PAC-Bayesian Estimation and Prediction in Sparse Additive Models

Benjamin Guedj (1) , Pierre Alquier (2)

1 LSTA - Laboratoire de Statistique Théorique et Appliquée
2 School of Mathematical Sciences [Dublin]

The present paper is about estimation and prediction in high-dimensional additive models under a sparsity assumption ($p\gg n$ paradigm). A PAC-Bayesian strategy is investigated, delivering oracle inequalities in probability. The implementation is performed through recent outcomes in high-dimensional MCMC algorithms, and the performance of our method is assessed on simulated data.

Mots clés: Additive models; sparsity; regression estimation; PAC-Bayesian bounds; oracle inequality; MCMC; stochastic search

Domaines: Méthodologie [stat.ME]; Théorie [stat.TH]

Benjamin Guedj, Pierre Alquier. PAC-Bayesian Estimation and Prediction in Sparse Additive Models. 2012. ⟨hal-00722969v1⟩