Locally Adaptive Bayes Nonparametric Regression via Nested Gaussian Processes

• 成果类型: Article
• 署名作者: Zhu, Bin; Dunson, David B.
• 署名单位: National Institutes of Health (NIH) - USA; NIH National Cancer Institute (NCI); NIH National Cancer Institute- Division of Cancer Epidemiology & Genetics; Duke University
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2013.838568
• 发表日期: 2013
• 页码: 1445-1456
• 关键词: mass-spectrometry data; variable selection; posterior consistency; splines; quantification

摘要

We propose a nested Gaussian process (nGP) as a locally adaptive prior for Bayesian nonparametric regression. Specified through a set of stochastic differential equations (SDEs), the nGP imposes a Gaussian process prior for the function's mth-order derivative. The nesting comes in through including a local instantaneous mean function, which is drawn from another Gaussian process inducing adaptivity to locally varying smoothness. We discuss the support of the nGP prior in terms of the closure of a reproducing kernel Hilbert space, and consider theoretical properties of the posterior. The posterior mean under the nGP prior is shown to be equivalent to the minimizer of a nested penalized sum-of-squares involving penalties for both the global and local roughness of the function. Using highly efficient Markov chain Monte Carlo for posterior inference, the proposed method performs well in simulation studies compared to several alternatives, and is scalable to massive data, illustrated through a proteomics application.