PAC-Bayesian Estimation and Prediction in Sparse Additive Models

Abstract

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.

28 pages

References in corpus (7)

• Lasso-type recovery of sparse representations for high-dimensional data
• High-dimensional generalized linear models and the lasso
• Sparsity in multiple kernel learning
• Fast learning rates in statistical inference through aggregation
• Fast learning rate of multiple kernel learning: Trade-off between sparsity and smoothness
• PAC-Bayesian Bounds for Randomized Empirical Risk Minimizers
• Pac-bayesian bounds for sparse regression estimation with exponential weights

Cited by in corpus (6)

• Simpler PAC-Bayesian Bounds for Hostile Data
• An Oracle Inequality for Quasi-Bayesian Non-Negative Matrix Factorization
• On Oracle Property and Asymptotic Validity of Bayesian Generalized Method of Moments
• PAC-Bayesian High Dimensional Bipartite Ranking
• A Quasi-Bayesian Perspective to Online Clustering
• PAC-Bayes Bounds for High-Dimensional Multi-Index Models with Unknown Active Dimension