%0 Journal Article
%T Sparse Bayesian Unsupervised Learning
%A Stephane Gaiffas
%A Bertrand Michel
%J Statistics
%D 2014
%I arXiv
%X 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.
%U http://arxiv.org/abs/1401.8017v1