Multiresolution analysis of ranking data

Abstract : This thesis introduces a multiresolution analysis framework for ranking data. Initiated in the 18th century in the context of elections, the analysis of ranking data has attracted a major interest in many fields of the scientific literature : psychometry, statistics, economics, operations research, machine learning or computational social choice among others. It has been even more revitalized by modern applications such as recommender systems, where the goal is to infer users preferences in order to make them the best personalized suggestions. In these settings, users express their preferences only on small and varying subsets of a large catalog of items. The analysis of such incomplete rankings poses however both a great statistical and computational challenge, leading industrial actors to use methods that only exploit a fraction of available information. This thesis introduces a new representation for the data, which by construction overcomes the two aforementioned challenges. Though it relies on results from combinatorics and algebraic topology, it shares several analogies with multiresolution analysis, offering a natural and efficient framework for the analysis of incomplete rankings. As it does not involve any assumption on the data, it already leads to overperforming estimators in small-scale settings and can be combined with many regularization procedures for large-scale settings. For all those reasons, we believe that this multiresolution representation paves the way for a wide range of future developments and applications
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https://pastel.archives-ouvertes.fr/tel-01668552
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Submitted on : Wednesday, December 20, 2017 - 10:15:42 AM
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Eric Sibony. Multiresolution analysis of ranking data. Statistics [math.ST]. Télécom ParisTech, 2016. English. ⟨NNT : 2016ENST0036⟩. ⟨tel-01668552⟩

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