The clique tree algorithm is the standard method for doing inference in Bayesian networks. It works by manipulating clique potentials - distributions over the variables in a clique. While this approach works well for many networks, it is limited by the need to maintain an exact representation of the clique potentials. This paper presents a new unified approach that combines approximate inference and the clique tree algorithm, thereby circumventing this limitation. Many known approximate inference algorithms can be viewed as instances of this approach. The algorithm essentially does clique tree propagation, using approximate inference to estimate the densities in each clique. In many settings, the computation of the approximate clique potential can be done easily using statistical importance sampling. Iterations are used to gradually improve the quality of the estimation.
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