mlsanityData to 7 Oct 2026

Characterizing the Generalization Error of Random Feature Regression with Arbitrary Data-Augmentation

arXiv 2605.10290 ↗First posted 11 May 2026stat.ML cs.LG math.STcited by 0

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Abstract (arXiv)

This paper aims at analyzing the regularization effect that data augmentation induces on supervised regression methods in the proportional regime, where the number of covariates grows proportionally to the number of samples. We provide a tight characterization of the test error, measured in mean squared error, in terms only of the population quantities of the true data, as well as first and second order statistics of the augmentation scheme. Our results are valid under misspecified feature maps, and for any network architecture where only the last readout layer is trained, and the rest of the network is either frozen or randomly initialized. We specify our results in the case of Gaussian data, and show that our asymptotic characterization is tight in this setting.

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21 of 39 references.

References · 21

  1. 2018Reconciling modern machine learning practice and the bias-variance trade-offcited by 919
  2. 2019Benign Overfitting in Linear Regressioncited by 544
  3. 2019The generalization error of random features regression: Precise asymptotics and double descent curvecited by 410
  4. 2021A Survey of Data Augmentation Approaches for NLPcited by 408
  5. 2019Fast AutoAugmentcited by 243
  6. 2020Time Series Data Augmentation for Deep Learning: A Surveycited by 225
  7. 2020An Empirical Survey of Data Augmentation for Time Series Classification with Neural Networkscited by 128
  8. 2020The Gaussian equivalence of generative models for learning with shallow neural networkscited by 113
  9. 2021A Survey on Data Augmentation for Text Classificationcited by 111
  10. 2019Faster AutoAugment: Learning Augmentation Strategies using Backpropagationcited by 96
  11. 2022Data Augmentation techniques in time series domain: A survey and taxonomycited by 41
  12. 2024A Comprehensive Survey on Data Augmentationcited by 38
9 more
  1. 2023Deterministic equivalent and error universality of deep random features learningcited by 35
  2. 2025Joint Embedding vs Reconstruction: Provable Benefits of Latent Space Prediction for Self Supervised Learningcited by 33
  3. 2022The good, the bad and the ugly sides of data augmentation: An implicit spectral regularization perspectivecited by 24
  4. 2023Image Data Augmentation Approaches: A Comprehensive Survey and Future directionscited by 23
  5. 2023Precise Asymptotic Analysis of Deep Random Feature Modelscited by 22
  6. 2023A Rainbow in Deep Network Black Boxescited by 18
  7. 2024Asymptotics of Learning with Deep Structured (Random) Featurescited by 13
  8. 2022Quantitative deterministic equivalent of sample covariance matrices with a general dependence structurecited by 9
  9. 2025Non-Asymptotic Analysis of Data Augmentation for Precision Matrix Estimationcited by 2

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