2011/11/30 by Anirban Bhattacharya, Debdeep Pati, David Dunson · 2 citations
Computer Science · Engineering · Mathematics · #Algorithm #Anisotropy #Applied mathematics #Bandwidth (computing) #Computer science #Control Systems and Identification #Gaussian #Gaussian Processes and Bayesian Inference #Gaussian process #Kriging #Mathematical analysis #Mathematical optimization #Mathematics #Minimax #Multivariate statistics #Nonparametric regression #Nonparametric statistics #Optics #Physics #Regression #Smoothness #Statistical Methods and Inference #Statistics #math.ST #stat.TH
paper · pdf · doi:10.1214/13-aos1192
published as Annals of Statistics 2014, Vol. 42, No. 1, 352-381 · Published in at http://dx.doi.org/10.1214/13-AOS1192 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)
openalex publication_date 2014/02/01 · arxiv created 2014/03/21 · arxiv updated 2015/03/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.