On some algorithms for estimation in Gaussian graphical models

Research output: Contribution to journal › Journal article › Research › peer-review

Standard

On some algorithms for estimation in Gaussian graphical models. / Højsgaard, Søren; Lauritzen, Steffen.

In: Biometrika, 2024.

Research output: Contribution to journal › Journal article › Research › peer-review

Harvard

Højsgaard, S & Lauritzen, S 2024, 'On some algorithms for estimation in Gaussian graphical models', Biometrika. https://doi.org/10.1093/biomet/asae028

APA

Højsgaard, S., & Lauritzen, S. (2024). On some algorithms for estimation in Gaussian graphical models. Biometrika. https://doi.org/10.1093/biomet/asae028

Vancouver

Højsgaard S, Lauritzen S. On some algorithms for estimation in Gaussian graphical models. Biometrika. 2024. https://doi.org/10.1093/biomet/asae028

Author

Højsgaard, Søren ; Lauritzen, Steffen. / On some algorithms for estimation in Gaussian graphical models. In: Biometrika. 2024.

Bibtex

@article{a6d403b84b9444ca843af35b18c3360b,
title = "On some algorithms for estimation in Gaussian graphical models",
abstract = "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.",
author = "S{\o}ren H{\o}jsgaard and Steffen Lauritzen",
year = "2024",
doi = "10.1093/biomet/asae028",
language = "English",
journal = "Biometrika",
issn = "0006-3444",
publisher = "Oxford University Press",

}

RIS

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