Title: Robust Bayesian Model Selection for Variable Clustering with the Gaussian Graphical Model,
Abstract: Variable clustering is important for explanatory analysis. However, only few
dedicated methods for variable clustering with the Gaussian graphical model
have been proposed. Even more severe, small insignificant partial correlations
due to noise can dramatically change the clustering result when evaluating for
example with the Bayesian Information Criteria (BIC). In this work, we try to
address this issue by proposing a Bayesian model that accounts for negligible
small, but not necessarily zero, partial correlations. Based on our model, we
propose to evaluate a variable clustering result using the marginal likelihood.
To address the intractable calculation of the marginal likelihood, we propose
two solutions: one based on a variational approximation, and another based on
MCMC. Experiments on simulated data shows that the proposed method is similarly
accurate as BIC in the no noise setting, but considerably more accurate when
there are noisy partial correlations. Furthermore, on real data the proposed
method provides clustering results that are intuitively sensible, which is not
always the case when using BIC or its extensions.