Dimension-free uniform concentration bound for logistic regression
Statistics Theory
2024-10-15 v5 Machine Learning
Statistics Theory
Abstract
We provide a novel dimension-free uniform concentration bound for the empirical risk function of constrained logistic regression. Our bound yields a milder sufficient condition for a uniform law of large numbers than conditions derived by the Rademacher complexity argument and McDiarmid's inequality. The derivation is based on the PAC-Bayes approach with second-order expansion and Rademacher-complexity-based bounds for the residual term of the expansion.
Keywords
Cite
@article{arxiv.2405.18055,
title = {Dimension-free uniform concentration bound for logistic regression},
author = {Shogo Nakakita},
journal= {arXiv preprint arXiv:2405.18055},
year = {2024}
}
Comments
28 pages; relaxed a condition