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The clique tree algorithm is the standard method for doing inference inBayesian networks. It works by manipulating clique potentials - distributionsover the variables in a clique. While this approach works well for manynetworks, it is limited by the need to maintain an exact representation of theclique potentials. This paper presents a new unified approach that combinesapproximate inference and the clique tree algorithm, thereby circumventing thislimitation. Many known approximate inference algorithms can be viewed asinstances of this approach. The algorithm essentially does clique treepropagation, using approximate inference to estimate the densities in eachclique. In many settings, the computation of the approximate clique potentialcan be done easily using statistical importance sampling. Iterations are usedto gradually improve the quality of the estimation.

A General Algorithm for Approximate Inference and its Application to Hybrid Bayes Nets