文章基本信息

标题：Gaussian field on the symmetric group: Prediction and learning
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作者：François Bachoc ; Baptiste Broto ; Fabrice Gamboa 等
期刊名称：Electronic Journal of Statistics
印刷版ISSN：1935-7524
出版年度：2020
卷号：14
期号：1
页码：503-546
DOI：10.1214/19-EJS1674
语种：English
出版社：Institute of Mathematical Statistics
摘要：In the framework of the supervised learning of a real function defined on an 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.
关键词：Learning; Gaussian processes; covariance functions; statistical ranking; partial rankings