Bayesian inference for latent chain graphs

Lu, Dunyue; Jasra, Ajay; Rosner, Gary L.

doi:10.3934/fods.2020003

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2023

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“…Lastly, in this paper we have only considered standard GGMs. However, it may be possible to extend this method to other types of graphical models such as multiple graphs [27,34], Gaussian copulas [12,24] and chain graphs [22,32].…”

Section: Discussionmentioning

confidence: 99%

On a wider class of prior distributions for graphical models

2023

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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.

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