Data augmented bootstrap: Unifying confidence interval construction by approximate invariance
2026-06-08 • Machine Learning
Machine Learning
AI summaryⓘ
The authors introduce a new method called data augmented bootstrap (DAB) that builds confidence intervals using data transformations that are only approximately the same when shuffled or altered. Their method includes existing techniques like conformal prediction and classical bootstrap as special cases. They provide theoretical guarantees for DAB that work even when exact patterns or symmetries aren't present. This approach allows the use of common data augmentation tricks from machine learning in traditional statistical methods. They also test DAB on various types of data, including images and language, to show how well it works.
bootstrapconfidence intervalsdata augmentationapproximate invarianceconformal predictionwild bootstrapMaximum Mean DiscrepancyKolmogorov distanceGaussian universalityU-statistics
Authors
Kevin Han Huang
Abstract
We propose the data augmented bootstrap (DAB), a framework for constructing confidence intervals from approximately invariant transformations of the data. As special cases, DAB recovers popular methods that rely on exact group symmetries, such as conformal prediction, wild bootstrap for Maximum Mean Discrepancy U-statistics and the recently proposed SymmPI. Meanwhile, DAB also recovers the classical bootstrap method, which exploits the dataset's approximate invariance under uniform sampling of data indices as the dataset size grows. For all DAB methods, we establish theoretical coverage results that interpolate between finite-sample and asymptotic guarantees according to the strength of the invariance, and without assuming a group structure. The approximate invariance is measured in the Kolmogorov distance and, for statistics that satisfy Gaussian universality, reduces to conditional mean and variance matching. This allows us to incorporate data augmentation (DA), a widely used machine learning heuristic based on approximate invariances, into known statistical methods. We empirically test the performance of incorporating DA into bootstrap, wild bootstrap and conformal prediction for simulated settings as well as for image, language and scientific data.