# Dimension-free uniform concentration bound for logistic regression

arXiv: https://arxiv.org/abs/2405.18055 · HTML: https://mlsanity.com/paper/2405.18055/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 41 references that are in the map.
- First posted on arXiv 28 May 2024.

## Builds on (most cited first, 16 of 16)

- [User-friendly introduction to PAC-Bayes bounds](https://mlsanity.com/paper/2110.11216/) (2021)
- [On the properties of variational approximations of Gibbs posteriors](https://mlsanity.com/paper/1506.04091/) (2015)
- [A modern maximum-likelihood theory for high-dimensional logistic regression](https://mlsanity.com/paper/1803.06964/) (2018)
- [Normalized Flat Minima: Exploring Scale Invariant Definition of Flat Minima for Neural Networks using PAC-Bayesian Analysis](https://mlsanity.com/paper/1901.04653/) (2019)
- [Generalization error in high-dimensional perceptrons: Approaching Bayes error with convex optimization](https://mlsanity.com/paper/2006.06560/) (2020)
- [Dimension free ridge regression](https://mlsanity.com/paper/2210.08571/) (2022)
- [The phase transition for the existence of the maximum likelihood estimate in high-dimensional logistic regression](https://mlsanity.com/paper/1804.09753/) (2018)
- [The Impact of Regularization on High-dimensional Logistic Regression](https://mlsanity.com/paper/1906.03761/) (2019)
- [Generalization Error of Generalized Linear Models in High Dimensions](https://mlsanity.com/paper/2005.00180/) (2020)
- [The Likelihood Ratio Test in High-Dimensional Logistic Regression Is Asymptotically a Rescaled Chi-Square](https://mlsanity.com/paper/1706.01191/) (2017)
- [Identifying Generalization Properties in Neural Networks](https://mlsanity.com/paper/1809.07402/) (2018)
- [The Asymptotic Distribution of the MLE in High-dimensional Logistic Models: Arbitrary Covariance](https://mlsanity.com/paper/2001.09351/) (2020)
- [On the sample complexity of parameter estimation in logistic regression with normal design](https://mlsanity.com/paper/2307.04191/) (2023)
- [Finite-Sample Analysis of Learning High-Dimensional Single ReLU Neuron](https://mlsanity.com/paper/2303.02255/) (2023)
- [Generalization Error Bounds for Multiclass Sparse Linear Classifiers](https://mlsanity.com/paper/2204.06264/) (2022)
- [Stability of decision trees and logistic regression](https://mlsanity.com/paper/1903.00816/) (2019)

## Built on by (most cited first, 1 of 1)

- [Improved generalization bounds for binary linear classification via isoperimetry](https://mlsanity.com/paper/2505.16713/) (2025)

## Abstract (arXiv)

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.