Sparse Bayesian Unsupervised Learning

Understand

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.