The Kendall interaction filter for variable interaction screening in high dimensional classification problems

References

• A. Alfons, C. Croux, and P. Filzmoser, Robust maximum association between data sets: the R package ccaPP, Austrian J. Stat. 45 (2016), pp. 71–79.
   Google Scholar
• U. Alon, N. Barka, D.A. Notterman, K. Gish, S. Ybarra, D. Mack, and A.J. Levine, Broad patterns of gene expression revealed by clustering analysis of tumor and normal colon tissues probed by oligonucleotide arrays, Proc. Natl. Acad. Sci. U.S.A. 96 (1999), pp. 6745–6750.
   PubMed Web of Science ®Google Scholar
• P.S. Bradley and O.L. Mangasarian, Feature selection via concave minimization and support vector machines, Proceedings of the Fifteenth International Conference on Machine Learning, San Francisco, CA. Morgan Kaufmann Publishers Inc., ICML '98, 1998, pp. 82–90.
   Google Scholar
• L. Ceriani and P. Verme, The origins of the Gini index: Extracts from variabilità e mutabilità (1912) by Corrado Gini, J. Econ. Inequal. 10 (2012), pp. 421–443.
   Web of Science ®Google Scholar
• H.J. Cordell, Detecting gene-gene interactions that underlie human diseases, Nat. Rev. Genet. 10 (2009), pp. 392–404.
   PubMed Web of Science ®Google Scholar
• H. Cui, R. Li, and W. Zhong, Model-free feature screening for ultrahigh dimensional discriminant analysis, J. Am. Stat. Assoc. 110 (2015), pp. 630–641.
   PubMed Web of Science ®Google Scholar
• M. Dettling and P. Bühlmann, Finding predictive gene groups from microarray data, J. Multivar. Anal. 90 (2004), pp. 106–131.
   Web of Science ®Google Scholar
• J. Fan, Y. Feng, and R. Song, Nonparametric independence screening in sparse ultra-high-dimensional additive models, J. Am. Stat. Assoc. 106 (2011), pp. 544–557.
   PubMed Web of Science ®Google Scholar
• J. Fan and J. Lv, Sure independence screening for ultrahigh dimensional feature space, J. R. Stat. Soc. Ser. B: Stat. Methodol. 70 (2008), pp. 849–911.
   PubMed Web of Science ®Google Scholar
• J. Fan and J. Lv, Sure independence screening, Wiley StatsRef: Statistics Reference Online, 2018.
   Google Scholar
• J. Fan and R. Song, Sure independence screening in generalized linear models with NP-dimensionality, Ann. Stat. 38 (2010), pp. 3567–3604.
   Web of Science ®Google Scholar
• Y. Fan, Y. Kong, D. Li, and J. Lv, Interaction pursuit with feature screening and selection, preprint (2016), Available at arXiv:1605.08933.
   Google Scholar
• Y. Fan, Y. Kong, D. Li, and Z. Zheng, Innovated interaction screening for high-dimensional nonlinear classification, Ann. Stat. 43 (2015), pp. 1243–1272.
   Web of Science ®Google Scholar
• P. Hall and J.H. Xue, On selecting interacting features from high-dimensional data, Comput. Stat. Data Anal. 71 (2014), pp. 694–708.
   Web of Science ®Google Scholar
• N. Hao and H.H. Zhang, Interaction screening for ultrahigh-Dimensional data, J. Am. Stat. Assoc. 109 (2014), pp. 1285–1301.
   PubMed Web of Science ®Google Scholar
• K. He, H. Xu, and J. Kang, A selective overview of feature screening methods with applications to neuroimaging data, Wiley Interdiscip. Rev.: Comput. Stat. 11 (2019), pp. 1–9.
   Google Scholar
• W. Hoeffding, Masstabinvariante korrelationstheorie, Schriften Mathe. Inst. Inst. Angewandte Math. Der Universitat Berlin 5 (1940), pp. 181–233.
   Google Scholar
• W. Hoeffding, Masstabinvariante korrelationsmasse für diskontinuierliche verteilungen, Arch. Mathe. Wirtschafts Sozialforschung 7 (1941), pp. 49–70.
   Google Scholar
• J.S.L. Hu, Probabilistic independence and joint cumulants, J. Eng. Mech. 117 (1991), pp. 640–652.
   Web of Science ®Google Scholar
• D. Huang, R. Li, and H. Wang, Feature screening for ultrahigh dimensional categorical data with applications, J. Bus. Econ. Stat. 32 (2014), pp. 237–244.
