Ensemble and Multiple Kernel Regressors: Which Is Better?

Akira TANAKA  Hirofumi TAKEBAYASHI  Ichigaku TAKIGAWA  Hideyuki IMAI  Mineichi KUDO  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E98-A   No.11   pp.2315-2324
Publication Date: 2015/11/01
Online ISSN: 1745-1337
DOI: 10.1587/transfun.E98.A.2315
Type of Manuscript: PAPER
Category: Neural Networks and Bioengineering
kernel regression,  ensemble kernel regressor,  multiple kernel regressor,  generalization error,  reproducing kernel Hilbert spaces,  

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For the last few decades, learning with multiple kernels, represented by the ensemble kernel regressor and the multiple kernel regressor, has attracted much attention in the field of kernel-based machine learning. Although their efficacy was investigated numerically in many works, their theoretical ground is not investigated sufficiently, since we do not have a theoretical framework to evaluate them. In this paper, we introduce a unified framework for evaluating kernel regressors with multiple kernels. On the basis of the framework, we analyze the generalization errors of the ensemble kernel regressor and the multiple kernel regressor, and give a sufficient condition for the ensemble kernel regressor to outperform the multiple kernel regressor in terms of the generalization error in noise-free case. We also show that each kernel regressor can be better than the other without the sufficient condition by giving examples, which supports the importance of the sufficient condition.