Modeling Causal Reinforcement and Undermining for Efficient CPT Elicitation

Representation of uncertain knowledge by using a Bayesian network requires the acquisition of a conditional probability table (CPT) for each variable. The CPT can be acquired by data mining or elicitation. When data are insufficient for supporting mining, causal modeling such as the noisy-OR aids elicitation by reducing the number of probability parameters to be acquired from human experts. Multiple causes can reinforce each other in producing the effect or can undermine the impact of each other. Most existing causal models do not consider causal interactions from the perspective of reinforcement or undermining. Our analysis shows that none can represent both interactions. Except for the RNOR, other models also limit parameters to probabilities of single-cause events. We present the first general causal model, that is, the nonimpeding noisy-AND tree, that allows encoding of both reinforcement and undermining. It supports efficient CPT acquisition by elicitating a partial ordering of causes in terms of a tree topology, plus the necessary numerical parameters. It also allows the incorporation of probabilities for multicause events.