# A Cheap Bootstrap Method for Fast Inference

arXiv: https://arxiv.org/abs/2202.00090 · HTML: https://mlsanity.com/paper/2202.00090/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 31 Jan 2022.

## Built on by (most cited first, 5 of 5)

- [Efficient Uncertainty Quantification and Reduction for Over-Parameterized Neural Networks](https://mlsanity.com/paper/2306.05674/) (2023)
- [Overlapping Batch Confidence Intervals on Statistical Functionals Constructed from Time Series: Application to Quantiles, Optimization, and Estimation](https://mlsanity.com/paper/2307.08609/) (2023)
- [Cheap Bootstrap for Fast Uncertainty Quantification of Stochastic Gradient Descent](https://mlsanity.com/paper/2310.11065/) (2023)
- [Orthogonal Bootstrap: Efficient Simulation of Input Uncertainty](https://mlsanity.com/paper/2404.19145/) (2024)
- [The V-fold jackknife for semiparametric inference: variance estimation, confidence intervals, and simultaneous confidence bands](https://mlsanity.com/paper/2607.22493/) (2026)

## Abstract (arXiv)

The bootstrap is a versatile inference method that has proven powerful in many statistical problems. However, when applied to modern large-scale models, it could face substantial computation demand from repeated data resampling and model fitting. We present a bootstrap methodology that uses minimal computation, namely with a resample effort as low as one Monte Carlo replication, while maintaining desirable statistical guarantees. We present the theory of this method that uses a twisted perspective from the standard bootstrap principle. We also present generalizations of this method to nested sampling problems and to a range of subsampling variants, and illustrate how it can be used for fast inference across different estimation problems.