Aggregation for Linear Inverse Problems

Mohamed Hebiri (1) , Jean-Michel Loubes (2) , Paul Rochet (3)

1 LAMA - Laboratoire d'Analyse et de Mathématiques Appliquées
2 IMT - Institut de Mathématiques de Toulouse UMR5219
3 LMJL - Laboratoire de Mathématiques Jean Leray

In the framework of inverse problems, we consider the question of aggregating estimators taken from a given collection. Extending usual results for the direct case, we propose a new penalty to achieve the best aggregation. An oracle inequality provides the asymptotic behavior of this estimator. We investigate here the price for considering indirect observations.

Mots clés: Aggregation; Inverse problem; LASSO

Domaines: Statistiques [math.ST]; Théorie [stat.TH]

Mohamed Hebiri, Jean-Michel Loubes, Paul Rochet. Aggregation for Linear Inverse Problems. 2014. ⟨hal-00994717⟩