title: ANISOTROPIC FUNCTION ESTIMATION USING MULTI-BANDWIDTH GAUSSIAN PROCESSES.
abstract: In nonparametric regression problems involving multiple predictors, there is typically interest in estimating an anisotropic multivariate regression surface in the important predictors while discarding the unimportant ones. Our focus is on defining a Bayesian procedure that leads to the minimax optimal rate of posterior contraction (up to a log factor) adapting to the unknown dimension and anisotropic smoothness of the true surface. We propose such an approach based on a Gaussian process prior with dimension-specific scalings, which are assigned carefully-chosen hyperpriors. We additionally show that using a homogenous Gaussian process with a single bandwidth leads to a sub-optimal rate in anisotropic cases.
authors.affiliation: Duke University.
authors.forename: Anirban
authors.initials: A
authors.lastname: Bhattacharya
authors.affiliation: Florida State University.
authors.forename: Debdeep
authors.initials: D
authors.lastname: Pati
authors.affiliation: Duke University.
authors.forename: David
authors.initials: D
authors.lastname: Dunson
keywords: Adaptive; Anisotropic; Bayesian nonparametrics; Function estimation; Gaussian process; Rate of convergence