Real World Networks

To assess the quality of the bound propagation algorithm for more challenging networks, we computed bounds for a Bayesian network (Section ), that is commonly used in articles as a representative of a real world problem. Secondly, we show that the bound propagation method can be used to find many tight bounds for a large Ising grid (Section  and finally, in Section , we show results for a bi-partite graph. For these networks, we will briefly discuss bound propagation in relation with the cluster variation method kappen02novel which is one of the better approximation methods for general graphs. Whenever possible, we show the exact marginals.