Recursive noisy OR - a rule for estimating complex probabilistic interactions

This paper focuses on approaches that address the intractability of knowledge acquisition of conditional probability tables in causal or Bayesian belief networks. We state a rule that we term the "recursive noisy OR" (RNOR) which allows combinations of dependent causes to be entered and later used for estimating the probability of an effect. In the development of this paper, we investigate the axiomatic correctness and semantic meaning of this rule and show that the recursive noisy OR is a generalization of the well-known noisy OR. We introduce the concept of positive causality and demonstrate its utility in axiomatic correctness of the RNOR. We also introduce concepts describing the ways in which dependent causes can work together as being either "synergistic" or "interfering." We provide a formalization to quantify these concepts and show that they are preserved by the RNOR. Finally, we present a method for the determination of Conditional Probability Tables from this causal theory.