Bayes-Ball: The Rational Pastime (for Determining Irrelevance and Requisite Information in Belief Networks and Influence Diagrams)
This work provides a more efficient method for inference and decision-making in probabilistic graphical models, which is incremental over prior approaches.
The paper tackles the problem of efficiently determining irrelevant sets and requisite information in belief networks and influence diagrams, resulting in a new algorithm called Bayes-Ball that operates in linear time relative to the graph size.
One of the benefits of belief networks and influence diagrams is that so much knowledge is captured in the graphical structure. In particular, statements of conditional irrelevance (or independence) can be verified in time linear in the size of the graph. To resolve a particular inference query or decision problem, only some of the possible states and probability distributions must be specified, the "requisite information." This paper presents a new, simple, and efficient "Bayes-ball" algorithm which is well-suited to both new students of belief networks and state of the art implementations. The Bayes-ball algorithm determines irrelevant sets and requisite information more efficiently than existing methods, and is linear in the size of the graph for belief networks and influence diagrams.