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Communication Dans Un Congrès Année : 2010

Empirical Bernstein Inequalities for U-Statistics

Résumé

We present original empirical Bernstein inequalities for U-statistics with bounded symmetric kernels q. They are expressed with respect to empirical estimates of either the variance of q or the conditional variance that appears in the Bernstein-type inequality for U-statistics derived by Arcones. Our result subsumes other existing empirical Bernstein inequalities, as it reduces to them when U-statistics of order 1 are considered. In addition, it is based on a rather direct argument using two applications of the same (non-empirical) Bernstein inequality for U-statistics. We discuss potential applications of our new inequalities, especially in the realm of learning ranking/scoring functions. In the process, we exhibit an efficient pro- cedure to compute the variance estimates for the special case of bipartite ranking that rests on a sorting argument. We also argue that our results may provide test set bounds and particularly interesting empirical racing algorithms for the problem of online learning of scoring functions.
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Dates et versions

hal-00634710 , version 1 (22-10-2011)

Identifiants

  • HAL Id : hal-00634710 , version 1

Citer

Thomas Peel, Sandrine Anthoine, Liva Ralaivola. Empirical Bernstein Inequalities for U-Statistics. Neural Information Processing Systems (NIPS), Dec 2010, Vancouver, Canada. pp.1903-1911. ⟨hal-00634710⟩
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