# Distributed Bootstrap for Simultaneous Inference Under High Dimensionality

arXiv: https://arxiv.org/abs/2102.10080 · HTML: https://mlsanity.com/paper/2102.10080/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 41 references that are in the map.
- First posted on arXiv 19 Feb 2021.

## Builds on (most cited first, 19 of 19)

- [Confidence Intervals and Hypothesis Testing for High-Dimensional Regression](https://mlsanity.com/paper/1306.3171/) (2013)
- [Communication-Efficient Algorithms for Decentralized and Stochastic Optimization](https://mlsanity.com/paper/1701.03961/) (2017)
- [Efficient Distributed Learning with Sparsity](https://mlsanity.com/paper/1605.07991/) (2016)
- [Communication-Efficient Accurate Statistical Estimation](https://mlsanity.com/paper/1906.04870/) (2019)
- [Hypothesis Testing in High-Dimensional Regression under the Gaussian Random Design Model: Asymptotic Theory](https://mlsanity.com/paper/1301.4240/) (2013)
- [Quantile Regression Under Memory Constraint](https://mlsanity.com/paper/1810.08264/) (2018)
- [First-order Newton-type Estimator for Distributed Estimation and Inference](https://mlsanity.com/paper/1811.11368/) (2018)
- [Uniformly Valid Post-Regularization Confidence Regions for Many Functional Parameters in Z-Estimation Framework](https://mlsanity.com/paper/1512.07619/) (2015)
- [A Distributed One-Step Estimator](https://mlsanity.com/paper/1511.01443/) (2015)
- [Distributed inference for quantile regression processes](https://mlsanity.com/paper/1701.06088/) (2017)
- [High-dimensional simultaneous inference with the bootstrap](https://mlsanity.com/paper/1606.03940/) (2016)
- [Least Squares Approximation for a Distributed System](https://mlsanity.com/paper/1908.04904/) (2019)
- [hdm: High-Dimensional Metrics](https://mlsanity.com/paper/1608.00354/) (2016)
- [A subsampled double bootstrap for massive data](https://mlsanity.com/paper/1508.01126/) (2015)
- [Divide and Conquer in Non-standard Problems and the Super-efficiency Phenomenon](https://mlsanity.com/paper/1605.04446/) (2016)
- [Simultaneous Inference for Pairwise Graphical Models with Generalized Score Matching](https://mlsanity.com/paper/1905.06261/) (2019)
- [Simultaneous Inference for Massive Data: Distributed Bootstrap](https://mlsanity.com/paper/2002.08443/) (2020)
- [Distributed Estimation for Principal Component Analysis: an Enlarged Eigenspace Analysis](https://mlsanity.com/paper/2004.02336/) (2020)
- [Improved Optimization of Finite Sums with Minibatch Stochastic Variance Reduced Proximal Iterations](https://mlsanity.com/paper/1706.07001/) (2017)

## Built on by (most cited first, 4 of 4)

- [Differentially Private Federated Learning: Servers Trustworthiness, Estimation, and Statistical Inference](https://mlsanity.com/paper/2404.16287/) (2024)
- [High-Dimensional Differentially Private Quantile Regression: Distributed Estimation and Statistical Inference](https://mlsanity.com/paper/2508.05212/) (2025)
- [Distributed Estimation and Inference for Semi-parametric Binary Response Models](https://mlsanity.com/paper/2210.08393/) (2022)
- [Distributed Linear Regression with Compositional Covariates](https://mlsanity.com/paper/2310.13969/) (2023)

## Abstract (arXiv)

We propose a distributed bootstrap method for simultaneous inference on high-dimensional massive data that are stored and processed with many machines. The method produces an ℓ_∞-norm confidence region based on a communication-efficient de-biased lasso, and we propose an efficient cross-validation approach to tune the method at every iteration. We theoretically prove a lower bound on the number of communication rounds τmin that warrants the statistical accuracy and efficiency. Furthermore, τmin only increases logarithmically with the number of workers and the intrinsic dimensionality, while nearly invariant to the nominal dimensionality. We test our theory by extensive simulation studies, and a variable screening task on a semi-synthetic dataset based on the US Airline On-Time Performance dataset. The code to reproduce the numerical results is available at GitHub: https://github.com/skchao74/Distributed-bootstrap.