TY - JOUR

T1 - On the theoretical guarantees for parameter estimation of Gaussian random field models

T2 - A sparse precision matrix approach

AU - Tajbakhsh, Sam Davanloo

AU - Aybat, Necdet S.

AU - Castillo, Enrique Del

N1 - Publisher Copyright:
© 2020 Sam Davanloo Tajbakhsh, Necdet Serhat Aybat and Enrique del Castillo. License: CC-BY 4.0, see https://creativecommons.org/licenses/by/4.0/. Attribution requirements are provided at http://jmlr.org/papers/v21/14-241.html.

PY - 2020/10

Y1 - 2020/10

N2 - 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.

AB - 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.

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M3 - Article

AN - SCOPUS:85098467043

SN - 1532-4435

VL - 21

JO - Journal of Machine Learning Research

JF - Journal of Machine Learning Research

ER -