ANISOTROPIC FUNCTION ESTIMATION USING MULTI-BANDWIDTH GAUSSIAN PROCESSES. Academic Article

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

• Bhattacharya, Anirban
• Pati, Debdeep

published proceedings

• Ann Stat

author list (cited authors)

• Bhattacharya, A., Pati, D., & Dunson, D.

citation count

• 40

complete list of authors

• Bhattacharya, Anirban||Pati, Debdeep||Dunson, David

publication date

• February 2014

publisher

• Institute of Mathematical Statistics  Publisher

published in

• ANNALS OF STATISTICS  Journal

keywords

• Adaptive
• Anisotropic
• Bayesian Nonparametrics
• Function Estimation
• Gaussian Process
• Rate Of Convergence

PubMed Central ID

• 25288827

Digital Object Identifier (DOI)

• 10.1214/13-AOS1192

start page

• 352

end page

• 381

volume

• 42

issue

• 1

URL

• http://dx.doi.org/10.1214/13-aos1192