Context-specific independence, decomposition of conditional probabilities, and inference in Bayesian networks

Three kinds of independence are of interest in the context of Bayesian networks, namely conditional independence, independence of causal influence, and context-specific independence. It is well-known that conditional independence enables one to factorize a joint probability into a list of conditional probabilities and thereby renders inference feasible. It has recently been shown that independence of causal in-fluence leads to further factorizations of some of the conditional probabilities and consequently makes inference faster. This paper studies context-specific independence. We show that context-specific independence can be used to further decompose some of the conditional probabilities. We present an inference algorithm that takes advantage of the decompositions and provide, for the first time, empirical evidence that demonstrates the computational benefits of exploiting context-specific independence.