10.1214/11-AOS957
Uhler, Caroline
Caroline
Uhler0000-0002-7008-0216
Geometry of maximum likelihood estimation in Gaussian graphical models
Institute of Mathematical Statistics
2012
2018-12-11T12:00:33Z
2019-08-02T12:37:58Z
journal_article
/record/2959
/record/2959.json
We study maximum likelihood estimation in Gaussian graphical models from a geometric point of view. An algebraic elimination criterion allows us to find exact lower bounds on the number of observations needed to ensure that the maximum likelihood estimator (MLE) exists with probability one. This is applied to bipartite graphs, grids and colored graphs. We also study the ML degree, and we present the first instance of a graph for which the MLE exists with probability one, even when the number of observations equals the treewidth.