We revisit Rahimi and Recht (2007)'s kernel random Fourier features (RFF) method through the lens of the PAC-Bayesian theory. While the primary goal of RFF is to approximate a kernel, we look at the Fourier transform as a prior distribution over trigonometric hypotheses. It naturally suggests learning a posterior on these hypotheses. We derive generalization bounds that are optimized by learning a pseudo-posterior obtained from a closed-form expression. Based on this study, we consider two learning strategies: The first one finds a compact landmarks-based representation of the data where each landmark is given by a distribution-tailored similarity measure, while the second one provides a PAC-Bayesian justification to the kernel alignment method of Sinha and Duchi (2016).
@article{arxiv.1810.12683,
title = {Pseudo-Bayesian Learning with Kernel Fourier Transform as Prior},
author = {Gaël Letarte and Emilie Morvant and Pascal Germain},
journal= {arXiv preprint arXiv:1810.12683},
year = {2019}
}