Empirical bounds for functions with weak interactions
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Proceedings of the 31st Conference On Learning Theory, PMLR 75:9871010, 2018.
Abstract
We provide sharp empirical estimates of expectation, variance and normal approximation for a class of statistics whose variation in any argument does not change too much when another argument is modified. Examples of such weak interactions are furnished by U and Vstatistics, Lipschitz Lstatistics and various error functionals of $\ell_2$regularized algorithms and Gibbs algorithms.
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