Searching a multivariate partition space using weighted MAX-SAT

Because of the huge number of partitions of even\ud a moderately sized dataset, even when Bayes factors\ud have a closed form, a comprehensive search\ud for the highest scoring (MAP) partition is usually\ud impossible. Therefore, both deterministic or random\ud search algorithms traverse only a small proportion\ud of partitions of a large dataset. The main\ud contribution of this paper is to encode the formal\ud Bayes factor search on partitions as a weighted\ud MAX-SAT problem and use well-known solvers\ud for that problem to search for partitions. We\ud demonstrate how, with the appropriate priors\ud over the partition space, this method can be used\ud to fully search the space of partitions in smaller\ud problems and how it can be used to enhance the\ud performance of more familiar algorithms in large\ud problems. We illustrate our method on clustering\ud of time-course microarray experiments.