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Selection and estimation for mixed graphical models

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  • Shizhe Chen
  • Daniela M. Witten
  • Ali Shojaie

Abstract

We consider the problem of estimating the parameters in a pairwise graphical model in which the distribution of each node, conditioned on the others, may have a different exponential family form. We identify restrictions on the parameter space required for the existence of a well-defined joint density, and establish the consistency of the neighbourhood selection approach for graph reconstruction in high dimensions when the true underlying graph is sparse. Motivated by our theoretical results, we investigate the selection of edges between nodes whose conditional distributions take different parametric forms, and show that efficiency can be gained if edge estimates obtained from the regressions of particular nodes are used to reconstruct the graph. These results are illustrated with examples of Gaussian, Bernoulli, Poisson and exponential distributions. Our theoretical findings are corroborated by evidence from simulation studies.

Suggested Citation

  • Shizhe Chen & Daniela M. Witten & Ali Shojaie, 2015. "Selection and estimation for mixed graphical models," Biometrika, Biometrika Trust, vol. 102(1), pages 47-64.
    • Handle: RePEc:oup:biomet:v:102:y:2015:i:1:p:47-64.
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    File URL: http://hdl.handle.net/10.1093/biomet/asu051
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    Cited by:

    1. Forzani, Liliana & Rodriguez, Daniela & Smucler, Ezequiel & Sued, Mariela, 2019. "Sufficient dimension reduction and prediction in regression: Asymptotic results," Journal of Multivariate Analysis, Elsevier, vol. 171(C), pages 339-349.
    2. Anindya Bhadra & Arvind Rao & Veerabhadran Baladandayuthapani, 2018. "Inferring network structure in non†normal and mixed discrete†continuous genomic data," Biometrics, The International Biometric Society, vol. 74(1), pages 185-195, March.
    3. Aaron Hudson & Ali Shojaie, 2022. "Covariate-Adjusted Inference for Differential Analysis of High-Dimensional Networks," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 84(1), pages 345-388, June.
    4. Jianqing Fan & Han Liu & Yang Ning & Hui Zou, 2017. "High dimensional semiparametric latent graphical model for mixed data," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 79(2), pages 405-421, March.
    5. Kevin H. Lee & Qian Chen & Wayne S. DeSarbo & Lingzhou Xue, 2022. "Estimating Finite Mixtures of Ordinal Graphical Models," Psychometrika, Springer;The Psychometric Society, vol. 87(1), pages 83-106, March.
    6. van Wieringen, Wessel N. & Stam, Koen A. & Peeters, Carel F.W. & van de Wiel, Mark A., 2020. "Updating of the Gaussian graphical model through targeted penalized estimation," Journal of Multivariate Analysis, Elsevier, vol. 178(C).

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