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Uniform joint screening for ultra-high dimensional graphical models

Author

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  • Zheng, Zemin
  • Shi, Haiyu
  • Li, Yang
  • Yuan, Hui

Abstract

Identifying large-scale conditional dependence structures through graphical models is a challenging yet practical problem. Under ultra-high dimensional settings, a screening procedure is generally suggested before variable selection to reduce computational costs. However, most existing screening methods examine the marginal correlations, thus not suitable to discover the conditional dependence in graphical models. To overcome this issue, we propose a new procedure called graphical uniform joint screening (GUS) for edge identification in graphical models. Instead of screening out edges nodewisely, GUS utilizes a uniform threshold for all statistics indicating the significance of different edges to adapt to various kinds of graphical structures. We demonstrate that GUS enjoys the sure screening property and even the screening consistency by preserving the rankings of the significant edges. Furthermore, a scalable implementation of GUS is developed for big data applications. Simulation and real data studies are provided to illustrate the effectiveness of the proposed method.

Suggested Citation

  • Zheng, Zemin & Shi, Haiyu & Li, Yang & Yuan, Hui, 2020. "Uniform joint screening for ultra-high dimensional graphical models," Journal of Multivariate Analysis, Elsevier, vol. 179(C).
    • Handle: RePEc:eee:jmvana:v:179:y:2020:i:c:s0047259x20302268
    DOI: 10.1016/j.jmva.2020.104645
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    References listed on IDEAS

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    1. Jian Guo & Elizaveta Levina & George Michailidis & Ji Zhu, 2011. "Joint estimation of multiple graphical models," Biometrika, Biometrika Trust, vol. 98(1), pages 1-15.
    2. Zhao, Sihai Dave & Li, Yi, 2012. "Principled sure independence screening for Cox models with ultra-high-dimensional covariates," Journal of Multivariate Analysis, Elsevier, vol. 105(1), pages 397-411.
    3. Fan, Jianqing & Feng, Yang & Song, Rui, 2011. "Nonparametric Independence Screening in Sparse Ultra-High-Dimensional Additive Models," Journal of the American Statistical Association, American Statistical Association, vol. 106(494), pages 544-557.
    4. Peng, Jie & Wang, Pei & Zhou, Nengfeng & Zhu, Ji, 2009. "Partial Correlation Estimation by Joint Sparse Regression Models," Journal of the American Statistical Association, American Statistical Association, vol. 104(486), pages 735-746.
    5. Runze Li & Wei Zhong & Liping Zhu, 2012. "Feature Screening via Distance Correlation Learning," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(499), pages 1129-1139, September.
    6. Ming Yuan & Yi Lin, 2007. "Model selection and estimation in the Gaussian graphical model," Biometrika, Biometrika Trust, vol. 94(1), pages 19-35.
    7. Shujie Ma & Runze Li & Chih-Ling Tsai, 2017. "Variable Screening via Quantile Partial Correlation," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(518), pages 650-663, April.
    8. Jianqing Fan & Jinchi Lv, 2008. "Sure independence screening for ultrahigh dimensional feature space," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 70(5), pages 849-911, November.
    9. Teng Zhang & Hui Zou, 2014. "Sparse precision matrix estimation via lasso penalized D-trace loss," Biometrika, Biometrika Trust, vol. 101(1), pages 103-120.
    10. Xiangyu Wang & Chenlei Leng, 2016. "High dimensional ordinary least squares projection for screening variables," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 78(3), pages 589-611, June.
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    Cited by:

    1. Zhou, Jia & Li, Yang & Zheng, Zemin & Li, Daoji, 2022. "Reproducible learning in large-scale graphical models," Journal of Multivariate Analysis, Elsevier, vol. 189(C).

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