Local Conditioning on undirected graphs

This paper proposes Local Conditioning as a truly distributed exact version of Belief Propagation for cyclic undirected graphical models. It is shown how to derive explicit recursive updates for messages and beliefs that are truly distributed in the sense that messages are passed between individual nodes of the graph rather than between clustered nodes. Such a distributed algorithm is especially relevant for problems that require a distributed implementation, for example sensor networks. In order to compare its complexity and ease of implementation with a clustered version of Belief Propagation, we illustrate both in a Min-Sum block interpolation problem within the context of an Ising model.