# A Fast Bootstrap Algorithm for Causal Inference with Large Data

arXiv: https://arxiv.org/abs/2302.02859 · HTML: https://mlsanity.com/paper/2302.02859/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 4 of its 51 references that are in the map.
- First posted on arXiv 6 Feb 2023.

## Builds on (most cited first, 4 of 4)

- [Using simulation studies to evaluate statistical methods](https://mlsanity.com/paper/1712.03198/) (2017)
- [Sensitivity analysis for inverse probability weighting estimators via the percentile bootstrap](https://mlsanity.com/paper/1711.11286/) (2017)
- [Combining observational and experimental data to find heterogeneous treatment effects](https://mlsanity.com/paper/1611.02385/) (2016)
- [A Causal Bootstrap](https://mlsanity.com/paper/1807.02737/) (2018)

## Built on by (most cited first, 3 of 3)

- [Gaussian and Bootstrap Approximation for Matching-based Average Treatment Effect Estimators](https://mlsanity.com/paper/2412.17181/) (2024)
- [Leveraging Large Language Models for Rare Disease Named Entity Recognition](https://mlsanity.com/paper/2508.09323/) (2025)
- [Fast Uncertainty Quantification for Kernel-Based Estimators in Large-Scale Causal Inference](https://mlsanity.com/paper/2603.13662/) (2026)

## Abstract (arXiv)

Estimating causal effects from large experimental and observational data has become increasingly prevalent in both industry and research. The bootstrap is an intuitive and powerful technique used to construct standard errors and confidence intervals of estimators. Its application however can be prohibitively demanding in settings involving large data. In addition, modern causal inference estimators based on machine learning and optimization techniques exacerbate the computational burden of the bootstrap. The bag of little bootstraps has been proposed in non-causal settings for large data but has not yet been applied to evaluate the properties of estimators of causal effects. In this paper, we introduce a new bootstrap algorithm called causal bag of little bootstraps for causal inference with large data. The new algorithm significantly improves the computational efficiency of the traditional bootstrap while providing consistent estimates and desirable confidence interval coverage. We describe its properties, provide practical considerations, and evaluate the performance of the proposed algorithm in terms of bias, coverage of the true 95% confidence intervals, and computational time in a simulation study. We apply it in the evaluation of the effect of hormone therapy on the average time to coronary heart disease using a large observational data set from the Women's Health Initiative.