# Federated Learning of Quantile Inference under Local Differential Privacy

arXiv: https://arxiv.org/abs/2509.21800 · HTML: https://mlsanity.com/paper/2509.21800/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 27 of its 51 references that are in the map.
- First posted on arXiv 26 Sep 2025.

## Builds on (most cited first, 27 of 27)

- [Federated Optimization in Heterogeneous Networks](https://mlsanity.com/paper/1812.06127/) (2018)
- [Accurate, Large Minibatch SGD: Training ImageNet in 1 Hour](https://mlsanity.com/paper/1706.02677/) (2017)
- [Federated Learning: Strategies for Improving Communication Efficiency](https://mlsanity.com/paper/1610.05492/) (2016)
- [Local SGD Converges Fast and Communicates Little](https://mlsanity.com/paper/1805.09767/) (2018)
- [Scalable Extraction of Training Data from (Production) Language Models](https://mlsanity.com/paper/2311.17035/) (2023)
- [cpSGD: Communication-efficient and differentially-private distributed SGD](https://mlsanity.com/paper/1805.10559/) (2018)
- [Collecting Telemetry Data Privately](https://mlsanity.com/paper/1712.01524/) (2017)
- [Distributed Differential Privacy via Shuffling](https://mlsanity.com/paper/1808.01394/) (2018)
- [Accelerating Federated Learning via Momentum Gradient Descent](https://mlsanity.com/paper/1910.03197/) (2019)
- [Local Differential Privacy based Federated Learning for Internet of Things](https://mlsanity.com/paper/2004.08856/) (2020)
- [Statistical Inference for Model Parameters in Stochastic Gradient Descent](https://mlsanity.com/paper/1610.08637/) (2016)
- [Instance-optimal Mean Estimation Under Differential Privacy](https://mlsanity.com/paper/2106.00463/) (2021)
- [Communication-Efficient Accurate Statistical Estimation](https://mlsanity.com/paper/1906.04870/) (2019)
- [Evaluating Treatment Prioritization Rules via Rank-Weighted Average Treatment Effects](https://mlsanity.com/paper/2111.07966/) (2021)
- [Private Federated Learning Without a Trusted Server: Optimal Algorithms for Convex Losses](https://mlsanity.com/paper/2106.09779/) (2021)
- [Localized Debiased Machine Learning: Efficient Inference on Quantile Treatment Effects and Beyond](https://mlsanity.com/paper/1912.12945/) (2019)
- [Smoothed Quantile Regression with Large-Scale Inference](https://mlsanity.com/paper/2012.05187/) (2020)
- [Differentially Private Quantiles](https://mlsanity.com/paper/2102.08244/) (2021)
- [First-order Newton-type Estimator for Distributed Estimation and Inference](https://mlsanity.com/paper/1811.11368/) (2018)
- [fairadapt: Causal Reasoning for Fair Data Pre-processing](https://mlsanity.com/paper/2110.10200/) (2021)
- [The Role of Interactivity in Local Differential Privacy](https://mlsanity.com/paper/1904.03564/) (2019)
- [High Confidence Level Inference is Almost Free using Parallel Stochastic Optimization](https://mlsanity.com/paper/2401.09346/) (2024)
- [A Distributed and Integrated Method of Moments for High-Dimensional Correlated Data Analysis](https://mlsanity.com/paper/1910.02986/) (2019)
- [Forecasting with Economic News](https://mlsanity.com/paper/2203.15686/) (2022)
- [Online Local Differential Private Quantile Inference via Self-normalization](https://mlsanity.com/paper/2306.10260/) (2023)
- [Asymptotic Time-Uniform Inference for Parameters in Averaged Stochastic Approximation](https://mlsanity.com/paper/2410.15057/) (2024)
- [Does Worst-Performing Agent Lead the Pack? Analyzing Agent Dynamics in Unified Distributed SGD](https://mlsanity.com/paper/2409.17499/) (2024)

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

- [How Much is Left? LLMs Linearly Encode Their Remaining Output Length](https://mlsanity.com/paper/2607.05316/) (2026)
- [Locally Private Inference for Riemannian Stochastic Optimization](https://mlsanity.com/paper/2609.22642/) (2026)

## Abstract (arXiv)

In this paper, we investigate federated learning for quantile inference under local differential privacy (LDP). We propose an estimator based on local stochastic gradient descent (SGD), whose local gradients are perturbed via a randomized mechanism with global parameters, making the procedure tolerant of communication and storage constraints without compromising statistical efficiency. Although the quantile loss and its corresponding gradient do not satisfy standard smoothness conditions typically assumed in existing literature, we establish asymptotic normality for our estimator as well as a functional central limit theorem. The proposed method accommodates data heterogeneity and allows each server to operate with an individual privacy budget. Furthermore, we construct confidence intervals for the target value through a self-normalization approach, thereby circumventing the need to estimate additional nuisance parameters. Extensive numerical experiments and real data application validate the theoretical guarantees of the proposed methodology.