This was part of Expressing and Exploiting Structure in Modeling, Theory, and Computation with Gaussian Processes

Scalable Gaussian-Process Inference Using Vecchia Approximations

Matthias Katzfuss, Texas A&M University
Tuesday, August 30, 2022

Abstract: Gaussian processes (GPs) are popular, flexible, and interpretable probabilistic models for functions in geospatial analysis, computer-model emulation, and machine learning. However, direct application of GPs involves dense covariance matrices and is computationally infeasible for large datasets. We consider a framework for fast GP inference based on the so-called Vecchia approximation, which implies a sparse Cholesky factor of the inverse covariance matrix. The approximation can be written in closed form and computed in parallel, and it includes many popular existing approximations as special cases. We discuss various applications and extensions of the framework, including latent and nonisotropic GPs.