The Annals of Statistics· 2026Q1
Gaussian and non-Gaussian universality of data augmentation
- 1citations
- Q1SCImago
- 2026year
Short summary
Data augmentation's effect on estimate uncertainty and limiting distributions can be quantified by simple surrogates, revealing it may increase uncertainty and shift double-descent peaks, contrary to some machine learning assumptions.
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Key points
- Data augmentation's impact on estimate uncertainty and limiting distributions can be predicted by simple surrogates.
- Data augmentation may increase, rather than decrease, estimate uncertainty (e.g., empirical prediction risk).
- Data augmentation can act as a regularizer but fails in certain high-dimensional problems.
- The effects of data augmentation are not universally beneficial or detrimental but depend on data distribution, estimator properties, and scale/dimensionality.
AI-generated from the title and abstract; the full text is not read.
Abstract
We provide universality results that quantify how data augmentation affects the variance and limiting distribution of estimates through simple surrogates, and analyze several specific models in detail. The results confirm some observations made in machine learning practice, but also lead to unexpected findings: Data augmentation may increase rather than decrease the uncertainty of estimates, such as the empirical prediction risk. It can act as a regularizer, but fails to do so in certain high-dimensional problems, and it may shift the double-descent peak of an empirical risk. Overall, the analysis shows that several properties attributed to data augmentation are not either true or false, but rather depend on a combination of factors—notably the data distribution, the properties of the estimator, and the interplay of sample size, number of augmentations and dimension. As our main theoretical tool, we develop an adaptation of Lindeberg’s technique for block dependence. The resulting universality regime may be Gaussian or non-Gaussian.
The authors' abstract, as published at the source. The Annals of Statistics, 2026 · DOI ↗
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Field: Statistics and Probability
Statistics and ProbabilityMathematics