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2020 Gaussian field on the symmetric group: Prediction and learning
François Bachoc, Baptiste Broto, Fabrice Gamboa, Jean-Michel Loubes
Electron. J. Statist. 14(1): 503-546 (2020). DOI: 10.1214/19-EJS1674

Abstract

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.

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François Bachoc. Baptiste Broto. Fabrice Gamboa. Jean-Michel Loubes. "Gaussian field on the symmetric group: Prediction and learning." Electron. J. Statist. 14 (1) 503 - 546, 2020. https://doi.org/10.1214/19-EJS1674

Information

Received: 1 April 2019; Published: 2020
First available in Project Euclid: 28 January 2020

zbMATH: 07163265
MathSciNet: MR4056265
Digital Object Identifier: 10.1214/19-EJS1674

Subjects:
Primary: 60G15
Secondary: 62M20

Keywords: covariance functions , Gaussian processes , learning , partial rankings , statistical ranking

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Vol.14 • No. 1 • 2020
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