Flexible High-dimensional Classification Machines and Their Asymptotic Properties

• DOI: 10.48550/arxiv.1310.3004
• Publication Date: 2013-01-01
• Authors: Xingye Qiao; Lingsong Zhang
• Keywords: Overfitting; Decision boundary; Margin (machine learning); Sample (material)

Classification is an important topic in statistics and machine learning with great potential many real applications. In this paper, we investigate two popular large margin classification methods, Support Vector Machine (SVM) Distance Weighted Discrimination (DWD), under contexts: the high-dimensional, low-sample size data imbalanced data. A unified family of machines, FLexible Assortment MachinE (FLAME) proposed, within which DWD SVM are special cases. The FLAME helps to identify similarities differences between DWD. It well known that classifiers overfit high-dimensional setting; others sensitive data, is, class a larger sample overly influences classifier pushes decision boundary towards minority class. resistant issue, but it overfits sets by showing undesired data-piling phenomena. method was proposed improve setting, its ratio sizes. Our understand intrinsic connection DWD, improves both methods providing better trade-off sensitivity overfitting Several asymptotic properties studied. Simulations applications investigated illustrate usefulness classifiers.