# Distributed, communication-efficient, and differentially private estimation of KL divergence

**Authors:** Mary Scott, Sayan Biswas, Graham Cormode, Carsten Maple  
**arXiv:** [2411.16478](https://arxiv.org/abs/2411.16478)  
**Date:** 2024-11-25  
**Summary page:** https://www.summarizepaper.com/en/paper/2411.16478v1/

## Key points

- Authors: Mary Scott, Sayan Biswas, Graham Cormode, Carsten Maple
- Topic: Distributed, Communication-Efficient, and Differentially Private Estimation of KL Divergence
- Importance: Managing distributed sensitive data accurately; supporting federated learning and analytics tasks
- Challenge: Sharing information in practical settings due to privacy concerns or high communication costs
- Solution: Novel algorithmic approaches for estimating KL divergence across federated models while ensuring differential privacy
- Theoretical analysis of algorithms
- Empirical study evaluating performance
- Exploration of parameter settings for enhanced accuracy tailored to specific scenarios
- Development of private estimators achieving comparable accuracy levels to baseline algorithms with differential privacy guarantees

## Summary

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In their paper titled "Distributed, Communication-Efficient, and Differentially Private Estimation of KL Divergence," authors Mary Scott, Sayan Biswas, Graham Cormode, and Carsten Maple address the crucial task of managing distributed, sensitive data by accurately measuring changes in distribution. This understanding is essential for supporting various federated learning and analytics tasks. However, sharing such information in practical settings can be challenging due to privacy concerns or high communication costs. To tackle this challenge, the authors propose novel algorithmic approaches for estimating the Kullback-Leibler (KL) divergence of data across federated models while ensuring differential privacy. They delve into the theoretical properties of these algorithms and conduct an empirical study to evaluate their performance. By exploring parameter settings that enhance algorithm accuracy tailored to specific scenarios, they offer sub-variations that cater to real-world tasks with varying trust level requirements. The experimental results presented in the study demonstrate that the private estimators developed by the authors achieve accuracy levels comparable to a baseline algorithm without compromising on differential privacy guarantees. This research contributes valuable insights into efficiently estimating KL divergence in distributed environments while safeguarding sensitive data through differential privacy mechanisms.