基于拟凸损失的核正则化成对学习算法的收敛速度  

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

作　　者：王淑华 王英杰 陈振龙[1] 盛宝怀[2] WANG Shuhua;WANG Yingjie;CHEN Zhenlong;SHENG Baohuai(School of Statistics and Mathematics,Zhejiang Gongshang University,Hangzhou 310018;Department of Applied Statistics,Shaoxing University,Shaoocing 312000;College of Informatics,Huazhong Agricutural University,Wuhan 430070)

机构地区：[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　　处：《系统科学与数学》2020年第3期389-409,共21页Journal of Systems Science and Mathematical Sciences

基　　金：国家自然科学基金(61877039,11971432);教育部人文社会科学研究规划基金(18YJA910001)资助课题。

摘　　要：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.

关 键 词：成对学习 拟凸函数 核正则化算法 收敛速度 

分 类 号：TP181[自动化与计算机技术—控制理论与控制工程] O223[自动化与计算机技术—控制科学与工程]