Intrinsic Gaussian processes on complex constrained domains

• 成果类型: Article
• 署名作者: Niu, Mu; Cheung, Pokman; Lin, Lizhen; Dai, Zhenwen; Lawrence, Neil; Dunson, David
• 署名单位: University of Plymouth; University of Notre Dame; University of Sheffield; Amazon.com; Duke University
• 刊物名称: JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
• ISSN/ISSBN: 1369-7412
• DOI: 10.1111/rssb.12320
• 发表日期: 2019
• 页码: 603-627
• 关键词: brownian-motion; time

摘要

We propose a class of intrinsic Gaussian processes (GPs) for interpolation, regression and classification on manifolds with a primary focus on complex constrained domains or irregularly shaped spaces arising as subsets or submanifolds of R, R2, R3 and beyond. For example, intrinsic GPs can accommodate spatial domains arising as complex subsets of Euclidean space. Intrinsic GPs respect the potentially complex boundary or interior conditions as well as the intrinsic geometry of the spaces. The key novelty of the approach proposed is to utilize the relationship between heat kernels and the transition density of Brownian motion on manifolds for constructing and approximating valid and computationally feasible covariance kernels. This enables intrinsic GPs to be practically applied in great generality, whereas existing approaches for smoothing on constrained domains are limited to simple special cases. The broad utilities of the intrinsic GP approach are illustrated through simulation studies and data examples.