Estimating Power-Law Exponent with Edge Differential Privacy

2026-04-22

AI Summary

This work addresses the challenge of accurately estimating the power-law exponent α of sensitive edge relationships in graphs under edge differential privacy. The authors propose a novel paradigm that directly perturbs low-dimensional sufficient statistics, circumventing the high distortion inherent in conventional approaches that first release noisy degree distributions and then fit the exponent. The method supports two efficient fitting strategies—discrete approximation and maximum likelihood estimation—and includes algorithms tailored for both centralized and local differential privacy models. Experimental results across diverse graph datasets, privacy budgets, and tail-truncation settings demonstrate that the proposed approach significantly outperforms existing noisy degree-distribution release mechanisms, with particular gains in the local model where releasing logarithmic statistics proves superior to publishing raw degree sequences.

Technology Category

• Machine Learning: Graph-based Machine Learning
• Data Mining & Knowledge Management: Graph Mining, Social Network Analysis & Community
• Search and Optimization: Distributed Search

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Security and Privacy: Large-scale security measurements
• Web Mining and Content Analysis: Content-based information diffusion

Abstract

Many real-world graphs have degree distributions that are well approximated by a power-law, and the corresponding scaling parameter $α$ provides a compact summary of that structure which is useful for graph analysis and system optimization. When graphs contain sensitive relationship data, $α$ must be estimated without revealing information about individual edges. This paper studies power-law exponent estimation under edge differential privacy. Instead of first releasing a noisy degree distribution and then fitting a power-law model, we propose privatizing only the low-dimensional sufficient statistics needed to estimate $α$, thereby avoiding the high distortion introduced by traditional approaches. Using these released statistics, we support both discrete approximation and likelihood-based numerical optimization for efficient parameter estimation. We develop edge-DP algorithms for both centralized and local DP models, compare degree release and log-statistic release in the local setting, and evaluate the resulting methods on various graph datasets across multiple privacy budgets and tail-cutoff settings.

Problem

• power-law exponent
• edge differential privacy
• degree distribution
• privacy-preserving estimation
• graph analysis

Innovation

• edge differential privacy
• power-law exponent estimation
• sufficient statistics
• degree distribution
• local differential privacy