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

Baiguo An, Guozhong Feng and Jianhua Guo ()
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Baiguo An: Capital University of Economics and Business
Guozhong Feng: Northeast Normal University
Jianhua Guo: Northeast Normal University

Journal of Classification, 2022, vol. 39, issue 1, No 8, 122-146

Abstract: 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.

Keywords: Clique set; Kullback-Leibler divergence; Naïve Bayes; Screening; Supervised classification; Ultra-high dimension (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s00357-021-09399-0

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