Structuring uncertain knowledge with hierarchical bayesian networks

Abstract

This paper presents structural extensions of Bayesian networks which improve their applicability for complex systems that are modeled by a large set of random variables with a lot of dependencies between them. A Hierarchical Bayesian network (HBN) architecture is developed where elementary random variables are successively combined to new ones, thus yielding compact summaries of the components information. This joint knowledge representation on different levels of abstraction is maintained by suitable transformation functions for consecutive description layers.

Additionally, the basic interconnection scheme within a single layer is further structured by iteratively subdividing each nodes causal predecessors into smaller subsets. The influence of the predecessor set is computed by merging its subsets effects, which e.g. can be performed with the rules of fuzzy logic. In this way, the degree of dependency between random variables will determine the computational effort for evaluating their joint impact on other variables.

An outline of a HBNs description and connection hierarchy is given for a sensor fusion problem, where the various information sources of a robot are combined to build an internal map of its external environment.