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Asymptotic Bayesian structure learning using graph supports for Gaussian graphical models

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  • Marrelec, Guillaume
  • Benali, Habib
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    Abstract

    The theory of Gaussian graphical models is a powerful tool for independence analysis between continuous variables. In this framework, various methods have been conceived to infer independence relations from data samples. However, most of them result in stepwise, deterministic, descent algorithms that are inadequate for solving this issue. More recent developments have focused on stochastic procedures, yet they all base their research on strong a priori knowledge and are unable to perform model selection among the set of all possible models. Moreover, convergence of the corresponding algorithms is slow, precluding applications on a large scale. In this paper, we propose a novel Bayesian strategy to deal with structure learning. Relating graphs to their supports, we convert the problem of model selection into that of parameter estimation. Use of non-informative priors and asymptotic results yield a posterior probability for independence graph supports in closed form. Gibbs sampling is then applied to approximate the full joint posterior density. We finally give three examples of structure learning, one from synthetic data, and the two others from real data.

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    Bibliographic Info

    Article provided by Elsevier in its journal Journal of Multivariate Analysis.

    Volume (Year): 97 (2006)
    Issue (Month): 6 (July)
    Pages: 1451-1466

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    Handle: RePEc:eee:jmvana:v:97:y:2006:i:6:p:1451-1466

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    Related research

    Keywords: Bayesian analysis Partial correlation coefficients Gaussian graphical models Conditional independence graphs Gibbs sampler;

    References

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    1. Laurent, M. & Poljak, S. & Rendl, F., 1997. "Connections between semidefinite relaxations of the max-cut and stable set problems," Open Access publications from Tilburg University urn:nbn:nl:ui:12-3959842, Tilburg University.
    2. Laurent, M. & Poljak, S., 1995. "On a positive semidefinite relaxation of the cut polytope," Open Access publications from Tilburg University urn:nbn:nl:ui:12-3959893, Tilburg University.
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