On a wider class of prior distributions for graphical models. (English) Zbl 07808668
Summary: 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 \(\mathcal{G}_n\), 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 \(\mathcal{G}_n\). In this paper we study subsets that are vector subspaces with the cycle space \(\mathcal{C}_n\) as the main example. We propose a novel prior on \(\mathcal{C}_n\) based on linear combinations of cycle basis elements and present its theoretical properties. Using this prior, we implement a Markov chain Monte Carlo algorithm, and show that (i) posterior edge inclusion estimates computed with our technique are comparable to estimates from the standard technique despite searching a smaller graph space, and (ii) the vector space perspective enables straightforward implementation of MCMC algorithms.
MSC:
| 62H22 | Probabilistic graphical models |
| 05C80 | Random graphs (graph-theoretic aspects) |
| 05C90 | Applications of graph theory |
Keywords:
Gaussian graphical model; Bayesian statistics; network inference; cycle space; Markov chain Monte Carlo; vector spaceReferences:
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