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Interaction Identification and Clique Screening for Classification with Ultra-high Dimensional Discrete Features

Author

Listed:
  • Baiguo An

    (Capital University of Economics and Business)

  • Guozhong Feng

    (Northeast Normal University)

  • Jianhua Guo

    (Northeast Normal University)

Abstract

Interactions have greatly influenced recent scientific discoveries, but the identification of interactions is challenging in ultra-high dimensions. In this study, we propose an interaction identification method for classification with ultra-high dimensional discrete features. We utilize clique sets to capture interactions among features, where features in a common clique have interactions that can be used for classification. The number of features related to the interaction is the size of the clique. Hence, our method can consider interactions caused by more than two feature variables. We propose a Kullback-Leibler divergence-based approach to correctly identify the clique sets with a probability that tends to 1 as the sample size tends to infinity. A clique screening method is then proposed to filter out clique sets that are useless for classification, and the strong sure screening property can be guaranteed. Finally, a clique naïve Bayes classifier is proposed for classification. Numerical studies demonstrate that our proposed approach performs very well.

Suggested Citation

  • Baiguo An & Guozhong Feng & Jianhua Guo, 2022. "Interaction Identification and Clique Screening for Classification with Ultra-high Dimensional Discrete Features," Journal of Classification, Springer;The Classification Society, vol. 39(1), pages 122-146, March.
    • Handle: RePEc:spr:jclass:v:39:y:2022:i:1:d:10.1007_s00357-021-09399-0
    DOI: 10.1007/s00357-021-09399-0
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    References listed on IDEAS

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    1. 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.
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    3. 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.
    4. Ning Hao & Hao Helen Zhang, 2014. "Interaction Screening for Ultrahigh-Dimensional Data," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(507), pages 1285-1301, September.
    5. Danyang Huang & Runze Li & Hansheng Wang, 2014. "Feature Screening for Ultrahigh Dimensional Categorical Data With Applications," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 32(2), pages 237-244, April.
    6. 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.
    7. Ming Yuan & Yi Lin, 2006. "Model selection and estimation in regression with grouped variables," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(1), pages 49-67, February.
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