The Annals of Statistics
- Ann. Statist.
- Volume 40, Number 1 (2012), 238-261.
Geometry of maximum likelihood estimation in Gaussian graphical models
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.
Ann. Statist., Volume 40, Number 1 (2012), 238-261.
First available in Project Euclid: 29 March 2012
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Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Gaussian graphical model maximum likelihood estimation matrix completion problems duality algebraic statistics algebraic variety number of observations sufficient statistics treewidth elimination ideal ML degree bipartite graphs
Uhler, Caroline. Geometry of maximum likelihood estimation in Gaussian graphical models. Ann. Statist. 40 (2012), no. 1, 238--261. doi:10.1214/11-AOS957. https://projecteuclid.org/euclid.aos/1333029964