Intersecting singularities for multi-structured estimation

Emile Richard (1, 2) , Francis Bach (3, 4) , Jean-Philippe Vert (2, 1)

1 CBIO - Centre de Bioinformatique
2 Cancer et génome: Bioinformatique, biostatistiques et épidémiologie d'un système complexe
3 SIERRA - Statistical Machine Learning and Parsimony
4 LIENS - Laboratoire d'informatique de l'école normale supérieure

We address the problem of designing a convex nonsmooth regularizer encouraging multiple structural effects simultaneously. Focus- ing 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 in- equalities and compressed sensing results ensuring the quality of our regularized estimator. We also provide algorithms and support- ing numerical experiments.

Domaines: Apprentissage [cs.LG]

Emile Richard, Francis Bach, Jean-Philippe Vert. Intersecting singularities for multi-structured estimation. ICML 2013 - 30th International Conference on Machine Learning, Jun 2013, Atlanta, United States. ⟨hal-00918253⟩