# Optimal Federated Learning for Nonparametric Regression with Heterogeneous Distributed Differential Privacy Constraints

arXiv: https://arxiv.org/abs/2406.06755 · HTML: https://mlsanity.com/paper/2406.06755/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Builds on 42 of its 93 references that are in the map.
- First posted on arXiv 10 Jun 2024.

## Builds on (most cited first, 30 of 42)

- [Federated Learning: Challenges, Methods, and Future Directions](https://mlsanity.com/paper/1908.07873/) (2019)
- [Federated Learning for Mobile Keyboard Prediction](https://mlsanity.com/paper/1811.03604/) (2018)
- [Federated Optimization: Distributed Machine Learning for On-Device Intelligence](https://mlsanity.com/paper/1610.02527/) (2016)
- [RAPPOR: Randomized Aggregatable Privacy-Preserving Ordinal Response](https://mlsanity.com/paper/1407.6981/) (2014)
- [Collecting Telemetry Data Privately](https://mlsanity.com/paper/1712.01524/) (2017)
- [Federated Learning for Emoji Prediction in a Mobile Keyboard](https://mlsanity.com/paper/1906.04329/) (2019)
- [Minimax Optimal Procedures for Locally Private Estimation](https://mlsanity.com/paper/1604.02390/) (2016)
- [Finite Sample Differentially Private Confidence Intervals](https://mlsanity.com/paper/1711.03908/) (2017)
- [Privately Learning High-Dimensional Distributions](https://mlsanity.com/paper/1805.00216/) (2018)
- [Fingerprinting Codes and the Price of Approximate Differential Privacy](https://mlsanity.com/paper/1311.3158/) (2013)
- [Private Mean Estimation of Heavy-Tailed Distributions](https://mlsanity.com/paper/2002.09464/) (2020)
- [Learning with User-Level Privacy](https://mlsanity.com/paper/2102.11845/) (2021)
- [Differentially Private Assouad, Fano, and Le Cam](https://mlsanity.com/paper/2004.06830/) (2020)
- [Deep Federated Learning for Autonomous Driving](https://mlsanity.com/paper/2110.05754/) (2021)
- [Communication Lower Bounds for Statistical Estimation Problems via a Distributed Data Processing Inequality](https://mlsanity.com/paper/1506.07216/) (2015)
- [Local Differential Privacy for Deep Learning](https://mlsanity.com/paper/1908.02997/) (2019)
- [Learning discrete distributions: user vs item-level privacy](https://mlsanity.com/paper/2007.13660/) (2020)
- [Geometric Lower Bounds for Distributed Parameter Estimation under Communication Constraints](https://mlsanity.com/paper/1802.08417/) (2018)
- [Optimal Schemes for Discrete Distribution Estimation under Locally Differential Privacy](https://mlsanity.com/paper/1702.00610/) (2017)
- [Tight and Robust Private Mean Estimation with Few Users](https://mlsanity.com/paper/2110.11876/) (2021)
- [Differentially Private Testing of Identity and Closeness of Discrete Distributions](https://mlsanity.com/paper/1707.05128/) (2017)
- [Optimal and Differentially Private Data Acquisition: Central and Local Mechanisms](https://mlsanity.com/paper/2201.03968/) (2022)
- [Fisher information under local differential privacy](https://mlsanity.com/paper/2005.10783/) (2020)
- [Score Attack: A Lower Bound Technique for Optimal Differentially Private Learning](https://mlsanity.com/paper/2303.07152/) (2023)
- [Context-Aware Local Differential Privacy](https://mlsanity.com/paper/1911.00038/) (2019)
- [Distributed Gaussian Mean Estimation under Communication Constraints: Optimal Rates and Communication-Efficient Algorithms](https://mlsanity.com/paper/2001.08877/) (2020)
- [Discrete Distribution Estimation under User-level Local Differential Privacy](https://mlsanity.com/paper/2211.03757/) (2022)
- [Local differential privacy: Elbow effect in optimal density estimation and adaptation over Besov ellipsoids](https://mlsanity.com/paper/1903.01927/) (2019)
- [Private High-Dimensional Hypothesis Testing](https://mlsanity.com/paper/2203.01537/) (2022)
- [Optimality guarantees for distributed statistical estimation](https://mlsanity.com/paper/1405.0782/) (2014)

## Built on by (most cited first, 10 of 10)

- [Minimax And Adaptive Transfer Learning for Nonparametric Classification under Distributed Differential Privacy Constraints](https://mlsanity.com/paper/2406.20088/) (2024)
- [Federated PCA and Estimation for Spiked Covariance Matrices: Optimal Rates and Efficient Algorithm](https://mlsanity.com/paper/2411.15660/) (2024)
- [Optimal Federated Learning for Functional Mean Estimation under Heterogeneous Privacy Constraints](https://mlsanity.com/paper/2412.18992/) (2024)
- [Optimal Differentially Private Ranking from Pairwise Comparisons](https://mlsanity.com/paper/2507.09388/) (2025)
- [High-Dimensional Differentially Private Quantile Regression: Distributed Estimation and Statistical Inference](https://mlsanity.com/paper/2508.05212/) (2025)
- [Minimax and Adaptive Covariance Matrix Estimation under Differential Privacy](https://mlsanity.com/paper/2603.19703/) (2026)
- [Statistical Limits and Efficient Algorithms for Differentially Private Federated Learning](https://mlsanity.com/paper/2605.18656/) (2026)
- [Federated fairness-aware classification under differential privacy](https://mlsanity.com/paper/2603.24392/) (2026)
- [A Van Trees Lower Bound for Fully Interactive Differentially Private Federated Learning](https://mlsanity.com/paper/2605.19813/) (2026)
- [Differentially Private Nonparametric Modal Learning with Applications to Regression and Clustering](https://mlsanity.com/paper/2607.29675/) (2026)

## Abstract (arXiv)

This paper studies federated learning for nonparametric regression in the context of distributed samples across different servers, each adhering to distinct differential privacy constraints. The setting we consider is heterogeneous, encompassing both varying sample sizes and differential privacy constraints across servers. Within this framework, both global and pointwise estimation are considered, and optimal rates of convergence over the Besov spaces are established. Distributed privacy-preserving estimators are proposed and their risk properties are investigated. Matching minimax lower bounds, up to a logarithmic factor, are established for both global and pointwise estimation. Together, these findings shed light on the tradeoff between statistical accuracy and privacy preservation. In particular, we characterize the compromise not only in terms of the privacy budget but also concerning the loss incurred by distributing data within the privacy framework as a whole. This insight captures the folklore wisdom that it is easier to retain privacy in larger samples, and explores the differences between pointwise and global estimation under distributed privacy constraints.