Large dimensional analysis of general margin based classification methods
Large dimensional analysis of general margin based classification methods
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DOI：
10.1088/1742-5468/ac2edd
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发表时间：
2021-11-01
影响因子：
2.4
通讯作者：
Yang, Qinglong
中科院分区：
文献类型：
--
作者：
Huang, Hanwen;Yang, Qinglong
基于边缘的分类器在机器学习和统计分类问题中都很受欢迎。由于大量的分类器是可用的，一个自然的问题是哪种类型的分类器应该被使用给定的一个特定的分类任务。我们回答这个问题，通过调查的两个组件的混合模型下的数据维数p和样本n都很大的情况下，一个家庭的大利润分类器的渐近性能。这个家族涵盖了广泛的分类器，包括支持向量机，距离加权判别，惩罚逻辑回归和大边缘统一机作为特殊情况。渐近结果描述了一组非线性方程组，我们观察到他们的密切配合与Monte Carlo模拟有限的数据样本。我们的分析研究揭示了新的光如何选择最好的分类器之间的各种分类方法，以及如何选择最佳的调整参数为一个给定的方法。
Margin-based classifiers have been popular in both machine learning and statistics for classification problems. Since a large number of classifiers are available, one natural question is which type of classifiers should be used given a particular classification task. We answer this question by investigating the asymptotic performance of a family of large-margin classifiers under the two component mixture models in situations where the data dimension p and the sample n are both large. This family covers a broad range of classifiers including support vector machine, distance weighted discrimination, penalized logistic regression, and large-margin unified machine as special cases. The asymptotic results are described by a set of nonlinear equations and we observe a close match of them with Monte Carlo simulation on finite data samples. Our analytical studies shed new light on how to select the best classifier among various classification methods as well as on how to choose the optimal tuning parameters for a given method.