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Title: On perfectness in Gaussian graphical models
Knowing when a graphical model perfectly encodes the conditional independence structure of a distribution is essential in applications, and this is particularly important when performing inference from data. When the model is perfect, there is a one-to-one correspondence between conditional independence statements in the distribution and separation statements in the graph. Previous work has shown that almost all models based on linear directed acyclic graphs as well as Gaussian chain graphs are perfect, the latter of which subsumes Gaussian graphical models (i.e., the undirected Gaussian models) as a special case. In this paper, we directly approach the problem of perfectness for the Gaussian graphical models, and provide a new proof, via a more transparent parametrization, that almost all such models are perfect. Our approach is based on, and substantially extends, a construction of Lněnička and Matúš showing the existence of a perfect Gaussian distribution for any graph. The analysis involves constructing a probability measure on the set of normalized covariance matrices Markov with respect to a graph that may be of independent interest.  more » « less
Award ID(s):
1945667
NSF-PAR ID:
10336066
Author(s) / Creator(s):
; ;
Editor(s):
Camps-Valls, G.; Ruiz, F. J.; Valera, I.
Date Published:
Journal Name:
Proceedings of The 25th International Conference on Artificial Intelligence and Statistics
Volume:
151
Page Range / eLocation ID:
7505-7517
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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