Title: Probabilistic Reasoning in Hierarchical Markov Networks
Speaker: Jidong Liu <liuji114@cs.uregina.ca>
Seminar: CS 900 010
Abstract:

Hierarchical Markov Networks (HMNs) were recently proposed as a new
representation of Bayesian Networks (BNs). HMNs are very important
as they posses many advantages when compared to other
representations of BNs such as Markov Networks (MNs).

We discuss two significant advances in the study of
HMNs. First, a practical algorithm for probabilistic
inference in HMNs will be presented. The crux of our algorithm has been 
implemented.  Experimental results demonstrate the effectiveness of our
approach.

The second discussion will concentrate on the theoretical foundation
of HMNs. It is well-known that the logical implication of
conditional independence (CI) in probability theory and embedded
multivalued dependency (EMVD) in relational database theory
coincides for the class of BNs and for the class of MNs. It is
also well-known that the logical implication of CI and EMVD
differs in general.  Surprisingly, our research shows that the
logical implication of CI and EMVD differs for the class of HMNs.
This intriguing result is important as it provides a lower
upper-bound on where the logical implication of CI and EMVD
diverge.