Abstract

Introduction Graphical models provide a formalism in which to express and manipulate conditional independence statements. Inference algorithms for graphical models exploit these independence statements, using them to compute conditional probabilities while avoiding brute force marginalization over the joint probability table. Many inference algorithms, in particular the clustering algorithms, make explicit their usage of conditional independence by constructing a data structure that captures the essential Markov properties underlying the graph. That is, the algorithm groups interacting variables into clusters, such that the hypergraph of clusters has Markov properties that allow simple local algorithms to be employed for inference. In the best case, in which the original graph is sparse and without long cycles, the clusters are small and inference is efficient. In the worst case, such as the case of a dense graph, the clusters are large and inference is inefficient (complexity

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