Adaptive Variable Clustering in Gaussian Graphical Models

Gaussian graphical models (GGMs) are widely-used to describe the relationship between random variables. In many real-world applications, GGMs have a block structure in the sense that the variables can be clustered into groups so that inter-group correlation is much weaker than intra-group correlation. We present a novel nonparametric Bayesian generative model for such a block-structured GGM and an efficient inference algorithm to find the clustering of variables in this GGM by combining a Gibbs sampler and a split-merge Metropolis-Hastings algorithm. Experimental results show that our method performs well on both synthetic and real data. In particular, our method outperforms generic clustering algorithms and can automatically identify the true number of clusters.