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中国工业与应用数学学会会刊
主管：中华人民共和国教育部
主办：西安交通大学
ISSN 1005-3085  CN 61-1269/O1
工程数学学报

工程数学学报 ›› 2023, Vol. 40 ›› Issue (2): 310-320.doi: 10.3969/j.issn.1005-3085.2023.02.010

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在线Group Lasso学习

郑乃嘉1,2,   张   海1   

  1. 1. 西北大学数学学院，西安  710127
    2. 西北工业大学机电学院，西安 710072
  • 收稿日期:2020-12-07 接受日期:2021-03-29 出版日期:2023-04-15 发布日期:2023-06-20
  • 基金资助:
    国家自然科学基金---广东省大数据重大项目 (U1811461)；陕西省自然科学基金 (2021JQ-429).

Group Lasso Online Learning

ZHENG Naijia1,2,  ZHANG Hai1   

  1. 1. School of Mathematics, Northwest University, Xi'an 710127
    2. School of Mechanical Engineering, Northwestern Polytechnical University, Xi'an 710072
  • Received:2020-12-07 Accepted:2021-03-29 Online:2023-04-15 Published:2023-06-20
  • Supported by:
    The National Natural Science Foundation of China---Guangdong Joint Fund (U1811461); the Natural Science Foundation of Shaanxi Province (2021JQ-429).

PDF (PC)

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摘要：

对高维流式数据的在线组变量选择问题进行了研究，提出了带Group Lasso惩罚的逻辑斯蒂回归在线估计方法，并给出了GFTPRL (Group Follow the Proximally Regularized Leader) 算法。通过给出 GFTPRL 算法的缺憾界，证明了算法在理论上是有效的。实验结果表明，对于稀疏模型 GFTPRL 算法的预测分类准确率明显优于其他主流稀疏在线算法。

关键词: 机器学习, Group Lasso, 在线学习, 逻辑斯蒂回归

Abstract:

Aiming at solving the Group Lasso of high-dimensional data or streaming data, the online learning model for the group lasso is proposed, and a closed-form solution of this model is obtained. Then the GFTPRL (Group Follow the Proximally Regularized Leader) algorithm is applied to logistic regression. Moreover, the GFTPRL algorithm's regret bound is proved to be good in online framework. Finally, the numerical results show that the prediction accuracy of the GFTPRL algorithm is significantly better than that of other mainstream sparse online algorithms when the sample size is large and the final model is sparse.

Key words: machine learning, Group Lasso, online learning, logistic regression

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