Multiple Hypothesis Testing and Quasi Essential Graph for Comparing Two Sets of Bayesian Networks

In machine learning, graphical models like Bayesian networks are one of important visualization tools that can be learned from data to represent pictorially a complex system. In order to compare two complex systems (or one complex system functioning in two different contexts), one usually compares directly their representative graphs. However, with small sample size data, it is hard to learn the graph that represents precisely the system. That's why ensemble methods (e.g. Bootstrapping, evolutionary algorithm, etc...) are proposed to learn from data of each system a set of graphs that represents more precisely this system. Then, for comparing two systems, one needs a mechanism to compare two sets of graphs. We propose in this work an approach based on multiple hypothesis testing and quasi essential graph (QEG) to compare two sets of Bayesian networks.