IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v180y2023ics016794732200264x.html
   My bibliography  Save this article

Unified model-free interaction screening via CV-entropy filter

Author

Listed:
  • Xiong, Wei
  • Chen, Yaxian
  • Ma, Shuangge

Abstract

For many practical high-dimensional problems, interactions have been increasingly found to play important roles beyond main effects. A representative example is gene-gene interaction. Joint analysis, which analyzes all interactions and main effects in a single model, can be seriously challenged by high dimensionality. For high-dimensional data analysis in general, marginal screening has been established as effective for reducing computational cost, increasing stability, and improving estimation/selection performance. Most of the existing marginal screening methods are designed for the analysis of main effects only. The existing screening methods for interaction analysis are often limited by making stringent model assumptions, lacking robustness, and/or requiring predictors to be continuous (and hence lacking flexibility). A unified marginal screening approach tailored to interaction analysis is developed, which can be applied to regression, classification, and survival analysis. Predictors are allowed to be continuous and discrete. The proposed approach is built on Coefficient of Variation (CV) filters based on information entropy. Statistical properties are rigorously established. It is shown that the CV filters are almost insensitive to the distribution tails of predictors, correlation structure among predictors, and sparsity level of signals. An efficient two-stage algorithm is developed to make the proposed approach scalable to ultrahigh-dimensional data. Simulations and the analysis of TCGA LUAD data further establish the practical superiority of the proposed approach.

