Efficient probabilistic reasoning in BNs with mutual exclusion and context-specific independence

Prior work has shown that context-specific independence (CSI) in Bayes networks can be exploited to speed up belief updating. We examine how networks with variables exhibiting mutual exclusion (e.g., "selector variables"), as well as CSI, can be efficiently updated. In particular, directed-path singly connected and polytree networks that have an additional common selector variable can be updated in linear time (given null and general conjunctive evidence, respectively), where quadratic time would be needed without the mutual exclusion requirement. The above results have direct applications, as such network topologies can be used in predicting the ramifications of user selection in some multimedia data browsing systems.