Aggregation by exponential weighting, sharp PAC-Bayesian bounds and sparsity

Arnak S. Dalalyan (1) , Alexandre Tsybakov (1)

1 LPMA - Laboratoire de Probabilités et Modèles Aléatoires

We study the problem of aggregation under the squared loss in the model of regression with deterministic design. We obtain sharp PAC-Bayesian risk bounds for aggregates defined via exponential weights, under general assumptions on the distribution of errors and on the functions to aggregate. We then apply these results to derive sparsity oracle inequalities.

Mots clés: aggregation; nonparametric regression; oracle inequalities; sparsity

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

Arnak S. Dalalyan, Alexandre Tsybakov. Aggregation by exponential weighting, sharp PAC-Bayesian bounds and sparsity. Machine Learning, 2008, 72 (1-2), pp.39-61. ⟨10.1007/s10994-008-5051-0⟩. ⟨hal-00265651v2⟩