Intrinsic Gaussian processes on complex constrained domains

Niu, M., Cheung, P., Lin, L., Dai, Z., Lawrence, N. and Dunson, D. (2019) Intrinsic Gaussian processes on complex constrained domains. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 81(3), pp. 603-627. (doi: 10.1111/rssb.12320)

Abstract

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.

• Item Type: Articles
• Additional Information: Lizhen Lin acknowledges support for this paper from National Science Foundation grants DMS CAREER 1654579 and IIS 1663870.
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Niu, Dr Mu
• Authors: Niu, M., Cheung, P., Lin, L., Dai, Z., Lawrence, N., and Dunson, D.
• College/School: College of Science and Engineering > School of Mathematics and Statistics > Statistics
• Journal Name: Journal of the Royal Statistical Society: Series B (Statistical Methodology)
• Publisher: Wiley
• ISSN: 1369-7412
• ISSN (Online): 1467-9868
• Published Online: 19 April 2019
• Copyright Holders: Copyright © 2019 Royal Statistical Society
• First Published: First published in Journal of the Royal Statistical Society: Series B (Statistical Methodology) 81(3):603-627
• Publisher Policy: Reproduced in accordance with the copyright policy of the publisher