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Gaussian field on the symmetric group: prediction and learning. (English) Zbl 1443.60035
Summary: 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.

60G15 Gaussian processes
62M20 Inference from stochastic processes and prediction
Full Text: DOI Euclid
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