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Graphical model selection and estimation for high dimensional tensor data

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  • He, Shiyuan
  • Yin, Jianxin
  • Li, Hongzhe
  • Wang, Xing

Abstract

Multi-way tensor data are prevalent in many scientific areas such as genomics and biomedical imaging. We consider a K-way tensor-normal distribution, where the precision matrix for each way has a graphical interpretation. We develop an l1 penalized maximum likelihood estimation and an efficient coordinate descent-based algorithm for model selection and estimation in such tensor normal graphical models. When the dimensions of the tensor are fixed, we drive the asymptotic distributions and oracle property for the proposed estimates of the precision matrices. When the dimensions diverge as the sample size goes to infinity, we present the rates of convergence of the estimates and sparsistency results. Simulation results demonstrate that the proposed estimation procedure can lead to better estimates of the precision matrices and better identifications of the graph structures defined by the precision matrices than the standard Gaussian graphical models. We illustrate the methods with an analysis of yeast gene expression data measured over different time points and under different experimental conditions.

Suggested Citation

  • He, Shiyuan & Yin, Jianxin & Li, Hongzhe & Wang, Xing, 2014. "Graphical model selection and estimation for high dimensional tensor data," Journal of Multivariate Analysis, Elsevier, vol. 128(C), pages 165-185.
    • Handle: RePEc:eee:jmvana:v:128:y:2014:i:c:p:165-185
    DOI: 10.1016/j.jmva.2014.03.007
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    References listed on IDEAS

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    1. P. Tseng, 2001. "Convergence of a Block Coordinate Descent Method for Nondifferentiable Minimization," Journal of Optimization Theory and Applications, Springer, vol. 109(3), pages 475-494, June.
    2. Yin, Jianxin & Li, Hongzhe, 2012. "Model selection and estimation in the matrix normal graphical model," Journal of Multivariate Analysis, Elsevier, vol. 107(C), pages 119-140.
    3. Lam, Clifford & Fan, Jianqing, 2009. "Sparsistency and rates of convergence in large covariance matrix estimation," LSE Research Online Documents on Economics 31540, London School of Economics and Political Science, LSE Library.
    4. Ming Yuan & Yi Lin, 2007. "Model selection and estimation in the Gaussian graphical model," Biometrika, Biometrika Trust, vol. 94(1), pages 19-35.
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    Cited by:

    1. Niu, Lu & Liu, Xiumin & Zhao, Junlong, 2020. "Robust estimator of the correlation matrix with sparse Kronecker structure for a high-dimensional matrix-variate," Journal of Multivariate Analysis, Elsevier, vol. 177(C).

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