Bayesian Learning with Mixtures of Trees

Abstract

We present a Bayesian method for learning mixtures of graphical models. In particular, we focus on data clustering with a tree-structured model for each cluster. We use a Markov chain Monte Carlo method to draw a sample of clusterings, while the likelihood of a clustering is computed by exact averaging over the model class, including the dependency structure on the variables. Experiments on synthetic data show that this method usually outperforms the expectation–maximization algorithm by Meilă and Jordan [1] when the number of observations is small (hundreds) and the number of variables is large (dozens). We apply the method to study how much single nucleotide polymorphisms carry information about the structure of human populations.