ANISOTROPIC FUNCTION ESTIMATION USING MULTI-BANDWIDTH GAUSSIAN PROCESSES

• 成果类型: Article
• 署名作者: Bhattacharya, Anirban; Pati, Debdeep; Dunson, David
• 署名单位: Texas A&M University System; Texas A&M University College Station; State University System of Florida; Florida State University; Duke University
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/13-AOS1192
• 发表日期: 2014
• 页码: 352-381
• 关键词: bayesian density-estimation; posterior distributions; variable selection; convergence-rates; model selection; inference; bounds

摘要

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.