We give a distribution-dependent concentration inequality for functions of independent variables. The result extends Bernstein’s inequality from sums to more general functions, whose variation in any argument does not depend too much on the other arguments. Applications sharpen existing bounds for U-statistics and the generalization error of regularized least squares.
"A Bernstein-type inequality for functions of bounded interaction." Bernoulli 25 (2) 1451 - 1471, May 2019. https://doi.org/10.3150/18-BEJ1026