Open Access
February 2014 Anisotropic function estimation using multi-bandwidth Gaussian processes
Anirban Bhattacharya, Debdeep Pati, David Dunson
Ann. Statist. 42(1): 352-381 (February 2014). DOI: 10.1214/13-AOS1192


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. Zanten (2009) showed that rescaling a homogeneous smooth


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Anirban Bhattacharya. Debdeep Pati. David Dunson. "Anisotropic function estimation using multi-bandwidth Gaussian processes." Ann. Statist. 42 (1) 352 - 381, February 2014.


Published: February 2014
First available in Project Euclid: 19 March 2014

zbMATH: 1360.62168
MathSciNet: MR3189489
Digital Object Identifier: 10.1214/13-AOS1192

Primary: 62G07 , 62G20
Secondary: 60K35

Keywords: adaptive , anisotropic , Bayesian nonparametrics , Function estimation , Gaussian process , rate of convergence

Rights: Copyright © 2014 Institute of Mathematical Statistics

Vol.42 • No. 1 • February 2014
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