Seminario IMC: Regularized estimation for highly multivariate spatial Gaussian random fields

El Instituto de Ingeniería Matemática y Computacional (IMC) invita al seminario que se dictará el miércoles 6 de mayo.

Miércoles 6 de mayo de 2026, 13:40 hrs. (Presencial en sala segundo piso (DILAB), Edificio Carreras Interdisciplinarias). Link Zoom disponible escribiendo a imc@uc.cl)

ABSTRACT

Estimating covariance parameters for multivariate spatial Gaussian random fields is computationally challenging, as the number of parameters grows rapidly with the number of variables, and likelihood evaluation requires operations of order O((np)^3). In many applications, however, not all cross-dependencies between variables are relevant, suggesting that sparse covariance structures may be both statistically advantageous and practically necessary. We propose a LASSO-penalized estimation framework that induces sparsity in the Cholesky factor of the multivariate Matérn correlation matrix, enabling automatic identification of uncorrelated variable pairs while preserving positive semidefiniteness. Estimation is carried out via a projected block coordinate descent algorithm that decomposes the optimization into tractable subproblems, with constraints enforced at each iteration through appropriate projections. Regularization parameter selection is discussed for both the likelihood and composite likelihood approaches. We conduct a simulation study demonstrating the ability of the method to recover sparse correlation structures and reduce estimation error relative to unpenalized approaches. We illustrate our procedure through an application to a geochemical dataset with p = 36 variables and n = 3998 spatial locations, showing the practical impact of the method and making spatial prediction feasible in a setting where standard approaches fail entirely.

BIO

Francisco Cuevas is an Assistant Professor at Federico Santa María Technical University. He obtained a Mathematical Engineering degree and a Mathematics MSc from UTFSM, followed by a PhD in Mathematics/Statistics from Aalborg University (Denmark) after working as a data analyst at BCI. His research focuses on estimation, prediction, and inference methods for geostatistical data and point patterns.

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