Max Welling, Yee Teh
Belief propagation on cyclic graphs is an efﬁcient algorithm for comput- ing approximate marginal probability distributions over single nodes and neighboring nodes in the graph. In this paper we propose two new al- gorithms for approximating joint probabilities of arbitrary pairs of nodes and prove a number of desirable properties that these estimates fulﬁll. The ﬁrst algorithm is a propagation algorithm which is shown to con- verge if belief propagation converges to a stable ﬁxed point. The second algorithm is based on matrix inversion. Experiments compare a number of competing methods.