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On a wider class of prior distributions for graphical models
- Part of
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- Journal:
- Journal of Applied Probability / Volume 61 / Issue 1 / March 2024
- Published online by Cambridge University Press:
- 08 June 2023, pp. 230-243
- Print publication:
- March 2024
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- Article
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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.
