LOCAL UNCERTAINTY SAMPLING FOR LARGE-SCALE MULTICLASS LOGISTIC REGRESSION

• 成果类型: Article
• 署名作者: Han, Lei; Tan, Kean Ming; Yang, Ting; Zhang, Tong
• 署名单位: Tencent; University of Michigan System; University of Michigan; Hong Kong University of Science & Technology; Hong Kong University of Science & Technology
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/19-AOS1867
• 发表日期: 2020
• 页码: 1770-1788
• 关键词: models

摘要

A major challenge for building statistical models in the big data era is that the available data volume far exceeds the computational capability. A common approach for solving this problem is to employ a subsampled dataset that can be handled by available computational resources. We propose a general subsampling scheme for large-scale multiclass logistic regression and examine the variance of the resulting estimator. We show that asymptotically, the proposed method always achieves a smaller variance than that of the uniform random sampling. Moreover, when the classes are conditionally imbalanced, significant improvement over uniform sampling can be achieved. Empirical performance of the proposed method is evaluated and compared to other methods via both simulated and real-world datasets, and these results match and confirm our theoretical analysis.