Gaussian Processes indexed 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 CEA - Commissariat à l'énergie atomique et aux énergies alternatives
3 IMT - Institut de Mathématiques de Toulouse UMR5219

In the framework of the supervised learning of a real function defined on a space X , the so called Kriging method stands on a real Gaussian field defined on X. The Euclidean case 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. In this setting, we propose and study an harmonic analysis of the covariance operators that enables to consider Gaussian processes models and forecasting issues. Our theory is motivated by statistical ranking problems.

Mots clés: Kernel Methods; Ranks; Gaussian processes

Domaines: Machine Learning [stat.ML]

François Bachoc, Baptiste Broto, Fabrice Gamboa, Jean-Michel Loubes. Gaussian Processes indexed on the symmetric group: prediction and learning. 2018. ⟨hal-01731251v1⟩