@article{4cedc8db2f5346fd977abfdb86cbf3d0,
title = "Boosted Kernel Ridge Regression: Optimal Learning Rates and Early Stopping",
abstract = "In this paper, we introduce a learning algorithm, boosted kernel ridge regression (BKRR), that combines L2-Boosting with the kernel ridge regression (KRR). We analyze the learning performance of this algorithm in the framework of learning theory. We show that BKRR provides a new bias-variance trade-off via tuning the number of boosting iterations, which is different from KRR via adjusting the regularization parameter. A (semi-)exponential bias-variance trade-off is derived for BKRR, exhibiting a stable relationship between the generalization error and the number of iterations. Furthermore, an adaptive stopping rule is proposed, with which BKRR achieves the optimal learning rate without saturation.",
keywords = "Boosting, Integral operator, Kernel ridge regression, Learning theory",
author = "Lin, {Shao Bo} and Yunwen Lei and Zhou, {Ding Xuan}",
note = "Funding Information: The authors would like to thank two anonymous referees for their constructive suggestions. The work of Shao-Bo Lin is supported partially by the National Natural Science Foundation of China (Grant Numbers 61876133, 11771021). The work of Yunwen Lei is supported partially by the National Natural Science Foundation of China (Grant No. 61806091) and the Shenzhen Peacock Plan (Grant No. KQTD2016112514355531). The work of DingXuan Zhou is supported partially by the Research Grants Council of Hong Kong [Project No. CityU 11303915] and by National Natural Science Foundation of China under Grant 11461161006. Part of the work was done when the last author visited Shanghai Jiaotong University (SJTU), for which the support from SJTU and the Ministry of Education is greatly appreciated. The corresponding author is Yunwen Lei. Publisher Copyright: {\textcopyright} 2019 Shao-Bo Lin, Yunwen Lei and Ding-Xuan Zhou.",
year = "2019",
month = feb,
language = "English",
volume = "20",
journal = "Journal of Machine Learning Research",
issn = "1532-4435",
publisher = "Microtome Publishing",
}