mlsanityData to 7 Oct 2026

Distributed Bootstrap for Simultaneous Inference Under High Dimensionality

arXiv 2102.10080 ↗First posted 19 Feb 2021stat.ME math.ST stat.MLcited by 4

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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.

Key facts. Cited by 4 papers in the map (data through 7 Oct 2026). Builds on 19 of its 41 references that are in the map. First posted on arXiv 19 Feb 2021.

Builds on

19 of 41 references.

References · 19

  1. 2013Confidence Intervals and Hypothesis Testing for High-Dimensional Regressioncited by 78
  2. 2017Communication-Efficient Algorithms for Decentralized and Stochastic Optimizationcited by 42
  3. 2016Efficient Distributed Learning with Sparsitycited by 38
  4. 2019Communication-Efficient Accurate Statistical Estimationcited by 32
  5. 2013Hypothesis Testing in High-Dimensional Regression under the Gaussian Random Design Model: Asymptotic Theorycited by 18
  6. 2018Quantile Regression Under Memory Constraintcited by 17
  7. 2018First-order Newton-type Estimator for Distributed Estimation and Inferencecited by 16
  8. 2015Uniformly Valid Post-Regularization Confidence Regions for Many Functional Parameters in Z-Estimation Frameworkcited by 12
  9. 2015A Distributed One-Step Estimatorcited by 11
  10. 2017Distributed inference for quantile regression processescited by 11
  11. 2016High-dimensional simultaneous inference with the bootstrapcited by 9
  12. 2019Least Squares Approximation for a Distributed Systemcited by 8
7 more
  1. 2016hdm: High-Dimensional Metricscited by 6
  2. 2015A subsampled double bootstrap for massive datacited by 5
  3. 2016Divide and Conquer in Non-standard Problems and the Super-efficiency Phenomenoncited by 5
  4. 2019Simultaneous Inference for Pairwise Graphical Models with Generalized Score Matchingcited by 5
  5. 2020Simultaneous Inference for Massive Data: Distributed Bootstrapcited by 4
  6. 2020Distributed Estimation for Principal Component Analysis: an Enlarged Eigenspace Analysiscited by 3
  7. 2017Improved Optimization of Finite Sums with Minibatch Stochastic Variance Reduced Proximal Iterationscited by 1

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Citing papers per year: 2022: 1; 2023: 1; 2024: 1; 2025: 1.

4 papers.

  1. 2024Differentially Private Federated Learning: Servers Trustworthiness, Estimation, and Statistical Inferencecited by 2
  2. 2025High-Dimensional Differentially Private Quantile Regression: Distributed Estimation and Statistical Inferencecited by 1
  3. 2022Distributed Estimation and Inference for Semi-parametric Binary Response Modelscited by 0
  4. 2023Distributed Linear Regression with Compositional Covariatescited by 0