基于自适应惩罚的潜变量高斯图模型结构学习

吉林大学学报(理学版) ›› 2023, Vol. 61 ›› Issue (5): 1056-1062.

基于自适应惩罚的潜变量高斯图模型结构学习

郑倩贞¹, 徐平峰²

1. 长春工业大学数学与统计学院, 长春 130012； 2. 东北师范大学前沿交叉研究院，长春 130024

收稿日期:2023-01-04 出版日期:2023-09-26 发布日期:2023-09-26
通讯作者: 徐平峰 E-mail:xupf_stat@126.com

Structure Learning of Gaussian Graphical Models with Latent Variables Based on Adaptive Penalties

ZHENG Qianzhen¹， XU Pingfeng²

1. School of Mathematics and Statistics, Changchun University of Technology, Changchun 130012, China;
2. Academy for Advanced Interdisciplinary Studies, Northeast Normal University, Changchun 130024, China

Received:2023-01-04 Online:2023-09-26 Published:2023-09-26

摘要/Abstract

摘要： 采用自适应惩罚似然方法解决含潜变量高斯图模型的结构学习问题. 模拟结果表明, 自适应惩罚显著优于非自适应惩罚, 可有效降低估计偏差, 更准确地估计给定潜变量时观测变量间的条件独立性关系.

关键词: 潜变量高斯图模型, 自适应LASSO惩罚, 自适应核范数惩罚, 交替方向乘子法

Abstract: We used the adaptive penalized likelihood method to solve the structure learning problem of Gaussian graphical models with latent variables. The simulation results show that the adaptive penalties are significantly superior to the non-adaptive penalties, which can effectively reduce the estimation bias and more accurately estimate the conditional independence relationships among observed variables given latent variables.

Key words: latent variable Gaussian graphical model, adaptive LASSO penalty, adaptive nuclear norm penalty, alternating direction method of multipliers

中图分类号:

郑倩贞, 徐平峰. 基于自适应惩罚的潜变量高斯图模型结构学习[J]. 吉林大学学报(理学版), 2023, 61(5): 1056-1062.

ZHENG Qianzhen, XU Pingfeng. Structure Learning of Gaussian Graphical Models with Latent Variables Based on Adaptive Penalties[J]. Journal of Jilin University Science Edition, 2023, 61(5): 1056-1062.