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 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.
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