On a wider class of prior distributions for graphical models
share
Gaussian graphical models are useful tools for conditional independence structure inference of multivariate random variables. Unfortunately, Bayesian inference of latent graph structures is challenging due to exponential growth of 𝒢_n, the set of all graphs in n vertices. One approach that has been proposed to tackle this problem is to limit search to subsets of 𝒢_n. In this paper, we study subsets that are vector subspaces with the cycle space 𝒞_n as main example. We propose a novel prior on 𝒞_n based on linear combinations of cycle basis elements and present its theoretical properties. Using this prior, we implemented a Markov chain Monte Carlo algorithm and show that (i) posterior edge inclusion estimates compared to the standard technique are comparable despite searching a smaller graph space and (ii) the vector space perspective enables straightforward MCMC algorithms.
READ FULL TEXT