Variable selection method based on BIC with consistency for non-zero partial correlations under a large-dimensional setting

This paper addresses the problem of selecting non-zero partial correlations under the assumption of normality. It is cumbersome to compute variable selection criteria for all subsets of variable pairs when the number of variables is large, even if it is smaller than the sample size. To tackle this p...

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Bibliographic Details
Published inComputational statistics Vol. 40; no. 7; pp. 3585 - 3611
Main Authors Yamada, Takayuki, Sakurai, Tetsuro, Fujikoshi, Yasunori
Format Journal Article
LanguageEnglish
Published Heidelberg Springer Nature B.V 01.09.2025
Subjects
Asymptotic methods
Correlation
Discriminant analysis
Feature selection
Normal distribution
Normality
Regularization methods
Variables
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ISSN0943-4062
1613-9658
DOI10.1007/s00180-025-01628-z

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Summary:This paper addresses the problem of selecting non-zero partial correlations under the assumption of normality. It is cumbersome to compute variable selection criteria for all subsets of variable pairs when the number of variables is large, even if it is smaller than the sample size. To tackle this problem, we propose a fast and consistent variable selection method based on Bayesian information criterion (BIC). The consistency of the method is provided in a high-dimensional asymptotic framework such that the sample size and the number of variables both tend toward infinity under a certain rule. Through numerical simulations, it is shown that the proposed method has a high probability of selecting the true subset of pairs of non-zero partial correlation.
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ISSN:0943-4062
1613-9658
DOI:10.1007/s00180-025-01628-z