GEOMETRY OF MAXIMUM LIKELIHOOD ESTIMATION IN GAUSSIAN GRAPHICAL MODELS
成果类型：
Article
署名作者：
Uhler, Caroline
署名单位：
Institute of Science & Technology - Austria
刊物名称：
ANNALS OF STATISTICS
ISSN/ISSBN：
0090-5364
DOI：
10.1214/11-AOS957
发表日期：
2012
页码：
238-261
关键词：
摘要：
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.