On some algorithms for estimation in Gaussian graphical models
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On some algorithms for estimation in Gaussian graphical models. / Højsgaard, Søren; Lauritzen, Steffen.
I: Biometrika, 2024.Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt
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TY - JOUR
T1 - On some algorithms for estimation in Gaussian graphical models
AU - Højsgaard, Søren
AU - Lauritzen, Steffen
PY - 2024
Y1 - 2024
N2 - In Gaussian graphical models, the likelihood equations must typically be solved iteratively. We investigate two algorithms: A version of iterative proportional scaling which avoids inversion of large matrices, and an algorithm based on convex duality and operating on the covariance matrix by neighbourhood coordinate descent, corresponding to the graphical lasso with zero penalty. For large, sparse graphs, the iterative proportional scaling algorithm appears feasible and has simple convergence properties. The algorithm based on neighbourhood coordinate descent is extremely fast and less dependent on sparsity, but needs a positive definite starting value to converge. We give an algorithm for finding such a starting value for graphs with low colouring number. As a consequence, we also obtain a simplified proof for existence of the maximum likelihood estimator in such cases.
AB - In Gaussian graphical models, the likelihood equations must typically be solved iteratively. We investigate two algorithms: A version of iterative proportional scaling which avoids inversion of large matrices, and an algorithm based on convex duality and operating on the covariance matrix by neighbourhood coordinate descent, corresponding to the graphical lasso with zero penalty. For large, sparse graphs, the iterative proportional scaling algorithm appears feasible and has simple convergence properties. The algorithm based on neighbourhood coordinate descent is extremely fast and less dependent on sparsity, but needs a positive definite starting value to converge. We give an algorithm for finding such a starting value for graphs with low colouring number. As a consequence, we also obtain a simplified proof for existence of the maximum likelihood estimator in such cases.
U2 - 10.1093/biomet/asae028
DO - 10.1093/biomet/asae028
M3 - Journal article
JO - Biometrika
JF - Biometrika
SN - 0006-3444
ER -
ID: 395024443