Geometry of maximum likelihood estimation in Gaussian graphical models

Abstract

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.

Published in at http://dx.doi.org/10.1214/11-AOS957 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)

References in corpus (2)

• Estimation of means in graphical Gaussian models with symmetries
• Lattices of Graphical Gaussian Models with Symmetries

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