# Optimal Federated Learning for Functional Mean Estimation under Heterogeneous Privacy Constraints

arXiv: https://arxiv.org/abs/2412.18992 · HTML: https://mlsanity.com/paper/2412.18992/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 35 references that are in the map.
- First posted on arXiv 25 Dec 2024.

## Builds on (most cited first, 17 of 17)

- [Federated Learning for Emoji Prediction in a Mobile Keyboard](https://mlsanity.com/paper/1906.04329/) (2019)
- [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)
- [Learning discrete distributions: user vs item-level privacy](https://mlsanity.com/paper/2007.13660/) (2020)
- [Tight and Robust Private Mean Estimation with Few Users](https://mlsanity.com/paper/2110.11876/) (2021)
- [Fisher information under local differential privacy](https://mlsanity.com/paper/2005.10783/) (2020)
- [Unified lower bounds for interactive high-dimensional estimation under information constraints](https://mlsanity.com/paper/2010.06562/) (2020)
- [Discrete Distribution Estimation under User-level Local Differential Privacy](https://mlsanity.com/paper/2211.03757/) (2022)
- [Optimal Federated Learning for Nonparametric Regression with Heterogeneous Distributed Differential Privacy Constraints](https://mlsanity.com/paper/2406.06755/) (2024)
- [Optimal Rates for Nonparametric Density Estimation under Communication Constraints](https://mlsanity.com/paper/2107.10078/) (2021)
- [On the Statistical Complexity of Estimation and Testing under Privacy Constraints](https://mlsanity.com/paper/2210.02215/) (2022)
- [Federated Nonparametric Hypothesis Testing with Differential Privacy Constraints: Optimal Rates and Adaptive Tests](https://mlsanity.com/paper/2406.06749/) (2024)
- [Dimension-free Private Mean Estimation for Anisotropic Distributions](https://mlsanity.com/paper/2411.00775/) (2024)
- [Private Distribution Testing with Heterogeneous Constraints: Your Epsilon Might Not Be Mine](https://mlsanity.com/paper/2309.06068/) (2023)
- [Minimax And Adaptive Transfer Learning for Nonparametric Classification under Distributed Differential Privacy Constraints](https://mlsanity.com/paper/2406.20088/) (2024)
- [Optimal estimation in private distributed functional data analysis](https://mlsanity.com/paper/2412.06582/) (2024)
- [Sampling depth trade-off in function estimation under a two-level design](https://mlsanity.com/paper/2310.02968/) (2023)

## Built on by (most cited first, 1 of 1)

- [A Van Trees Lower Bound for Fully Interactive Differentially Private Federated Learning](https://mlsanity.com/paper/2605.19813/) (2026)

## Abstract (arXiv)

Federated learning (FL) is a distributed machine learning technique designed to preserve data privacy and security, and it has gained significant importance due to its broad range of applications. This paper addresses the problem of optimal functional mean estimation from discretely sampled data in a federated setting. We consider a heterogeneous framework where the number of individuals, measurements per individual, and privacy parameters vary across one or more servers, under both common and independent design settings. In the common design setting, the same design points are measured for each individual, whereas in the independent design, each individual has their own random collection of design points. Within this framework, we establish minimax upper and lower bounds for the estimation error of the underlying mean function, highlighting the nuanced differences between common and independent designs under distributed privacy constraints. We propose algorithms that achieve the optimal trade-off between privacy and accuracy and provide optimality results that quantify the fundamental limits of private functional mean estimation across diverse distributed settings. These results characterize the cost of privacy and offer practical insights into the potential for privacy-preserving statistical analysis in federated environments.