对于支向量机器来说,一个新的有限损失框架
1College of Mathematics and Statistics, Chongqing University, Chongqing, 401331, China.
概括
这项研究引入了支持向量机 (SVM) 和支持向量回归 (SVR) 的新型边界指数级量子损失 (Leq-loss). 这种新的损失函数增强了对异常值和重新采样的稳定性,提高了模型的稳定性和性能.
科学领域:
- 机器学习 机器学习
- 统计学学习理论
背景情况:
- 支向量机 (SVM) 和支向量回归 (SVR) 是用于分类和回归的强大算法.
- 传统的SVM/SVR可能对异常值和数据扰动敏感,限制了它们的稳定性.
- 现有的损失函数可能无法充分解决这些稳定性问题.
研究的目的:
- 为SVM和SVR引入一个新的有限损失框架.
- 开发一个有界的指数量子损失 (Leq-loss),增强对异常值和重新采样的稳定性.
- 从理论上分析这些属性,并推导出拟议模型的泛化误差界限.
主要方法:
- 设计了一个受限指数量子损失 (Leq-loss),灵感来自Pinball损失.
- 构建了增强的量子支持向量机器 (EQSVM) 和增强的量子支持向量回归 (EQSVR).
- 利用凸过程 (CCCP) 和ClipDCD算法进行优化.
- 使用Rademacher复杂度推导影响函数,分解点下限和概括错误界限.
主要成果:
- Leq-loss显示了SVM和SVR对异常值的增强稳定性.
- 与标准SVM相比,EQSVM显示了对重新采样的更好的稳定性.
- 影响函数被证明是有界的,分解点的下限达到1/2.
- 为EQSVM推导出了泛化误差界限.
结论:
- 拟议的Leq损失框架有效地提高了SVM和SVR的稳定性.
- EQSVM和EQSVR提供了更好的稳定性和可靠性,特别是在有噪音数据的情况下.
- 理论分析支持通过实验证明的实际有效性.
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