Large-Scale Online Kernel Learning with Random Feature Reparameterization

Abstract

A typical online kernel learning method faces two fundamental issues: the complexity in dealing with a huge number of observed data points (a.k.a the curse of kernelization) and the difficulty in learning kernel parameters, which often assumed to be fixed. Random Fourier feature is a recent and effective approach to address the former by approximating the shift-invariant kernel function via Bocher's theorem, and allows the model to be maintained directly in the random feature space with a fixed dimension, hence the model size remains constant w.r.t. data size. We further introduce in this paper the reparameterized random feature (RRF), a random feature framework for large-scale online kernel learning to address both aforementioned challenges. Our initial intuition comes from the so-called "reparameterization trick" [Kingma et al., 2014] to lift the source of randomness of Fourier components to another space which can be independently sampled, so that stochastic gradient of the kernel parameters can be analytically derived. We develop a well-founded underlying theory for our method, including a general way to reparameterize the kernel, and a new tighter error bound on the approximation quality. This view further inspires a direct application of stochastic gradient descent for updating our model under an online learning setting. We then conducted extensive experiments on several large-scale datasets where we demonstrate that our work achieves state-of-the-art performance in both learning efficacy and efficiency.