Diverse M-Best Solutions in Markov Random Fields

Much effort has been directed at algorithms for obtaining the highest probability (MAP) configuration in probabilistic (random field) models. In many situations, one could benefit from additional high probability solutions. Current methods for computing the M most probable configurations produce solutions that tend to be very similar to the MAP solution and each other. This is often an undesirable property. In this paper we propose an algorithm for the Diverse MBest problem, which involves finding a diverse set of highly probable solutions under a discrete probabilistic model. Given a dissimilarity function measuring closeness of two solutions, our formulation involves maximizing a linear combination of the probability and dissimilarity to previous solutions. Our formulation generalizes the MBest MAP problem and we show that for certain families of dissimilarity functions we can guarantee that these solutions can be found as easily as the MAP solution.