Suggested Citation

  • Xiong, Wei & Chen, Yaxian & Ma, Shuangge, 2023. "Unified model-free interaction screening via CV-entropy filter," Computational Statistics & Data Analysis, Elsevier, vol. 180(C).
    • Handle: RePEc:eee:csdana:v:180:y:2023:i:c:s016794732200264x
    DOI: 10.1016/j.csda.2022.107684
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S016794732200264X
    Download Restriction: Full text for ScienceDirect subscribers only.
    File URL: https://libkey.io/10.1016/j.csda.2022.107684?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Jingyuan Liu & Runze Li & Rongling Wu, 2014. "Feature Selection for Varying Coefficient Models With Ultrahigh-Dimensional Covariates," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(505), pages 266-274, March.
    2. Yang Li & Jun S. Liu, 2019. "Robust Variable and Interaction Selection for Logistic Regression and General Index Models," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 114(525), pages 271-286, January.
    3. Ning Hao & Hao Helen Zhang, 2017. "A Note on High-Dimensional Linear Regression With Interactions," The American Statistician, Taylor & Francis Journals, vol. 71(4), pages 291-297, October.
    4. Rui Song & Wenbin Lu & Shuangge Ma & X. Jessie Jeng, 2014. "Censored rank independence screening for high-dimensional survival data," Biometrika, Biometrika Trust, vol. 101(4), pages 799-814.
    5. 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.
    6. Hengjian Cui & Runze Li & Wei Zhong, 2015. "Model-Free Feature Screening for Ultrahigh Dimensional Discriminant Analysis," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(510), pages 630-641, June.
    7. 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.
    8. Lyu Ni & Fang Fang, 2016. "Entropy-based model-free feature screening for ultrahigh-dimensional multiclass classification," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 28(3), pages 515-530, September.
    9. 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.
    10. 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.
    11. Hall, Peter & Xue, Jing-Hao, 2014. "On selecting interacting features from high-dimensional data," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 694-708.
    12. Xuesen Wu & Li Jin & Momiao Xiong, 2009. "Mutual Information for Testing Gene-Environment Interaction," PLOS ONE, Public Library of Science, vol. 4(2), pages 1-12, February.
    13. Choi, Nam Hee & Li, William & Zhu, Ji, 2010. "Variable Selection With the Strong Heredity Constraint and Its Oracle Property," Journal of the American Statistical Association, American Statistical Association, vol. 105(489), pages 354-364.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Randall Reese & Guifang Fu & Geran Zhao & Xiaotian Dai & Xiaotian Li & Kenneth Chiu, 2022. "Epistasis Detection via the Joint Cumulant," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 14(3), pages 514-532, December.
    2. Zhao, Shaofei & Fu, Guifang, 2022. "Distribution-free and model-free multivariate feature screening via multivariate rank distance correlation," Journal of Multivariate Analysis, Elsevier, vol. 192(C).
    3. Zhong, Wei & Wang, Jiping & Chen, Xiaolin, 2021. "Censored mean variance sure independence screening for ultrahigh dimensional survival data," Computational Statistics & Data Analysis, Elsevier, vol. 159(C).
    4. 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.
    5. Jing Zhang & Qihua Wang & Xuan Wang, 2022. "Surrogate-variable-based model-free feature screening for survival data under the general censoring mechanism," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 74(2), pages 379-397, April.
    6. Li, Yujie & Li, Gaorong & Lian, Heng & Tong, Tiejun, 2017. "Profile forward regression screening for ultra-high dimensional semiparametric varying coefficient partially linear models," Journal of Multivariate Analysis, Elsevier, vol. 155(C), pages 133-150.
    7. Jun Lu & Dan Wang & Qinqin Hu, 2022. "Interaction screening via canonical correlation," Computational Statistics, Springer, vol. 37(5), pages 2637-2670, November.
    8. He, Yong & Zhang, Liang & Ji, Jiadong & Zhang, Xinsheng, 2019. "Robust feature screening for elliptical copula regression model," Journal of Multivariate Analysis, Elsevier, vol. 173(C), pages 568-582.
    9. Yang, Baoying & Yin, Xiangrong & Zhang, Nan, 2019. "Sufficient variable selection using independence measures for continuous response," Journal of Multivariate Analysis, Elsevier, vol. 173(C), pages 480-493.
    10. Tang, Niansheng & Xia, Linli & Yan, Xiaodong, 2019. "Feature screening in ultrahigh-dimensional partially linear models with missing responses at random," Computational Statistics & Data Analysis, Elsevier, vol. 133(C), pages 208-227.
    11. Ping Wang & Lu Lin, 2023. "Conditional characteristic feature screening for massive imbalanced data," Statistical Papers, Springer, vol. 64(3), pages 807-834, June.
    12. Fengli Song & Peng Lai & Baohua Shen, 2020. "Robust composite weighted quantile screening for ultrahigh dimensional discriminant analysis," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 83(7), pages 799-820, October.
    13. Lyu Ni & Fang Fang & Fangjiao Wan, 2017. "Adjusted Pearson Chi-Square feature screening for multi-classification with ultrahigh dimensional data," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 80(6), pages 805-828, November.
    14. Jing Zhang & Yanyan Liu & Hengjian Cui, 2021. "Model-free feature screening via distance correlation for ultrahigh dimensional survival data," Statistical Papers, Springer, vol. 62(6), pages 2711-2738, December.
    15. Jing Zhang & Haibo Zhou & Yanyan Liu & Jianwen Cai, 2021. "Conditional screening for ultrahigh-dimensional survival data in case-cohort studies," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 27(4), pages 632-661, October.
    16. Shuaishuai Chen & Jun Lu, 2023. "Quantile-Composited Feature Screening for Ultrahigh-Dimensional Data," Mathematics, MDPI, vol. 11(10), pages 1-21, May.
    17. Pan, Yingli, 2022. "Feature screening and FDR control with knockoff features for ultrahigh-dimensional right-censored data," Computational Statistics & Data Analysis, Elsevier, vol. 173(C).
    18. Zhang, Shen & Zhao, Peixin & Li, Gaorong & Xu, Wangli, 2019. "Nonparametric independence screening for ultra-high dimensional generalized varying coefficient models with longitudinal data," Journal of Multivariate Analysis, Elsevier, vol. 171(C), pages 37-52.
    19. Lu, Jun & Lin, Lu & Wang, WenWu, 2021. "Partition-based feature screening for categorical data via RKHS embeddings," Computational Statistics & Data Analysis, Elsevier, vol. 157(C).
    20. Yuan, Qingcong & Chen, Xianyan & Ke, Chenlu & Yin, Xiangrong, 2022. "Independence index sufficient variable screening for categorical responses," Computational Statistics & Data Analysis, Elsevier, vol. 174(C).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:csdana:v:180:y:2023:i:c:s016794732200264x. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/csda .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.