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Model selection for Markov random fields on graphs under a mixing condition

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  • Leonardi, Florencia
  • Severino, Magno T.F.

Abstract

We propose a global model selection criterion to estimate the graph of conditional dependencies of a random vector. By global criterion, we mean optimizing a function over the set of possible graphs, eliminating the need to estimate individual neighborhoods and subsequently combine them to estimate the graph. We prove the almost sure convergence of the graph estimator. This convergence holds, provided the data is a realization of a multivariate stochastic process that satisfies a polynomial mixing condition. These are the first results to show the consistency of a model selection criterion for Markov random fields on graphs under non-independent data.

Suggested Citation

  • Leonardi, Florencia & Severino, Magno T.F., 2025. "Model selection for Markov random fields on graphs under a mixing condition," Stochastic Processes and their Applications, Elsevier, vol. 180(C).
    • Handle: RePEc:eee:spapps:v:180:y:2025:i:c:s030441492400231x
    DOI: 10.1016/j.spa.2024.104523
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    References listed on IDEAS

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    1. Löcherbach, Eva & Orlandi, Enza, 2011. "Neighborhood radius estimation for variable-neighborhood random fields," Stochastic Processes and their Applications, Elsevier, vol. 121(9), pages 2151-2185, September.
    2. Fabio Divino & Arnoldo Frigessi & Peter J. Green, 2000. "Penalized Pseudolikelihood Inference in Spatial Interaction Models with Covariates," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 27(3), pages 445-458, September.
    3. Johan Pensar & Henrik Nyman & Jukka Corander, 2017. "Structure Learning of Contextual Markov Networks using Marginal Pseudo-likelihood," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 44(2), pages 455-479, June.
    4. Ali Shojaie & George Michailidis, 2010. "Penalized likelihood methods for estimation of sparse high-dimensional directed acyclic graphs," Biometrika, Biometrika Trust, vol. 97(3), pages 519-538.
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