This is the core MCMC sampler for the Dirichlet Process Variable Clustering model described in
Konstantina Palla, David A. Knowles and Zoubin Ghahramani. A nonparametric variable clustering model. NIPS 2012.
Factor analysis models effectively summarise the covariance structure of high dimensional data, but the solutions are typically hard to interpret. This motivates attempting to find a disjoint partition, i.e. a simple clustering, of observed variables into highly correlated subsets. We introduce a Bayesian non-parametric approach to this problem, and demonstrate advantages over heuristic methods proposed to date. Our Dirichlet process variable clustering (DPVC) model can discover block-diagonal covariance structures in data. We evaluate our method on both synthetic and gene expression analysis problems.