A Large Scale Analysis of Logistic Regression: Asymptotic Performance and New Insights
A Large Scale Analysis of Logistic Regression: Asymptotic Performance and New Insights
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逻辑回归的大规模分析：渐近性能和新见解
DOI：
10.1109/icassp.2019.8683376
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发表时间：
2019
期刊：
影响因子：
--
通讯作者：
Romain Couillet
中科院分区：
文献类型：
--
作者：
Xiaoyi Mai;Zhenyu Liao;Romain Couillet
逻辑回归是最流行的机器学习二分类方法之一，长期以来一直被认为是无偏的。在本文中，我们考虑分离高维高斯向量的“硬”分类问题，其中数据维数p和样本量n都很大。基于随机矩阵理论和高维统计的最新进展，我们评估了逻辑回归分类器的渐近分布，从而提供了相关的分类性能。这为逻辑回归分类器的内部机制带来了新的见解，包括分离超平面中可能存在的偏差，以及超参数调优等实际问题，从而为新颖的rmt启发的改进打开了大门。
Logistic regression, one of the most popular machine learning binary classification methods, has been long believed to be unbiased. In this paper, we consider the "hard" classification problem of separating high dimensional Gaussian vectors, where the data dimension p and the sample size n are both large. Based on recent advances in random matrix theory (RMT) and high dimensional statistics, we evaluate the asymptotic distribution of the logistic regression classifier and consequently, provide the associated classification performance. This brings new insights into the internal mechanism of logistic regression classifier, including a possible bias in the separating hyperplane, as well as on practical issues such as hyper-parameter tuning, thereby opening the door to novel RMT-inspired improvements.
影响因子：
2
作者：
P. Sur;Yuxin Chen;E. Candès
通讯作者：
P. Sur;Yuxin Chen;E. Candès