Sparse Bayesian nonparametric regression.

Francois Caron, Arnaud Doucet

Abstract: One of the most common problems in machine learning and statistics consists of estimating the mean response Xβ from a vector of observations y assuming y = Xβ + ε where X is known, β is a vector of parameters of interest and ε a vector of stochastic errors. We are particularly interested here in the case where the dimension K of β is much higher than the dimension of y. We propose some flexible Bayesian models which can yield sparse estimates of β. We show that as K → ∞ these models are closely related to a class of Lévy processes. Simulations demonstrate that our models outperform significantly a range of popular alternatives.