B0660
Title: Bayesian projection pursuit regression
Authors: Gavin Collins - Sandia National Laboratories (United States)
Devin Francom - Los Alamos National Laboratory (United States) [presenting]
Kellin Rumsey - Los Alamos National Laboratory (United States)
Abstract: In projection pursuit regression (PPR), an unknown response function is approximated by the sum of M "ridge functions," which are flexible functions of one-dimensional projections of a multivariate input space. Traditionally, optimization routines are used to estimate the projection directions and ridge functions via a sequential algorithm, and M is typically chosen via cross-validation. The first (to the best knowledge) Bayesian version of PPR is introduced, which has the benefit of accurate uncertainty quantification. To learn the projection directions and ridge functions, novel adaptations of methods used for the single ridge function case $(M=1)$, called the single index model, for which Bayesian implementations do exist; then use reversible jump MCMC to learn the number of ridge functions M. The predictive ability of the model is evaluated in 20 simulation scenarios and for 23 real datasets, in a bake-off against an array of state-of-the-art regression methods. Its effective performance indicates that Bayesian projection pursuit regression is a valuable addition to the existing regression toolbox.
