## 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, resulting in increased speed when graphs are sparse. We compare this to an algorithm based on convex

duality and operating on the covariance matrix by neighbourhood coordinate descent, essentially corre- 15 sponding to the graphical lasso with zero penalty. For large, sparse graphs, this version of 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

sparse graphs. As a consequence, we obtain a simplified proof for existence of the maximum likelihood 20 estimator in graphs with low colouring number.

duality and operating on the covariance matrix by neighbourhood coordinate descent, essentially corre- 15 sponding to the graphical lasso with zero penalty. For large, sparse graphs, this version of 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

sparse graphs. As a consequence, we obtain a simplified proof for existence of the maximum likelihood 20 estimator in graphs with low colouring number.

Original language | English |
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Journal | Biometrika |

ISSN | 0006-3444 |

Publication status | Submitted - 2023 |