Microsoft Research - Decision Theory and Adaptive Systems Group
Multivariate Analysis & Graphical Models of Association (MAGMA 4) Workshop
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 (DAG) models and chain graphs with no hidden variables, including DAG models with several families of local distributions, are curved exponential families (CEFs) and, finally, graphical models with hidden variables are, what we term, stratified exponential families (SEFs). In addition, we illustrate how one can automatically generate independence and non-independence constraints on the distributions over the observable variables implied by a DAG model with hidden variables. The relevance of these results for model selection is examined.