Bayesian block-diagonal graphical models via the Fiedler prior

Daria Bystrova, Mario Beraha, Julyan Arbel

Abstract:

We study the problem of inferring the conditional independence structure
between the entries of a Gaussian random vector. Our focus is on finding groups of
independent variables. This can be translated into the estimation of a precision matrix
(inverse of the covariance matrix) with a block-diagonal structure. We borrow ideas from
spectral graph theory and spectral clustering and propose a novel prior called Fiedler prior
showing shrinkage properties towards block-diagonal precision matrices. We compare the
shrinkage induced by our prior and the popular Graphical Lasso prior, and compare their
performance on a simulated dataset.