Random feature approximation is arguably one of the most popular techniques to speed up kernel methods in large scale algorithms and provides a theoretical approach to the analysis of deep neural networks. We analyze generalization properties for a large class of spectral regularization methods combined with random features, containing kernel methods with implicit regularization such as gradient descent or explicit methods like Tikhonov regularization. For our estimators we obtain optimal learning rates over regularity classes (even for classes that are not included in the reproducing kernel Hilbert space), which are defined through appropriate source conditions. This improves or completes previous results obtained in related settings for specific kernel algorithms.

翻译：随机特征近似无疑是加速大规模算法中核方法的最流行技术之一，并为深度神经网络的分析提供了理论途径。我们分析了一类与随机特征结合的大规模谱正则化方法的泛化性质，这些方法包括具有隐式正则化的核方法（如梯度下降）或显式正则化方法（如Tikhonov正则化）。针对我们提出的估计量，在通过适当源条件定义的正则性类上（甚至包括那些不属于再生核希尔伯特空间的类），我们获得了最优学习速率。这改进或完善了先前在相关背景下针对特定核算法得到的结果。