Graphical Models and Exponential Families
Dan Geiger, Christopher Meek
We provide a classification of graphical models according to their representation as subfamilies of exponential families. Undirected graphical models with no hidden variables are linear exponential families (LEFs), directed acyclic graphical models and chain graphs with no hidden variables, including Bayesian networks with several families of local distributions, are curved exponential families (CEFs) and graphical models with hidden variables are stratified exponential families (SEFs). An SEF is a finite union of CEFs satisfying a frontier condition. In addition, we illustrate how one can automatically generate independence and non-independence constraints on the distributions over the observable variables implied by a Bayesian network with hidden variables. The relevance of these results for model selection is examined.
PDF Link: /papers/98/p156-geiger.pdf
AUTHOR = "Dan Geiger
and Christopher Meek",
TITLE = "Graphical Models and Exponential Families",
BOOKTITLE = "Proceedings of the Fourteenth Conference Annual Conference on Uncertainty in Artificial Intelligence (UAI-98)",
PUBLISHER = "Morgan Kaufmann",
ADDRESS = "San Francisco, CA",
YEAR = "1998",
PAGES = "156--165"