PAC-Bayesian Estimation and Prediction in Sparse Additive Models

TL;DR

This paper introduces a PAC-Bayesian approach for estimation and prediction in high-dimensional sparse additive models, providing theoretical guarantees and demonstrating effectiveness through simulations.

Contribution

It develops a novel PAC-Bayesian framework tailored for sparse additive models in high dimensions, with implementation via advanced MCMC algorithms.

Findings

Provides oracle inequalities with high probability

Demonstrates good performance on simulated data

Integrates recent high-dimensional MCMC methods

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.