# Distributed Nonparametric Estimation under Communication Constraints

arXiv: https://arxiv.org/abs/2204.10373 · HTML: https://mlsanity.com/paper/2204.10373/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 29 references that are in the map.
- First posted on arXiv 21 Apr 2022.

## Builds on (most cited first, 10 of 10)

- [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)
- [Distributed Gaussian Mean Estimation under Communication Constraints: Optimal Rates and Communication-Efficient Algorithms](https://mlsanity.com/paper/2001.08877/) (2020)
- [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 function estimation: adaptation using minimal communication](https://mlsanity.com/paper/2003.12838/) (2020)
- [Distributed Nonparametric Function Estimation: Optimal Rate of Convergence and Cost of Adaptation](https://mlsanity.com/paper/2107.00179/) (2021)
- [Optimal high-dimensional and nonparametric distributed testing under communication constraints](https://mlsanity.com/paper/2202.00968/) (2022)

## Built on by (most cited first, 2 of 2)

- [Order-Optimal Sequential 1-Bit Mean Estimation in General Tail Regimes](https://mlsanity.com/paper/2604.07796/) (2026)
- [Sequential 1-bit Mean Estimation with Near-Optimal Sample Complexity](https://mlsanity.com/paper/2509.21940/) (2025)

## Abstract (arXiv)

In the era of big data, it is necessary to split extremely large data sets across multiple computing nodes and construct estimators using the distributed data. When designing distributed estimators, it is desirable to minimize the amount of communication across the network because transmission between computers is slow in comparison to computations in a single computer. Our work provides a general framework for understanding the behavior of distributed estimation under communication constraints for nonparametric problems. We provide results for a broad class of models, moving beyond the Gaussian framework that dominates the literature. As concrete examples we derive minimax lower and matching upper bounds in the distributed regression, density estimation, classification, Poisson regression and volatility estimation models under communication constraints. To assist with this, we provide sufficient conditions that can be easily verified in all of our examples.