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Apprentissage de dictionnaire pour les représentations parcimonieuses

Rémi Gribonval 1 Rodolphe Jenatton 2, 3 Francis Bach 2, 4 Martin Kleinsteuber 5 Matthias Seibert 5
1 PANAMA - Parcimonie et Nouveaux Algorithmes pour le Signal et la Modélisation Audio
IRISA-D5 - SIGNAUX ET IMAGES NUMÉRIQUES, ROBOTIQUE, Inria Rennes – Bretagne Atlantique
2 SIERRA - Statistical Machine Learning and Parsimony
DI-ENS - Département d'informatique de l'École normale supérieure, Inria Paris-Rocquencourt, CNRS - Centre National de la Recherche Scientifique : UMR8548
Abstract : A popular approach within the signal processing and machine learning communities consists in modelling high-dimensional data as sparse linear combinations of atoms selected from a dictionary. Given the importance of the choice of the dictionary for the operational deployment of these tools, a growing interest for \emph{learned} dictionaries has emerged. The most popular dictionary learning techniques, which are expressed as large-scale matrix factorization through the optimization of a non convex cost function, have been widely disseminated thanks to extensive empirical evidence of their success and steady algorithmic progress. Yet, until recently they remained essentially heuristic. We will present recent work on statistical aspects of sparse dictionary learning, contributing to the characterization of the excess risk as a function of the number of training samples. The results cover non only sparse dictionary learning but also a much larger class of constrained matrix factorization problems.
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Rémi Gribonval, Rodolphe Jenatton, Francis Bach, Martin Kleinsteuber, Matthias Seibert. Apprentissage de dictionnaire pour les représentations parcimonieuses. 46e Journées de Statistique, Société Française de Statistique, Jun 2014, Rennes, France. ⟨hal-01054122⟩

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