Qualitative Approach to Bayesian Networks With Multiple Causes

Two approaches for extending a quantitative Bayesian network (BN) to deal with qualitative information include a qualitative probability network extension and causal independence. Both approaches help developers to remedy the gap between the complicated BN formalism and the actual problem. Lucas utilizes these two methods in establishing a theory of qualitative causal (QC) interaction patterns where qualitative probability influences (QPIs) (considering whether it is better to hold a single cause than not) affect the network model. QC patterns help to offer developers a high-level starting point when developing BNs. However, in real-world applications, usually, we need to know QPIs on multiple causes, namely, whether holding some subset of the causes will be a better choice than holding other subsets. To this end, we introduce a concept called causality probability from which QPIs can be easily induced. We investigate the local optima and global optima of causality probabilities considering multiple causes. For the local optima, we present the qualitative influences on all binary interaction types, while for the global optima, we achieve an upper bound of causality probability and discuss the conditions to reach the upper bound. Our results are useful for BN developers to get an overview of causality relations.