具有核化函数的部分线性模型及其应用  

Partially Linear Models with Kernelized Function and Their Application

作　　者：张波[1,2] 范超 Zhang Bo;Fan Chao

机构地区：[1]中国人民大学应用统计中心 [2]中国人民大学统计学院 [3]京东物流X事业部

出　　处：《统计研究》2020年第1期110-128,共19页Statistical Research

基　　金：国家自然科学基金“基于非结构化数据的个人信用评价”(71873137);国家自然科学基金“非对称随机波动建模及其在金融风险管理中的应用研究”(71471173)。

摘　　要：本文基于再生核希尔伯特空间中的再生核,将核技巧与高斯-赛责尔迭代算法相结合,提出了具有核化函数的部分线性模型(PLMKF)及其算法收敛性条件等相关内容,具体包括:(1)基于OLS的PLMKF;(2)基于岭估计的PLMKF;(3)基于GLS的PLMKF;(4)基于多核学习的PLMKF。它们构成了PLMKF家族,具有一定的相互转化关系。在数值模拟中,本文验证了各个算法的有效性,比较了基于OLS与GLS、单核与多核的PLMKF模拟结果。实际应用中,在大幅外推情景下,PLMKF仍保持了良好的泛化能力,预测精度高于PLM、GAM和SVR。On the basis of reproducing kernel in Reproducing Kernel Hilbert Spaces,according to GaussSeidel algorithm and combing with kernel trick,this paper proposes Partially Linear Models with Kernelized Function(PLMKF)and its algorithm,convergence conditions and other related contents.Specifically speaking,we propose:(1)PLMKF based on OLS;(2)PLMKF based on ridge regression;(3)PLMKF based on GLS;(4)PLMKF based on multiple kernel learning.These four models make up the family of PLMKF and have some transforming relationships between each other.In the numerical simulation,the effectiveness of the algorithm is verified.We compare PLMKF based on the OLS with that based on the GLS,PLMKF based on the single kernel with that based on the multiple kernels.In the practical application,PLMKF retains good generalization ability and its prediction accuracy is far higher than that of PLM,GAM and SVR in the case of wide extrapolation.

关 键 词：再生核 核技巧 核化回归 半参数模型 

分 类 号：O212[理学—概率论与数理统计]