Complexity reduction of influence nets using arc removal

Abstract

The model building of Influence Nets, a special instance of Bayesian belief networks, is a time-consuming and labor-intensive task. No formal process exists that decision makers/system analyst, who are typically not familiar with the underlying theory and assumptions of belief networks, can use to build concise and easy-to-interpret models. In many cases, the developed model is extremely dense, that is, it has a very high link-to-node ratio. The complexity of a network makes the already intractable task of belief updating more difficult. The problem is further intensified in dynamic domains where the structure of the built model is repeated for multiple time-slices. It is, therefore, desirable to do a post-processing of the developed models and to remove arcs having a negligible influence on the variable(s) of interests. The paper applies sensitivity of arc analysis to identify arcs that can be removed from an Influence Net without having a significant impact on its inferencing capability. A metric is suggested to gauge changes in the joint distribution of variables before and after the arc removal process. The results are benchmarked against the KL divergence metric. An empirical study based on several real Influence Nets is conducted to test the performance of the sensitivity of arc analysis in reducing the model complexity of an Influence Net without causing a significant change in its joint probability distribution.