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Equivalence class selection of categorical graphical models

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  • Castelletti, Federico
  • Peluso, Stefano

Abstract

Learning the structure of dependence relations between variables is a pervasive issue in the statistical literature. A directed acyclic graph (DAG) can represent a set of conditional independencies, but different DAGs may encode the same set of relations and are indistinguishable using observational data. Equivalent DAGs can be collected into classes, each represented by a partially directed graph known as essential graph (EG). Structure learning directly conducted on the EG space, rather than on the allied space of DAGs, leads to theoretical and computational benefits. Still, the majority of efforts has been dedicated to Gaussian data, with less attention to methods designed for multivariate categorical data. A Bayesian methodology for structure learning of categorical EGs is then proposed. Combining a constructive parameter prior elicitation with a graph-driven likelihood decomposition, a closed-form expression for the marginal likelihood of a categorical EG model is derived. Asymptotic properties are studied, and an MCMC sampler scheme developed for approximate posterior inference. The methodology is evaluated on both simulated scenarios and real data, with appreciable performance in comparison with state-of-the-art methods.

Suggested Citation

  • Castelletti, Federico & Peluso, Stefano, 2021. "Equivalence class selection of categorical graphical models," Computational Statistics & Data Analysis, Elsevier, vol. 164(C).
  • Handle: RePEc:eee:csdana:v:164:y:2021:i:c:s0167947321001389
    DOI: 10.1016/j.csda.2021.107304
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    References listed on IDEAS

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    1. Alain Hauser & Peter Bühlmann, 2015. "Jointly interventional and observational data: estimation of interventional Markov equivalence classes of directed acyclic graphs," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 77(1), pages 291-318, January.
    2. Guido Consonni & Luca La Rocca & Stefano Peluso, 2017. "Objective Bayes Covariate-Adjusted Sparse Graphical Model Selection," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 44(3), pages 741-764, September.
    3. J. Peters & P. Bühlmann, 2014. "Identifiability of Gaussian structural equation models with equal error variances," Biometrika, Biometrika Trust, vol. 101(1), pages 219-228.
    4. Jack Kuipers & Giusi Moffa, 2017. "Partition MCMC for Inference on Acyclic Digraphs," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(517), pages 282-299, January.
    5. Guido Consonni & Luca La Rocca, 2012. "Objective Bayes Factors for Gaussian Directed Acyclic Graphical Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 39(4), pages 743-756, December.
    6. Federico Castelletti, 2020. "Bayesian Model Selection of Gaussian Directed Acyclic Graph Structures," International Statistical Review, International Statistical Institute, vol. 88(3), pages 752-775, December.
    7. Steen A. Andersson & David Madigan & Michael D. Perlman, 2001. "Alternative Markov Properties for Chain Graphs," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 28(1), pages 33-85, March.
    8. Christine Peterson & Francesco C. Stingo & Marina Vannucci, 2015. "Bayesian Inference of Multiple Gaussian Graphical Models," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(509), pages 159-174, March.
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