广西师范大学学报（自然科学版） ›› 2026, Vol. 44 ›› Issue (1): 110-118.doi: 10.16088/j.issn.1001-6600.2025030703

• 数学与统计学 • 上一篇    下一篇

一种基于错误发现率的模型选择规则

荣晶晶, 冶继民*   

  1. 西安电子科技大学 数学与统计学院, 陕西 西安 710126
  • 收稿日期:2025-03-07 修回日期:2025-05-18 出版日期:2026-01-05 发布日期:2026-01-26
  • 通讯作者: 冶继民(1967—),男,陕西宝鸡人,西安电子科技大学教授,博士。E-mail: jmye@mail.xidian.edu.cn
  • 基金资助:
    国家自然科学基金(12272283)

A Model Selection Criterion Based on False Discovery Rate

RONG Jingjing, YE Jimin*   

  1. School of Mathematics and Statistics, Xidian University, Xi’an Shaanxi 710126, China
  • Received:2025-03-07 Revised:2025-05-18 Online:2026-01-05 Published:2026-01-26

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摘要： 针对高维稀疏线性回归模型,本文从后验估计角度提出基于错误发现率(false discovery rate, FDR)的模型选择FDR规则;之后在其基础上引入动态信噪比(signal-to-noise ratio, SNR)变化因子,提出对SNR变化更稳健且对数据尺度具有不变性的FDRR规则;结合OMP算法,仿真实验对比分别采用FDR规则、FDRR规则和已有规则下成功选择全部真正变量的概率和FDR值,结果表明,相较于其他规则,FDRR规则在高SNR或大样本量下更稳健,对数据缩放问题更加鲁棒,且错误发现率最低;最后,将所提方法应用到套细胞淋巴瘤患者的真实数据,筛选出影响细胞增殖的基因编号。

关键词: 高维模型选择, 错误发现率, FDRR, OMP算法, 信噪比

Abstract: For high-dimensional sparse linear regression models, this paper proposed an FDR rule for model selection based on false discovery rate (FDR) from the perspective of posterior estimation, and then introduced a dynamic signal-to-noise ratio (SNR) change factor on this basis. The FDRR rule, which was more robust to SNR variations and was invariant to data scale, was proposed. Combined with the OMP algorithm, simulation experiments compared the probabilities of successfully selecting all true variables and the FDR values for the FDR rule, FDRR rule, and existing rules. The results show that the FDRR rule is more robust than the other rules in high SNR or large sample sizes, more resistant to data scaling issues, and achieves the lowest FDR. Finally, the proposed method was applied to real data from patients with mantle cell lymphoma, identifying genes associated with cell proliferation.

Key words: high-dimensional model selection, FDR, FDRR, OMP algorithm, SNR

中图分类号:  O212.8

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