We consider the overfitting behavior of minimum norm interpolating solutions of Gaussian kernel ridge regression (i.e. kernel ridgeless regression), when the bandwidth or input dimension varies with the sample size. For fixed dimensions, we show that even with varying or tuned bandwidth, the ridgeless solution is never consistent and, at least with large enough noise, always worse than the null predictor. For increasing dimension, we give a generic characterization of the overfitting behavior for any scaling of the dimension with sample size. We use this to provide the first example of benign overfitting using the Gaussian kernel with sub-polynomial scaling dimension. All our results are under the Gaussian universality ansatz and the (non-rigorous) risk predictions in terms of the kernel eigenstructure.

本研究探讨了高斯核无岭回归的最小范数插值解决方案的过拟合行为，特别是当样本大小变化时带宽或输入维度的影响。研究表明，在固定维度下，即使带宽变化或调整，无岭解决方案也始终不一致，并且在较大噪声情况下始终优于无预测器；此外，随着维度的增加，本研究首次展示了在带有亚多项式缩放维度的高斯核下的良性过拟合现象。 

高斯核无岭回归的过拟合行为：带宽或维度的变化