Model Consistency for Learning with Mirror-Stratifiable Regularizers
Fadili, Jalal; Garrigos, Guillaume; Malick, Jérôme; Peyré, Gabriel (2019-04), Model Consistency for Learning with Mirror-Stratifiable Regularizers, 22nd International Conference on Artificial Intelligence and Statistics (AISTATS) 2019, 2019-04, Naha, Japan
TypeCommunication / Conférence
External document linkhttps://hal.archives-ouvertes.fr/hal-01988309
Conference title22nd International Conference on Artificial Intelligence and Statistics (AISTATS) 2019
MetadataShow full item record
Groupe de Recherche en Informatique, Image et Instrumentation de Caen [GREYC]
Université Paris 7
Laboratoire Jean Kuntzmann [LJK]
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Abstract (EN)Low-complexity non-smooth convex regular-izers are routinely used to impose some structure (such as sparsity or low-rank) on the coefficients for linear predictors in supervised learning. Model consistency consists then in selecting the correct structure (for instance support or rank) by regularized empirical risk minimization. It is known that model consistency holds under appropriate non-degeneracy conditions. However such conditions typically fail for highly correlated designs and it is observed that regularization methods tend to select larger models. In this work, we provide the theoretical underpinning of this behavior using the notion of mirror-stratifiable regular-izers. This class of regularizers encompasses the most well-known in the literature, including the 1 or trace norms. It brings into play a pair of primal-dual models, which in turn allows one to locate the structure of the solution using a specific dual certificate. We also show how this analysis is applicable to optimal solutions of the learning problem, and also to the iterates computed by a certain class of stochastic proximal-gradient algorithms.
Subjects / KeywordsMirror-Stratifiable Regularizers
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