mlsanityData to 13 Oct 2026

Dimension-free uniform concentration bound for logistic regression

arXiv 2405.18055 ↗First posted 28 May 2024math.ST stat.ML stat.THcited by 1

Not on the map. Why?

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.

Key facts. Cited by 1 paper in the map (data through 13 Oct 2026). Builds on 16 of its 41 references that are in the map. First posted on arXiv 28 May 2024.

Builds on

16 of 41 references.

References · 16

  1. 2021User-friendly introduction to PAC-Bayes boundscited by 237
  2. 2015On the properties of variational approximations of Gibbs posteriorscited by 121
  3. 2018A modern maximum-likelihood theory for high-dimensional logistic regressioncited by 79
  4. 2019Normalized Flat Minima: Exploring Scale Invariant Definition of Flat Minima for Neural Networks using PAC-Bayesian Analysiscited by 59
  5. 2020Generalization error in high-dimensional perceptrons: Approaching Bayes error with convex optimizationcited by 51
  6. 2022Dimension free ridge regressioncited by 50
  7. 2018The phase transition for the existence of the maximum likelihood estimate in high-dimensional logistic regressioncited by 45
  8. 2019The Impact of Regularization on High-dimensional Logistic Regressioncited by 35
  9. 2020Generalization Error of Generalized Linear Models in High Dimensionscited by 25
  10. 2017The Likelihood Ratio Test in High-Dimensional Logistic Regression Is Asymptotically a Rescaled Chi-Squarecited by 15
  11. 2018Identifying Generalization Properties in Neural Networkscited by 15
  12. 2020The Asymptotic Distribution of the MLE in High-dimensional Logistic Models: Arbitrary Covariancecited by 15
4 more
  1. 2023On the sample complexity of parameter estimation in logistic regression with normal designcited by 13
  2. 2023Finite-Sample Analysis of Learning High-Dimensional Single ReLU Neuroncited by 8
  3. 2022Generalization Error Bounds for Multiclass Sparse Linear Classifierscited by 6
  4. 2019Stability of decision trees and logistic regressioncited by 4

Built on by

Cited by year

Citing papers per year: 2025: 1.

1 paper.

  1. 2025Improved generalization bounds for binary linear classification via isoperimetrycited by 0