Reduced Parameter Representation of Model Components

Compact specification of relationships between variables in a graphical model requires reducing the number of parameters in the valuation (probability potential, belief function, or utility) expressing that relationship. Finding structure (such as logical relationships) among the possible outcomes suggests reduced parameter representations of valuations. The TS-set notation, introduced here, helps describe such logical relationships. An intelligent graphical belief model construction systems should provide resources for specifying structure at a variety of levels, specifically, the outcome set level, the parameter level, the valuation level and the graphical substructure level. This paper discusses some of the issues involved in constructing small pieces of graphical models and introduces notation to help simplify the specification.