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Statistical learning methods for ranking : theory, algorithms and applications

Abstract : Multipartite ranking is a statistical learning problem that consists in ordering observations that belong to a high dimensional feature space in the same order as the labels, so that the observations with the highest label appear at the top of the list. This work aims to understand the probabilistic nature of the multipartite ranking problem in order to obtain theoretical guarantees for ranking algorithms. In this context, the output of a ranking algorithm takes the form of a scoring function, a function that maps the space of the observation to the real line which order is induced using the values on the real line. The contributions of this manuscript are the following : First, we focus on the characterization of optimal solutions to multipartite ranking. The second research theme is the design of algorithms to produce scoring functions. We offer two methods, the first using an aggregation procedure, the second an approximation scheme. Finally, we return to the binary ranking problem to establish adaptive minimax rate of convergence.
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Sylvain Robbiano. Statistical learning methods for ranking : theory, algorithms and applications. Statistics [math.ST]. Télécom ParisTech, 2013. English. ⟨NNT : 2013ENST0033⟩. ⟨tel-01225608⟩

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