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.

翻译：饱和效应指的是当潜在真实函数的平滑度超过一定水平时，核岭回归（KRR）无法达到信息理论下界的现象。该效应在实践中已被广泛观测到，且关于KRR的饱和下界猜想已存在数十年。本文中，我们为这一长期存在的猜想提供了证明。