Sparse Bayesian Unsupervised Learning
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This paper is about variable selection, clustering and estimation in an unsupervised high-dimensional setting. Our approach is based on fitting constrained Gaussian mixture models, where we learn the number of clusters K and the set of relevant variables S using a generalized Bayesian posterior with a sparsity inducing prior. We prove a sparsity oracle inequality which shows that this procedure selects the optimal parameters K and S. This procedure is implemented using a Metropolis-Hastings algorithm, based on a clustering-oriented greedy proposal, which makes the convergence to the posterior very fast.
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