Electronic Journal of Statistics

Upper bounds and aggregation in bipartite ranking

Sylvain Robbiano

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One main focus of learning theory is to find optimal rates of convergence. In classification, it is possible to obtain optimal fast rates (faster than $n^{-1/2}$) in a minimax sense. Moreover, using an aggregation procedure, the algorithms are adaptive to the parameters of the class of distributions. Here, we investigate this issue in the bipartite ranking framework. We design a ranking rule by aggregating estimators of the regression function. We use exponential weights based on the empirical ranking risk. Under several assumptions on the class of distribution, we show that this procedure is adaptive to the margin parameter and smoothness parameter and achieves the same rates as in the classification framework. Moreover, we state a minimax lower bound that establishes the optimality of the aggregation procedure in a specific case.

Article information

Electron. J. Statist., Volume 7 (2013), 1249-1271.

First available in Project Euclid: 29 April 2013

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62F07: Ranking and selection 62C20: Minimax procedures
Secondary: 62G08: Nonparametric regression

Ranking aggregation minimax rates


Robbiano, Sylvain. Upper bounds and aggregation in bipartite ranking. Electron. J. Statist. 7 (2013), 1249--1271. doi:10.1214/13-EJS805. https://projecteuclid.org/euclid.ejs/1367242158

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