regularized estimator. We also provide algorithms and supporting numerical experiments.

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