Iterative methods for fitting a Gaussian Random Field (GRF) model via maximum likelihood (ML) estimation requires solving a nonconvex optimization problem. The problem is aggravated for anisotropic GRFs where the number of covariance function parameters increases with the dimension. Even evaluation of the likelihood function requires O(n3) floating point operations, where n denotes the number of data locations. In this paper1, we propose a new two-stage procedure to estimate the parameters of second-order stationary GRFs. First, a convex likelihood problem regularized with a weighted `1-norm, utilizing the available distance information between observation locations, is solved to fit a sparse precision (inverse covariance) matrix to the observed data. Second, the parameters of the covariance function are estimated by solving a least squares problem. Theoretical error bounds for the solutions of stage I and II problems are provided, and their tightness are investigated.
|Original language||English (US)|
|Journal||Journal of Machine Learning Research|
|State||Published - Oct 2020|
All Science Journal Classification (ASJC) codes
- Control and Systems Engineering
- Statistics and Probability
- Artificial Intelligence