Geometry of maximum likelihood estimation in Gaussian graphical models
Statistics Theory
2012-05-30 v2 Algebraic Geometry
Optimization and Control
Statistics Theory
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.
Cite
@article{arxiv.1012.2643,
title = {Geometry of maximum likelihood estimation in Gaussian graphical models},
author = {Caroline Uhler},
journal= {arXiv preprint arXiv:1012.2643},
year = {2012}
}
Comments
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)