# Optimal high-dimensional and nonparametric distributed testing under communication constraints

arXiv: https://arxiv.org/abs/2202.00968 · HTML: https://mlsanity.com/paper/2202.00968/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 45 references that are in the map.
- First posted on arXiv 2 Feb 2022.

## Builds on (most cited first, 13 of 13)

- [Communication Lower Bounds for Statistical Estimation Problems via a Distributed Data Processing Inequality](https://mlsanity.com/paper/1506.07216/) (2015)
- [Geometric Lower Bounds for Distributed Parameter Estimation under Communication Constraints](https://mlsanity.com/paper/1802.08417/) (2018)
- [Inference under Information Constraints I: Lower Bounds from Chi-Square Contraction](https://mlsanity.com/paper/1812.11476/) (2018)
- [Fundamental Limits of Online and Distributed Algorithms for Statistical Learning and Estimation](https://mlsanity.com/paper/1311.3494/) (2013)
- [Inference under Information Constraints II: Communication Constraints and Shared Randomness](https://mlsanity.com/paper/1905.08302/) (2019)
- [Distributed Gaussian Mean Estimation under Communication Constraints: Optimal Rates and Communication-Efficient Algorithms](https://mlsanity.com/paper/2001.08877/) (2020)
- [Hypothesis Testing For Densities and High-Dimensional Multinomials: Sharp Local Minimax Rates](https://mlsanity.com/paper/1706.10003/) (2017)
- [Optimality guarantees for distributed statistical estimation](https://mlsanity.com/paper/1405.0782/) (2014)
- [Adaptive distributed methods under communication constraints](https://mlsanity.com/paper/1804.00864/) (2018)
- [Distributed Nonparametric Regression under Communication Constraints](https://mlsanity.com/paper/1803.01302/) (2018)
- [Distributed function estimation: adaptation using minimal communication](https://mlsanity.com/paper/2003.12838/) (2020)
- [Optimal distributed composite testing in high-dimensional Gaussian models with 1-bit communication](https://mlsanity.com/paper/2012.04957/) (2020)
- [Distributed Nonparametric Function Estimation: Optimal Rate of Convergence and Cost of Adaptation](https://mlsanity.com/paper/2107.00179/) (2021)

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

- [Optimal Federated Learning for Nonparametric Regression with Heterogeneous Distributed Differential Privacy Constraints](https://mlsanity.com/paper/2406.06755/) (2024)
- [Federated Nonparametric Hypothesis Testing with Differential Privacy Constraints: Optimal Rates and Adaptive Tests](https://mlsanity.com/paper/2406.06749/) (2024)
- [Distributed Nonparametric Estimation under Communication Constraints](https://mlsanity.com/paper/2204.10373/) (2022)

## Abstract (arXiv)

We derive minimax testing errors in a distributed framework where the data is split over multiple machines and their communication to a central machine is limited to b bits. We investigate both the d- and infinite-dimensional signal detection problem under Gaussian white noise. We also derive distributed testing algorithms reaching the theoretical lower bounds. Our results show that distributed testing is subject to fundamentally different phenomena that are not observed in distributed estimation. Among our findings, we show that testing protocols that have access to shared randomness can perform strictly better in some regimes than those that do not. We also observe that consistent nonparametric distributed testing is always possible, even with as little as 1-bit of communication and the corresponding test outperforms the best local test using only the information available at a single local machine. Furthermore, we also derive adaptive nonparametric distributed testing strategies and the corresponding theoretical lower bounds.