Geometry of maximum likelihood estimation in Gaussian graphical models
Uhler C. 2012. Geometry of maximum likelihood estimation in Gaussian graphical models. Annals of Statistics. 40(1), 238–261.
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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.
Publishing Year
Date Published
2012-02-01
Journal Title
Annals of Statistics
Publisher
Institute of Mathematical Statistics
Acknowledgement
I wish to thank Bernd Sturmfels for many helpful discus- sions and Steffen Lauritzen for introducing me to the problem of the existence of the MLE in Gaussian graphical models. I would also like to thank two referees who provided helpful comments on the original version of this paper.
Volume
40
Issue
1
Page
238 - 261
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Cite this
Uhler C. Geometry of maximum likelihood estimation in Gaussian graphical models. Annals of Statistics. 2012;40(1):238-261. doi:10.1214/11-AOS957
Uhler, C. (2012). Geometry of maximum likelihood estimation in Gaussian graphical models. Annals of Statistics. Institute of Mathematical Statistics. https://doi.org/10.1214/11-AOS957
Uhler, Caroline. “Geometry of Maximum Likelihood Estimation in Gaussian Graphical Models.” Annals of Statistics. Institute of Mathematical Statistics, 2012. https://doi.org/10.1214/11-AOS957.
C. Uhler, “Geometry of maximum likelihood estimation in Gaussian graphical models,” Annals of Statistics, vol. 40, no. 1. Institute of Mathematical Statistics, pp. 238–261, 2012.
Uhler C. 2012. Geometry of maximum likelihood estimation in Gaussian graphical models. Annals of Statistics. 40(1), 238–261.
Uhler, Caroline. “Geometry of Maximum Likelihood Estimation in Gaussian Graphical Models.” Annals of Statistics, vol. 40, no. 1, Institute of Mathematical Statistics, 2012, pp. 238–61, doi:10.1214/11-AOS957.
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