关键词: 再生核, 核技巧, 核化回归, 半参数模型

Abstract: On the basis of reproducing kernel in Reproducing Kernel Hilbert Spaces, according to GaussSeidel 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.

Key words: Reproducing Kernel, Kernel Trick, Kernelized Regression, Semiparametric Model