Differentially Private Empirical Cumulative Distribution Functions

2025-02-10

AI Summary

This work addresses the privacy-preserving construction of a global empirical cumulative distribution function (ECDF) in federated learning. We propose the first systematic framework achieving ε-differential privacy for ECDF estimation. Methodologically, we design a dual-path solution: (i) a general-purpose differentially private mechanism and (ii) a dedicated protocol based on secure multi-party computation via secret sharing—both enabling distributed ECDF estimation without exposing local raw data. We provide rigorous theoretical proofs of ε-differential privacy and optimize privacy budget allocation to maximize statistical utility. Experiments on real-world datasets demonstrate that our approach significantly outperforms baseline methods, achieving superior privacy–utility trade-offs while preserving both the fidelity of distributional shape and functional integrity. Moreover, it improves privacy budget efficiency without compromising ECDF accuracy.

Technology Category

• Machine Learning: Distributed Machine Learning & Federated Learning
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Search and Optimization: Distributed Search

Application Category

• Security and Privacy: Data transparency and provenance
• Economics, Online Markets and Human Computation: Fairness, privacy, and diversity in economic environments
• User Modeling, Personalization and Recommendation: Federated recommendation systems and personalization

Abstract

In order to both learn and protect sensitive training data, there has been a growing interest in privacy preserving machine learning methods. Differential privacy has emerged as an important measure of privacy. We are interested in the federated setting where a group of parties each have one or more training instances and want to learn collaboratively without revealing their data. In this paper, we propose strategies to compute differentially private empirical distribution functions. While revealing complete functions is more expensive from the point of view of privacy budget, it may also provide richer and more valuable information to the learner. We prove privacy guarantees and discuss the computational cost, both for a generic strategy fitting any security model and a special-purpose strategy based on secret sharing. We survey a number of applications and present experiments.

Problem

• Develop differentially private empirical distribution functions
• Protect sensitive data in federated learning
• Balance privacy budget and information richness

Innovation

• Differentially private empirical distribution
• Federated learning for privacy
• Secret sharing strategy