Data Augmented Bootstrap: Unified Framework for Confidence Intervals via Approximate Invariance
Researchers have introduced the Data Augmented Bootstrap (DAB), a theoretical framework that unifies several existing methods for constructing statistical confidence intervals under a single principle of approximate data invariance. DAB recovers well-known techniques such as conformal prediction, wild bootstrap, and classical bootstrap as special cases, while also enabling the integration of machine learning data augmentation heuristics into formal statistical inference. The work bridges finite-sample and asymptotic guarantees, potentially improving uncertainty quantification in applied machine learning settings.
The Data Augmented Bootstrap (DAB), proposed in a preprint submitted to arXiv on June 8, 2026, offers a unifying framework for confidence interval construction based on approximately invariant transformations of data. The framework subsumes several established methods—including conformal prediction, wild bootstrap for Maximum Mean Discrepancy U-statistics, SymmPI, and the classical bootstrap—as special cases arising from different types of data symmetry. A key theoretical contribution is coverage guarantees that interpolate between finite-sample and asymptotic regimes depending on the strength of the invariance, without requiring a formal group structure. Approximate invariance is measured using Kolmogorov distance, and for statistics satisfying Gaussian universality, this reduces to matching conditional means and variances. The framework formally incorporates data augmentation (DA), a common but largely heuristic practice in machine learning, into principled statistical methods. Empirical evaluations span simulated data as well as image, language, and scientific datasets, testing DAB-enhanced versions of bootstrap, wild bootstrap, and conformal prediction.
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- arXiv cs.LGCenter
Data augmented bootstrap: Unifying confidence interval construction by approximate invariance
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