Empirical bounds for functions with weak interactions

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 V-statistics, Lipschitz L-statistics and various error functionals of L2-regularized algorithms and Gibbs algorithms.

References in corpus (2)

• A new method of normal approximation
• Non-convex learning via Stochastic Gradient Langevin Dynamics: a nonasymptotic analysis

Cited by in corpus (1)

• Robust Unsupervised Learning via L-Statistic Minimization