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, belief network inference reduces to a simple process of evaluating and differentiating multi-linear functions. We show here that mainstream inference algorithms based on jointrees are a special case of the approach based on multi-linear functions, in a very precise sense. We use this result to prove new properties of jointree algorithms. We also discuss some practical and theoretical implications of this new finding.