Open Access
November 2020 Learning the distribution of latent variables in paired comparison models with round-robin scheduling
Roland Diel, Sylvain Le Corff, Matthieu Lerasle
Bernoulli 26(4): 2670-2698 (November 2020). DOI: 10.3150/20-BEJ1203


Paired comparison data considered in this paper originate from the comparison of a large number $N$ of individuals in couples. The dataset is a collection of results of contests between two individuals when each of them has faced $n$ opponents, where $n\ll N$. Individuals are represented by independent and identically distributed random parameters characterizing their abilities. The paper studies the maximum likelihood estimator of the parameters distribution. The analysis relies on the construction of a graphical model encoding conditional dependencies of the observations which are the outcomes of the first $n$ contests each individual is involved in. This graphical model allows to prove geometric loss of memory properties and deduce the asymptotic behavior of the likelihood function. This paper sets the focus on graphical models obtained from round-robin scheduling of these contests. Following a classical construction in learning theory, the asymptotic likelihood is used to measure performance of the maximum likelihood estimator. Risk bounds for this estimator are finally obtained by sub-Gaussian deviation results for Markov chains applied to the graphical model.


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Roland Diel. Sylvain Le Corff. Matthieu Lerasle. "Learning the distribution of latent variables in paired comparison models with round-robin scheduling." Bernoulli 26 (4) 2670 - 2698, November 2020.


Received: 1 December 2018; Revised: 1 September 2019; Published: November 2020
First available in Project Euclid: 27 August 2020

zbMATH: 07256156
MathSciNet: MR4140525
Digital Object Identifier: 10.3150/20-BEJ1203

Keywords: latent variables , nonasymptotic risk bounds , nonparametric estimation , paired comparisons data

Rights: Copyright © 2020 Bernoulli Society for Mathematical Statistics and Probability

Vol.26 • No. 4 • November 2020
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