Random Feature (RF) models are used as efficient parametric approximations of
kernel methods. We investigate, by means of random matrix theory, the
connection between Gaussian RF models and Kernel Ridge Regression (KRR). For a
Gaussian RF model with $P$ features, $N$ data points, and a ridge $\lambda$, we
show that the average (i.e. expected) RF predictor is close to a KRR predictor
with an effective ridge $\tilde{\lambda}$. We show that $\tilde{\lambda} >
\lambda$ and $\tilde{\lambda} \searrow \lambda$ monotonically as $P$ grows,
thus revealing the implicit regularization effect of finite RF sampling. We
then compare the risk (i.e. test error) of the $\tilde{\lambda}$-KRR predictor
with the average risk of the $\lambda$-RF predictor and obtain a precise and
explicit bound on their difference. Finally, we empirically find an extremely
good agreement between the test errors of the average $\lambda$-RF predictor
and $\tilde{\lambda}$-KRR predictor.

本文探讨了随机特征模型和核岭回归之间的联系，并发现了有限 RF 取样的隐式正则化效应，同时对比了使用 KRR 预测器的风险和使用 RF 预测器的平均风险并获得了它们之间差异的明确界限，最终在实验中发现了平均 λ-RF 预测和 tilde λ-KRR 预测器之间的极好一致性。