Graph based Gaussian processes on restricted domains

David B. Dunson, Hau Tieng Wu, Nan Wu

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish (US)
Pages (from-to)414-439
Number of pages26
JournalJournal of the Royal Statistical Society. Series B: Statistical Methodology
Issue number2
StatePublished - Apr 2022


  • Bayesian
  • graph Laplacian
  • heat kernel
  • manifold
  • nonparametric regression
  • restricted domain
  • semi-supervised

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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