Score matching filters for Gaussian Markov random fields with a linear model of the precision matrix

0551812 - ÚI 2022 RIV US eng J - Journal Article
Turčičová, Marie - Mandel, J. - Eben, Kryštof
Score matching filters for Gaussian Markov random fields with a linear model of the precision matrix.
Foundations of Data Science. Roč. 3, č. 4 (2021), s. 793-824. E-ISSN 2639-8001
R&D Projects: GA TA ČR(CZ) TL01000238; GA TA ČR(CZ) TO01000219
Institutional support: RVO:67985807
Keywords : Score matching * ensemble filter * Gaussian Markov random field * covariance modelling
OECD category: Statistics and probability
Method of publishing: Open access
http://dx.doi.org/10.3934/fods.2021030

We present an ensemble filtering method based on a linear model for the precision matrix (the inverse of the covariance) with the parameters determined by Score Matching Estimation. The method provides a rigorous covariance regularization when the underlying random field is Gaussian Markov. The parameters are found by solving a system of linear equations. The analysis step uses the inverse formulation of the Kalman update. Several filter versions, differing in the construction of the analysis ensemble, are proposed, as well as a Score matching version of the Extended Kalman Filter.
Permanent Link: http://hdl.handle.net/11104/0327033