Gaussian field on the symmetric group: Prediction and learning

Abstract

In the framework of the supervised learning of a real function defined on an abstract space $\mathcal{X}$, Gaussian processes are widely used. The Euclidean case for $\mathcal{X}$ is well known and has been widely studied. In this paper, we explore the less classical case where $\mathcal{X}$ is the non commutative finite group of permutations (namely the so-called symmetric group $S_{N}$). We provide an application to Gaussian process based optimization of Latin Hypercube Designs. We also extend our results to the case of partial rankings.