Gaussian field on the symmetric group: Prediction and learning

François Bachoc (1) , Baptiste Broto (2) , Fabrice Gamboa (3) , Jean-Michel Loubes (3)

1 GdR MASCOT-NUM - Méthodes d'Analyse Stochastique des Codes et Traitements Numériques
2 LI3A (CEA, LIST) - Intelligence Artificielle et Apprentissage Automatique (CEA, LIST)
3 IMT - Institut de Mathématiques de Toulouse UMR5219

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

Mots clés: Kernel Methods; Gaussian processes; Learning; Ranks; statistical ranking

Domaines: Machine Learning [stat.ML]

François Bachoc, Baptiste Broto, Fabrice Gamboa, Jean-Michel Loubes. Gaussian field on the symmetric group: Prediction and learning. Electronic Journal of Statistics , 2020, 14, pp.503-546. ⟨10.1214/19-EJS1674⟩. ⟨hal-01731251v5⟩