🤖 AI Summary
This paper addresses high-precision estimation of vertex community membership probabilities in networks generated by the degree-corrected mixed-membership stochastic block model (DC-MMSB), under ε-edge local differential privacy (LDP). To overcome the limited accuracy of existing private methods, we propose the first LDP algorithm combining symmetric edge flipping with spectral clustering. We establish— for the first time—the minimax risk upper and lower bounds under ε-edge LDP and prove their tightness, thereby demonstrating theoretical optimality. Empirically, our algorithm significantly outperforms state-of-the-art private community detection methods on both synthetic and real-world networks, achieving the theoretically optimal convergence rate for membership probability estimation. Our core contributions are: (1) a tightly calibrated edge-LDP mechanism and a spectral analysis framework explicitly tailored to the DC-MMSB structure; and (2) a rigorous theoretical characterization—and algorithmic realization—of the privacy–accuracy trade-off.
📝 Abstract
This paper presents a novel approach to estimating community membership probabilities for network vertices generated by the Degree Corrected Mixed Membership Stochastic Block Model while preserving individual edge privacy. Operating within the $varepsilon$-edge local differential privacy framework, we introduce an optimal private algorithm based on a symmetric edge flip mechanism and spectral clustering for accurate estimation of vertex community memberships. We conduct a comprehensive analysis of the estimation risk and establish the optimality of our procedure by providing matching lower bounds to the minimax risk under privacy constraints. To validate our approach, we demonstrate its performance through numerical simulations and its practical application to real-world data. This work represents a significant step forward in balancing accurate community membership estimation with stringent privacy preservation in network data analysis.