Modeling uncertainty using enhanced tree structures in expert systems

Network structures, called belief networks, have been shown to be effective for representing uncertainty in expert systems. A problem faced when making inferences in belief networks is that schemes to propagate beliefs are generally of exponential complexity. A special class of networks, called trees, have been shown to provide an efficient framework for propagating beliefs. In this paper, we present a scheme called star-decomposition, originally proposed by Lazarsfeld [1966], to convert belief networks into trees. This scheme introduces auxiliary variables to represent higher order dependencies in tree structures. Such structures are called enhanced tree structures. We also describe a simple partitioning technique that creates local event groups which extends the applicability of star-decomposition. A framework is presented that identifies classes of belief networks that may be exactly represented using enhanced tree structures. For belief networks that are not amenable to exact representation, an enhanced tree structure preserves more dependencies in the belief network than representations that do not use the star-decomposition technique. The potential benefit of using enhanced trees as compared to simple tree structures is demonstrated