A differential semantics for jointree algorithms

A new approach to inference in belief networks has been recently proposed, which is based on an algebraic representation of belief networks using multi-linear functions. According to this approach, the key computational question is that of representing multi-linear functions compactly, since inference reduces to a simple process of evaluating and differentiating such functions. We show here that mainstream inference algorithms based on jointrees are a special case of this approach in a very precise sense. We use this result to prove new properties of jointree algorithms, and then discuss some of its practical and theoretical implications.