End-to-end Kernel Learning via Generative Random Fourier Features

Random Fourier features enable researchers to build feature map to learn the spectral distribution of the underlying kernel. Current distribution-based methods follow a two-stage scheme: they first learn and optimize the feature map by solving the kernel alignment problem, then learn a linear classifier on the features. However, since the ideal kernel in kernel alignment problem is not necessarily optimal in classification tasks, the generalization performance of the random features learned in this two-stage manner can perhaps be further improved. To address this issue, we propose an end-to-end, one-stage kernel learning approach, called generative random Fourier features, which jointly learns the features and the classifier. A generative network is involved to implicitly learn and to sample from the distribution of the latent kernel. Random features are then built via the generative weights and followed by a linear classifier parameterized as a full-connected layer. We jointly train the generative network and the classifier by solving the empirical risk minimization problem for a one-stage solution. Straightly minimizing the loss between predictive and true labels brings better generalization performance. Besides, this end-to-end strategy allows us to increase the depth of features, resulting in multi-layer architecture and exhibiting strong linear-separable pattern. Empirical results demonstrate the superiority of our method in classification tasks over other two-stage kernel learning methods. Finally, we investigate the robustness of proposed method in defending adversarial attacks, which shows that the randomization and resampling mechanism associated with the learned distribution can alleviate the performance decrease brought by adversarial examples.