M. Pawan Kumar 
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LEARNING A SMALL MIXTURE OF TREES M. Pawan Kumar and D. Koller In Proceedings of Advances in Neural Information Processing Systems (NIPS), 2009 The problem of approximating a given probability distribution using a simpler distribution plays an important role in several areas of machine learning, for example variational inference and classification. Within this context, we consider the task of learning a mixture of tree distributions. Although mixtures of trees can be learned by minimizing the KLdivergence using an EM algorithm, its success depends heavily on the initialization. We propose an efficient strategy for obtaining a good initial set of trees that attempts to cover the entire observed distribution by minimizing the $\alpha$divergence with $\alpha = \infty$. We formulate the problem using the fractional covering framework and present a convergent sequential algorithm that only relies on solving a convex program at each iteration. Compared to previous methods, our approach results in a significantly smaller mixture of trees that provides similar or better accuracies. We demonstrate the usefulness of our approach by learning pictorial structures for face recognition. 