Seminar:Posterior Covariance Structures in Gaussian Processes for Uncertainty Quantification

Seminar| Institute of Mathematical Sciences

Time:Friday, August 1th, 2025,14:30-15:30

Abstract: Gaussian process (GP) regression is a powerful tool for uncertainty quantification. A central task in GP lies in the computation of the posterior distribution, which can be prohibitively expensive due to the calculation of the posterior covariance matrix. In this talk, we present a comprehensive study on the posterior covariance. We offer geometric interpretations that reveal how the posterior covariance is affected by different factors, including observation data and the bandwidth parameter in the prior covariance. The new geometric understanding can be used to design efficient indicators for the posterior variance and covariance without having to compute the dense covariance matrix. It can also be used to design efficient preconditioners and approximations for the dense covariance matrix. Extensive experiments were conducted to demonstrate the theoretical findings, the performance of the proposed posterior indicators, as well as the failure of existing acceleration techniques when the bandwidth parameter falls out of certain range.