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Abstract:
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Finite mixture models provide a natural framework for analyzing data from heterogeneous populations. In practice, however, the number of mixture components (or order) may be unknown. We propose the Group-Sort-Fuse (GSF) procedure---a new penalized likelihood approach for simultaneous estimation of the order and mixing measure in multidimensional finite mixture models. Unlike methods which fit and compare mixtures with varying orders using criteria involving model complexity, our approach directly penalizes a continuous function of the model parameters. Specifically, given a conservative upper bound on the order, the GSF groups and sorts mixture component parameters in order to fuse those which are redundant. For a wide range of finite mixture models, we show that the GSF is consistent in estimating the true mixture order and achieves the parametric convergence rate for mixing measure estimation up to polylogarithmic factors, under a suitable Wasserstein distance.
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