mlsanityData to 7 Oct 2026

On the sample complexity of parameter estimation in logistic regression with normal design

arXiv 2307.04191 ↗First posted 9 Jul 2023math.ST cs.IT cs.LGcited by 13

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Abstract (arXiv)

The logistic regression model is one of the most popular data generation model in noisy binary classification problems. In this work, we study the sample complexity of estimating the parameters of the logistic regression model up to a given ℓ2 error, in terms of the dimension and the inverse temperature, with standard normal covariates. The inverse temperature controls the signal-to-noise ratio of the data generation process. While both generalization bounds and asymptotic performance of the maximum-likelihood estimator for logistic regression are well-studied, the non-asymptotic sample complexity that shows the dependence on error and the inverse temperature for parameter estimation is absent from previous analyses. We show that the sample complexity curve has two change-points in terms of the inverse temperature, clearly separating the low, moderate, and high temperature regimes.

Key facts. Cited by 13 papers in the map (data through 7 Oct 2026). Builds on 6 of its 30 references that are in the map. First posted on arXiv 9 Jul 2023.

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6 of 30 references.

References · 6

  1. 2018A modern maximum-likelihood theory for high-dimensional logistic regressioncited by 79
  2. 2018Logistic Regression: The Importance of Being Impropercited by 40
  3. 2019The Impact of Regularization on High-dimensional Logistic Regressioncited by 35
  4. 2014Logistic Regression: Tight Bounds for Stochastic and Online Optimizationcited by 30
  5. 2018Finite-sample analysis of M-estimators using self-concordancecited by 30
  6. 2019An improper estimator with optimal excess risk in misspecified density estimation and logistic regressioncited by 24

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Citing papers per year: 2023: 1; 2024: 2; 2025: 6; 2026: 4.

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  1. 2025Benefits of Early Stopping in Gradient Descent for Overparameterized Logistic Regressioncited by 9
  2. 2025Capturing Individual Human Preferences with Reward Featurescited by 8
  3. 2023Fast and Multiphase Rates for Nearest Neighbor Classifierscited by 1
  4. 2024Dimension-free uniform concentration bound for logistic regressioncited by 1
  5. 2025Exact Recovery of Sparse Binary Vectors from Generalized Linear Measurementscited by 1
  6. 2026Finite-Sample Performance of Gradient Descent in Logistic Regression with Gaussian Designcited by 1
  7. 2024The Nah Bandit: Modeling User Non-compliance in Recommendation Systemscited by 0
  8. 2025Near-Polynomially Competitive Active Logistic Regressioncited by 0
  9. 2025Improved generalization bounds for binary linear classification via isoperimetrycited by 0
  10. 2025On the Accuracy of Newton Step and Influence Function Data Attributionscited by 0
  11. 2026Hard labels sampled from sparse targets mislead rotation invariant algorithmscited by 0
  12. 2026Estimation-Prediction Tradeoff in Causal Probabilistic Temporal Graphscited by 0
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  1. 2026Minimax Optimal Estimator and Improved Error Rate for the MLE in Logistic Regression with Gaussian Designcited by 0