带混合三角噪声的最大相关熵回归模型  

Maximum Correntropy Regression Model with Mixture of Triangular Noise

作　　者：井迎 杨联强 王学军[3] JING YING;YANG LIANQIANG;WANG XUEJUN(School of Mathematics and Statistics,Suzhou University,Suzhou 234000,China;School of Artificial Intelligence,Anhui University,Hefei 230601,China;School of Big Data and Statistics,Anhui University,Hefei 230601,China)

机构地区：[1]宿州学院数学与统计学院,宿州234000 [2]安徽大学人工智能学院,合肥230601 [3]安徽大学大数据与统计学院,合肥230601

出　　处：《应用数学学报》2025年第2期280-293,共14页Acta Mathematicae Applicatae Sinica

基　　金：国家自然科学基金(11671012);安徽省自然科学基金(No.2208085MA06);安徽省高校自然科学基金(No.KJ2021A0049)资助项目。

摘　　要：本文在统计学习理论框架下,研究了最大相关熵回归模型在带有混合对称三角噪声下的学习速率,有限样本下的估计效果和稳健性,以及对真实数据的估计.结果显示最大相关熵回归模型具备渐近最优的收敛速率,在有限样本下有着良好的估计效果,并且具有比Huber和最小二乘回归更优良的稳健性.Within the framework of statistical learning theory,this paper studies the learning rate of the maximum correntropy regression model under a mixture of sym-metric triangular noise,the efficiency and robustness of estimates under the limited samples,and the application on real data.The results show that the maximum cor-rentropy regression model has the asymptotically optimal convergence rate,a good estimation effect under limited samples,and is better than the Huber regression model and least square regression model in robustness.

关 键 词：三角噪声 相关熵 非参数回归 

分 类 号：O212.7[理学—概率论与数理统计]