Data Augmented Bootstrap: Unified Framework for Confidence Intervals via Approximate Invariance
Researchers propose the data augmented bootstrap (DAB), a framework that constructs confidence intervals by leveraging approximately invariant transformations of data, unifying several existing statistical methods including conformal prediction and classical bootstrap approaches. The framework provides theoretical coverage guarantees that scale with the strength of invariance, measured using Kolmogorov distance, and incorporates data augmentation—a common machine learning technique—into established statistical methods. This work bridges machine learning heuristics and rigorous statistical inference, potentially improving confidence interval construction across diverse applications.
The paper introduces data augmented bootstrap (DAB), a theoretical framework that unifies confidence interval construction methods by exploiting approximate invariances in data transformations. DAB recovers several existing approaches as special cases, including conformal prediction, wild bootstrap for Maximum Mean Discrepancy U-statistics, and the recently proposed SymmPI, while also encompassing classical bootstrap methods. The authors establish theoretical coverage guarantees that interpolate between finite-sample and asymptotic results depending on invariance strength, without requiring explicit group structure assumptions. Approximate invariance is quantified using Kolmogorov distance, and for statistics satisfying Gaussian universality, reduces to matching conditional mean and variance. The framework enables integration of data augmentation—a widely-used machine learning heuristic based on approximate invariances—into known statistical methods, with empirical validation on simulated data and real applications in image, language, and scientific domains.
What's missing
The paper does not discuss computational complexity or scalability of DAB methods compared to existing approaches, nor does it address potential limitations when approximate invariance assumptions are severely violated in practice.
What different sources said
- arXiv cs.LGCenter
Data augmented bootstrap: Unifying confidence interval construction by approximate invariance
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