{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,12]],"date-time":"2026-05-12T03:47:46Z","timestamp":1778557666429,"version":"3.51.4"},"reference-count":32,"publisher":"Oxford University Press (OUP)","issue":"4","license":[{"start":{"date-parts":[[2024,6,14]],"date-time":"2024-06-14T00:00:00Z","timestamp":1718323200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/pages\/standard-publication-reuse-rights"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2024,12,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>In Gaussian graphical models, the likelihood equations must typically be solved iteratively. This paper investigates 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, which corresponds 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 provide an algorithm for finding such a starting value for graphs with low colouring number. As a consequence, we also obtain a simplified proof of existence of the maximum likelihood estimator in such cases.<\/jats:p>","DOI":"10.1093\/biomet\/asae028","type":"journal-article","created":{"date-parts":[[2024,6,15]],"date-time":"2024-06-15T02:04:37Z","timestamp":1718417077000},"page":"1201-1219","source":"Crossref","is-referenced-by-count":3,"title":["On some algorithms for estimation in Gaussian graphical models"],"prefix":"10.1093","volume":"111","author":[{"given":"S","family":"H\u00f8jsgaard","sequence":"first","affiliation":[{"name":"Department of Mathematical Sciences, Aalborg University , Skjernvej 4A , DK-9220 Aalborg,","place":["Denmark"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7176-6212","authenticated-orcid":false,"given":"S","family":"Lauritzen","sequence":"additional","affiliation":[{"name":"Department of Mathematical Sciences, University of Copenhagen, Universitetsparken 5 , DK-2100 Copenhagen,","place":["Denmark"]}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"286","published-online":{"date-parts":[[2024,6,14]]},"reference":[{"key":"2024112207520884900_asae028-B1","first-page":"485","article-title":"Model selection through sparse maximum likelihood estimation for multivariate Gaussian or binary data","volume":"9","author":"Banerjee","year":"2008","journal-title":"J. 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