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We explore the use of Optimal Mixture Models to represent topics. We analyze two broad classes of mixture models: set-based and weighted. We provide an original proof that estimation of set-based models is NP-hard, and therefore not feasible. We argue that weighted models are superior to set-based models, and the solution can be estimated by a simple gradient descent technique. We demonstrate that Optimal Mixture Models can be successfully applied to the task of document retrieval. Our experiments show that weighted mixtures outperform a simple language modeling baseline. We also observe that weighted mixtures are more robust than other approaches of estimating topical models.