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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.

MSC:
60G15 Gaussian processes
62M20 Inference from stochastic processes and prediction
Software:
EGO
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References:
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