基于spike-and-slab先验分布的贝叶斯变量选择方法

doi:10.6040/j.issn.1671-9352.0.2021.065

《山东大学学报(理学版)》 ›› 2021, Vol. 56 ›› Issue (12): 84-93.doi: 10.6040/j.issn.1671-9352.0.2021.065

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基于spike-and-slab先验分布的贝叶斯变量选择方法

张宪友,李东喜^Symbolj@@

太原理工大学数学学院, 山西太原 030024

发布日期:2021-11-25
作者简介:张宪友(1995— ),男,硕士研究生,研究方向为高维数据分析. E-mail:jiyoudog@sina.com*通信作者简介:李东喜(1982— ),男,博士,副教授,研究方向为数据挖掘. E-mail:dxli0426@126.com
基金资助:
国家自然科学基金资助项目(11571009);山西省应用基础研究计划资助项目(201901D111086)

A Bayesian approach for variable selection using spike-and-slab prior distribution

ZHANG Xian-you, LI Dong-xi^*

College of Mathematics, Taiyuan University of Technology, Taiyuan 030024, Shanxi, China

Published:2021-11-25

摘要/Abstract

摘要： 针对超高维数据,提出一种基于spike-and-slab先验分布的超高维线性回归模型的贝叶斯变量选择方法。该方法继承了弹性网方法和EM算法的优点,以较快的收敛速度来获得稀疏的预测模型。特别地,针对系数的spike-and-slab先验分布设置上,该方法允许系数从不同坐标借力、自动适应已知数据的稀疏信息以及进行多重调整。通过与常用方法的比较,证明了该方法的准确性和有效性。

关键词: 变量选择, 超高维, spike-and-slab先验分布, 弹性网, 稀疏模型

Abstract: For ultra-high dimensional data, a Bayesian approach using a novel spike-and-slab prior for variable selection in high-dimensional linear regression models is presented. The proposed method aims to inherit the advantages of the elastic net and the EM algorithm to obtain sparse prediction models with faster convergence speed. Furthermore, a spike-and-slab setting of coefficients which allows for borrowing strength across coordinates, adjust to data sparsity information and exert multiplicity adjustment is proposed. Finally, the accuracy and efficiency of the proposed method are demonstrated via comparisons and analyses with common methods.

Key words: variable selection, high dimensional, spike-and-slab prior distribution, elastic net, sparse model

中图分类号:

O212.1

张宪友,李东喜. 基于spike-and-slab先验分布的贝叶斯变量选择方法[J]. 《山东大学学报(理学版)》, 2021, 56(12): 84-93.

ZHANG Xian-you, LI Dong-xi. A Bayesian approach for variable selection using spike-and-slab prior distribution[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2021, 56(12): 84-93.

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基于spike-and-slab先验分布的贝叶斯变量选择方法

A Bayesian approach for variable selection using spike-and-slab prior distribution

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