On the Saturation Effect of Kernel Ridge Regression

Yicheng Li, Haobo Zhang, Qian Lin

Keywords: Kernel ridge regression, Saturation effect, Reproducing kernel Hilbert space, Learning theory

Abstract: The saturation effect refers to the phenomenon that the kernel ridge regression (KRR) fails to achieve the information theoretical lower bound when the smoothness of the underground truth function exceeds certain level. The saturation effect has been widely observed in practices and a saturation lower bound of KRR has been conjectured for decades. In this paper, we provide a proof of this long-standing conjecture.

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