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In this paper, we propose a simple algorithm that takes multidimensional neural input data and decomposes the joint likelihood into marginals using boosted mixtures of hidden Markov chains (BM-HMM). The algorithm applies techniques from boosting to create hierarchal dependencies between these marginal subspaces. Finally, borrowing ideas from mixture of experts, the local information is weighted and incorporated into an ensemble decision. Our results show that this algorithm is very simple to train and computationally efficient, while also providing the ability to reduce the input dimensionality for brain machine interfaces (BMIs).