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This paper presents an algorithm for order reduction of factors in High-Order Markov Random Fields (HOMRFs). Standard techniques for transforming arbitrary high-order factors into pairwise ones have been known for a long time. In this paper, the authors take a fresh look at this problem with the following motivation: It is important to keep in mind that order reduction is followed by an inference procedure on the order-reduced MRF. Since there are many possible ways of performing order reduction, a technique that generates "Easier" pairwise inference problems is a better reduction. With this motivation in mind, they introduce a new algorithm called Order Reduction Inference (ORI) that searches over a space of order reduction methods to minimize the difficulty of the resultant pairwise inference problem.
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