Estimation of the covariance matrix of a Gaussian Markov Random Field under a total positivity constraint

Baz, Juan ; Alonso, Pedro ; Peña, Juan Manuel (Universidad de Zaragoza) ; Pérez-Fernández, Raúl

Resumen: Gaussian Markov Random Fields are a popular statistical model that has been used successfully in many fields of application. Recent work has studied conditions under which the covariance matrix of a Gaussian Markov Random Field over a graph of paths is totally positive. In such case, many linear algebra operations concerning the covariance matrix can be performed with High Relative Accuracy (the relative error is of order of machine precision). Unfortunately, classical estimators of the covariance matrix do not necessarily yield a totally positive matrix, even when the population covariance matrix is totally positive. Essentially, this inconvenience prevents the available High Relative Accuracy methods to be used with real-life data. Here, we present a method for the estimation of the covariance matrix of a Gaussian Markov Random Field over a graph of paths assuring the estimated covariance matrix (or its inverse) is totally positive.

Idioma: Inglés

DOI: 10.1016/j.cam.2025.116543

Año: 2025

Publicado en: Journal of Computational and Applied Mathematics 464 (2025), 116543 [15 pp.]
ISSN: 0377-0427

Financiación: info:eu-repo/grantAgreement/ES/DGA/E41-23R
Financiación: info:eu-repo/grantAgreement/ES/MCIU/PID2022-138569NB-I00
Financiación: info:eu-repo/grantAgreement/ES/MCIU/PID2022-139886NB-I00
Financiación: info:eu-repo/grantAgreement/ES/MCIU/PID2022-140585NB-I00
Financiación: info:eu-repo/grantAgreement/ES/MICINN/RED2022-134176-T

Tipo y forma: Artículo (PrePrint)

Área (Departamento): Área Matemática Aplicada (Dpto. Matemática Aplicada)