Data augmented bootstrap: Unifying confidence interval construction by approximate invariance

2026-06-08 · Source: stat.ML updates on arXiv.org · Field: Science & Research — Mathematics & Computational Sciences, Research Methodology & Innovation · Depth: Expert, quick

Summary

The Data Augmented Bootstrap (DAB) is a novel framework designed for constructing confidence intervals using approximately invariant transformations of data. This method unifies several existing techniques, including conformal prediction, wild bootstrap for Maximum Mean Discrepancy U-statistics, SymmPI, and the classical bootstrap, by leveraging approximate data invariances. DAB provides theoretical coverage guarantees that adapt between finite-sample and asymptotic performance based on the strength of the invariance, without requiring a group structure. Approximate invariance is quantified using the Kolmogorov distance, or by matching conditional mean and variance for statistics exhibiting Gaussian universality. This framework allows for the integration of data augmentation, a common machine learning heuristic, into established statistical methods. Empirical tests demonstrate DAB's performance when incorporating data augmentation into bootstrap, wild bootstrap, and conformal prediction across simulated, image, language, and scientific datasets.

Key takeaway

For research scientists developing robust statistical inference methods, Data Augmented Bootstrap (DAB) offers a unified approach to confidence interval construction. You can integrate data augmentation heuristics into existing bootstrap and conformal prediction techniques, improving coverage guarantees across diverse data types. Consider DAB for more reliable uncertainty quantification in your models, especially when exact symmetries are absent, to enhance the robustness of your statistical conclusions.

Key insights

DAB unifies confidence interval construction by leveraging approximate data invariances, bridging classical and modern statistical methods.

Principles

• Approximate invariance enables robust CI construction.
• Invariance strength dictates coverage guarantees.
• Kolmogorov distance quantifies approximate invariance.

Method

DAB constructs confidence intervals using approximately invariant data transformations, measuring invariance via Kolmogorov distance or conditional mean/variance matching for Gaussian universality.

In practice

• Incorporate data augmentation into bootstrap methods.
• Apply DAB to image, language, and scientific data.
• Unify conformal prediction and classical bootstrap.

Topics

• Confidence Intervals
• Bootstrap Methods
• Data Augmentation
• Conformal Prediction
• Statistical Inference
• Approximate Invariance

Best for: AI Scientist, Machine Learning Engineer, Research Scientist

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Editorial summary, takeaway, and curation by AIssential. Original article published by stat.ML updates on arXiv.org.