## Boosted Kernel Ridge Regression: Optimal Learning Rates and Early Stopping

Shao-Bo Lin, Yunwen Lei, Ding-Xuan Zhou; 20(46):1−36, 2019.

### Abstract

In this paper, we introduce a learning algorithm, boosted kernel ridge regression (BKRR), that combines $L_2$-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.

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