Section: New Results

Axis 2: Pseudo-Bayesian learning with kernel Fourier transform as prior

Participant: Pascal Germain.

We revisit the 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, and corresponding learning algorithms.

This joint work with Emilie Morvant from Université Jean Monnet de Saint-Etienne (France), and Gaël Letarte from Université Laval (Québec, Canada) has been initiated in 2018 when Gaël Letarte was doing an internship at Inria, and led to a publication in the proceedings of AISTATS 2019 conference [36]. The same work has been prensented as a poster in the “Workshop on Machine Learning with guarantees @ NeurIPS 2019”.

An extension of this work, co-authored with Léo Gautheron, Amaury Habrard, Marc Sebban, and Valentina Zantedeschi – all from Université Jean Monnet de Saint-Etienne – has been presented at the national conference CAp 2019 [44]. It is also the topic of a technical report [64].