Extending Factor Graphs so as to Unify Directed and Undirected Graphical Models
Brendan Frey
Abstract:
The two most popular types of graphical model are directed models (Bayesian networks) and undirected models (Markov random fields, or MRFs). Directed and undirected models offer complementary properties in model construction, expressing conditional independencies, expressing arbitrary factorizations of joint distributions, and formulating messagepassing inference algorithms. We show that the strengths of these two representations can be combined in a single type of graphical model called a ``factor graph'. Every Bayesian network or MRF can be easily converted to a factor graph that expresses the same conditional independencies, expresses the same factorization of the joint distribution, and can be used for probabilistic inference through application of a single, simple messagepassing algorithm. In contrast to chain graphs, where messagepassing is implemented on a hypergraph, messagepassing can be directly implemented on the factor graph. We describe a modified ``Bayesball' algorithm for establishing conditional independence in factor graphs, and we show that factor graphs form a strict superset of Bayesian networks and MRFs. In particular, we give an example of a commonlyused ``mixture of experts' model fragment, whose independencies cannot be represented in a Bayesian network or an MRF, but can be represented in a factor graph. We finish by giving examples of realworld problems that are not well suited to representation in Bayesian networks and MRFs, but are wellsuited to representation in factor graphs
Keywords:
Pages: 257264
PS Link:
PDF Link: /papers/03/p257frey.pdf
BibTex:
@INPROCEEDINGS{Frey03,
AUTHOR = "Brendan Frey
",
TITLE = "Extending Factor Graphs so as to Unify Directed and Undirected Graphical Models",
BOOKTITLE = "Proceedings of the Nineteenth Conference Annual Conference on Uncertainty in Artificial Intelligence (UAI03)",
PUBLISHER = "Morgan Kaufmann",
ADDRESS = "San Francisco, CA",
YEAR = "2003",
PAGES = "257264"
}

