Uniform concentration and symmetrization for weak interactions
arXiv:1902.01911v414 citations
Originality Incremental advance
AI Analysis
This work provides theoretical tools for analyzing complex statistical models, but it is incremental as it builds on existing concentration methods.
The paper extends uniform concentration bounds from sample averages to nonlinear statistics, achieving tight bounds for U-statistics, smoothened L-statistics, and error functionals of l2-regularized algorithms.
The method to derive uniform bounds with Gaussian and Rademacher complexities is extended to the case where the sample average is replaced by a nonlinear statistic. Tight bounds are obtained for U-statistics, smoothened L-statistics and error functionals of l2-regularized algorithms.