Empirical bounds for functions with weak interactions
This work addresses the need for rigorous statistical guarantees in machine learning and statistics, offering incremental improvements in bounding techniques for weakly interacting functions.
The paper tackles the problem of providing sharp empirical bounds for expectation, variance, and normal approximation for statistics with weak interactions, such as U- and V-statistics, Lipschitz L-statistics, and error functionals of L2-regularized and Gibbs algorithms, achieving precise estimates for these classes.
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.