   PubMed Web of Science ®Google Scholar
• J. Kang, H.G. Hong, and Y. Li, Partition-based ultrahigh-dimensional variable screening, Biometrika 104 (2017), pp. 785–800.
   PubMed Web of Science ®Google Scholar
• Z.T. Ke, J. Jin, and J. Fan, Covariate assisted screening and estimation, Ann. Stat. 42 (2014),pp. 2202–2242.
   PubMed Web of Science ®Google Scholar
• Y. Kong, D. Li, Y. Fan, and J. Lv, Interaction pursuit in high-dimensional multi-response regression via distance correlation, Ann. Stat. 45 (2017), pp. 897–922.
   Web of Science ®Google Scholar
• G. Li, H. Peng, J. Zhang, and L. Zhu, Robust rank correlation based screening, Ann. Stat. 40 (2012), pp. 1846–1877.
   Web of Science ®Google Scholar
• R. Li, W. Zhong, and L. Zhu, Feature screening via distance correlation learning, J. Am. Stat. Assoc. 107 (2012), pp. 1129–1139.
   PubMed Web of Science ®Google Scholar
• Y. Li and J.S. Liu, Robust variable and interaction selection for logistic regression and general index models, J. Am. Stat. Assoc. 114 (2019), pp. 271–286.
   PubMed Web of Science ®Google Scholar
• Q. Mai and H. Zou, The Kolmogorov filter for variable screening in high-dimensional binary classification, Biometrika 100 (2013), pp. 229–234.
   Web of Science ®Google Scholar
• Q. Mai and H. Zou, The fused Kolmogorov filter: A nonparametric model-free screening method, Ann. Stat. 43 (2015), pp. 1471–1497.
   Web of Science ®Google Scholar
• J.H. Moore, The ubiquitous nature of epistasis in determining susceptibility to common human diseases, Hum. Hered. 56 (2003), pp. 73–82.
   PubMed Web of Science ®Google Scholar
• A. Nica and R. Speicher, Lectures on the combinatorics of free probability, London Mathematical Society Lecture Note Series, Cambridge University Press, Cambridge, 2006.
   Google Scholar
• W. Pan, X. Wang, W. Xiao, and H. Zhu, A generic sure independence screening procedure, J. Am. Stat. Assoc. 114 (2019), pp. 928–937.
   PubMed Web of Science ®Google Scholar
• W. Pan, X. Wang, H. Zhang, H. Zhu, and J. Zhu, Ball covariance: A generic measure of dependence in banach space, J. Am. Stat. Assoc. 115 (2020), pp. 307–317.
   PubMed Web of Science ®Google Scholar
• P.C. Phillips, Epistasis – the essential role of gene interactions in the structure and evolution of genetic systems, Nat. Rev. Genet. 9 (2008), pp. 855–867.
   PubMed Web of Science ®Google Scholar
• D. Qiu and J. Ahn, Grouped variable screening for ultra-high dimensional data for linear model, Comput. Stat. Data Anal. 144 (2020), pp. 106894.
   Web of Science ®Google Scholar
• R.D. Reese, Feature screening of ultrahigh dimensional feature spaces with applications in interaction screening, ProQuest Dissertations and Theses, Utah State University, 2018.
   Google Scholar
• G.J. Székely, M.L. Rizzo, and N.K. Bakirov, Measuring and testing dependence by correlation of distances, Ann. Stat. 35 (2007), pp. 2769–2794.
   Web of Science ®Google Scholar
• E. Tian, F. Zhan, R. Walker, E. Rasmussen, Y. Ma, B. Barlogie, and J.D. Shaughnessy Jr., The role of the Wnt-Signaling antagonist DKK1 in the development of osteolytic lesions in multiple Myeloma, New Engl. J. Med. 349 (2003), pp. 2483–2494.
   PubMed Web of Science ®Google Scholar
• R. Tibshirani, Regression shrinkage and selection via the Lasso, J. R. Stat. Soc.: Ser. B (Methodol.) 58 (1996), pp. 267–288.
   Google Scholar
• H. Wang, Factor profiled sure independence screening, Biometrika 99 (2012), pp. 15–28.
   Web of Science ®Google Scholar
• M. West, C. Blanchette, H. Dressman, E. Huang, S. Ishida, R. Spang, H. Zuzan, J.A. Olson, J.R. Marks, and J.R. Nevins, Predicting the clinical status of human breast cancer by using gene expression profiles, Proc. Natl. Acad. Sci. U.S.A. 98 (2001), pp. 11462–11467.
   PubMed Web of Science ®Google Scholar