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基于拟凸损失的核正则化成对学习算法的收敛速度

王淑华1,2,王英杰3,陈振龙1,盛宝怀2   

  1. 1. 浙江工商大学统计与数学学院, 杭州 310018;2. 绍兴文理学院应用统计系,  绍兴 312000;3. 华中农业大学信息学院,武汉 430070
  • 出版日期:2020-03-25 发布日期:2020-05-30

王淑华,王英杰,陈振龙,盛宝怀. 基于拟凸损失的核正则化成对学习算法的收敛速度[J]. 系统科学与数学, 2020, 40(3): 389-409.

WANG Shuhua, WANG Yingjie, CHEN Zhenlong, SHENG Baohuai. The Convergence Rate for Kernel-Based Regularized Pair Learning Algorithm with a Quasiconvex Loss[J]. Journal of Systems Science and Mathematical Sciences, 2020, 40(3): 389-409.

The Convergence Rate for Kernel-Based Regularized Pair Learning Algorithm with a Quasiconvex Loss

WANG Shuhua 1,2 ,WANG Yingjie3 ,CHEN Zhenlong1 ,SHENG Baohuai2   

  1. 1. School of Statistics and Mathematics, Zhejiang Gongshang University, Hangzhou 310018; 2. Department of Applied Statistics, Shaoxing University, Shaoxing 312000; 3. College of Informatics, Huazhong Agricutural University, Wuhan 430070
  • Online:2020-03-25 Published:2020-05-30

核正则化排序算法是目前机器学习理论领域讨论的热点问题, 而成对学习算 法是排序算法的推广. 文章给出一种基于拟凸损失的核正则化成对学习算法, 利用拟凸 分析理论对该算法进行误差分析, 给出算法的收敛速度. 分析结果表明, 算法的样本误 差与损失函数中的参数选择有关. 数值实验结果显示, 与基于最小二乘损失的排序算法相比较, 该算法有更稳健的学习性能.

Regularized ranking algorithm based on kernels has recently gained much attention in machine learning theory, and pairwise learning is the generalization of ranking problem. In this paper, a kernel-based regularized pairwise learning algorithm with a quasiconvex loss function is provided, the error estimate is given by using the quasiconvex analysis theory, and an explicit learning rate is obtained. It is shown that the sample error is influenced by the parameters in the loss function. The experiments show that our method is more robust compared with the ranking algorithm with the least square loss function.

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