Title: Fitting Gaussian random fields to large data sets
Speaker: Sam Davanloo Tajbakhsh (OSU, Industrial and Systems Engineering)
Abstract: Fitting a Gaussian Random Field (GRF) model to spatial data by maximizing the likelihood function suffers from nonconvexity. The problem is aggravated for anisotropic GRFs where the number of covariance function parameters increases with the domain dimension. In this work, we propose a new two-step GRF fitting procedure when the process is second-order stationary. First, a convex likelihood problem regularized with a weighted \ell_1 norm, utilizing the available distance information between observation locations, is solved to get a sparse precision (inverse covariance) matrix. Second, the GRF covariance function parameters are estimated by solving a least-square problem. Theoretical error bounds for the proposed estimator are provided; moreover, convergence of the estimator is shown as the number of samples per location increases.
Seminar URL: u.osu.edu/probability
