Title: Functional BART
Authors: Carlos Carvalho - The University of Texas at Austin (United States) [presenting]
Abstract: The aim is to introduce functional BART, a new approach for functional response regression--that is, estimating a functional mean response $f(t)$ that depends upon a set of scalar covariates $x$. Functional BART, or funBART, is based on the Bayesian Additive Regression Trees (BART) model. The original BART model is an ensemble of regression trees; funBART extends this model to an ensemble of functional regression trees, in which the terminal nodes of each tree are parametrized by functions rather than scalar responses. Just like the original BART model, funBART offers an appealing combination of flexibility with user-friendliness: it captures complex nonlinear relationships and interactions among the predictors, while eliminating many of the onerous ``researcher degrees of freedom'' involved in function-on-scalar regression using standard tools. In particular, functional BART does not require the user to specify a functional form or basis set for $f(t)$, to manually choose interactions, or to use a multi-step approach to select model terms or basis coefficients. Our model replaces all of these choices by a single smoothing parameter, which can either be chosen to reflect prior knowledge or tuned in a data-dependent way.