Graph based Gaussian processes on restricted domains

David B. Dunson, Hau‐Tieng Wu and Nan Wu

Journal of the Royal Statistical Society Series B, 2022, vol. 84, issue 2, 414-439

Abstract: In nonparametric regression, it is common for the inputs to fall in a restricted subset of Euclidean space. Typical kernel‐based methods that do not take into account the intrinsic geometry of the domain across which observations are collected may produce sub‐optimal results. In this article, we focus on solving this problem in the context of Gaussian process (GP) models, proposing a new class of Graph Laplacian based GPs (GL‐GPs), which learn a covariance that respects the geometry of the input domain. As the heat kernel is intractable computationally, we approximate the covariance using finitely‐many eigenpairs of the Graph Laplacian (GL). The GL is constructed from a kernel which depends only on the Euclidean coordinates of the inputs. Hence, we can benefit from the full knowledge about the kernel to extend the covariance structure to newly arriving samples by a Nyström type extension. We provide substantial theoretical support for the GL‐GP methodology, and illustrate performance gains in various applications.

Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://doi.org/10.1111/rssb.12486

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:bla:jorssb:v:84:y:2022:i:2:p:414-439

Ordering information: This journal article can be ordered from
http://ordering.onli ... 1111/(ISSN)1467-9868

Access Statistics for this article

Journal of the Royal Statistical Society Series B is currently edited by P. Fryzlewicz and I. Van Keilegom

More articles in Journal of the Royal Statistical Society Series B from Royal Statistical Society Contact information at EDIRC.
Bibliographic data for series maintained by Wiley Content Delivery ().