Misclassification Rate and Privacy-Utility Trade-offs in Graph Convolutional Networks via Subsampling Stability

2026-05-03

AI Summary

Graph convolutional networks (GCNs) under differential privacy face a fundamental challenge in balancing privacy guarantees with model utility, particularly due to the lack of theoretical understanding regarding the impact of subsampling mechanisms. This work proposes the first stability analysis framework tailored to GCNs that explicitly accounts for subsampling, rigorously deriving an upper bound on the misclassification rate as a function of the subsampling probability. Building on this bound, the study characterizes the trade-off between privacy and utility in a principled manner. The analysis not only identifies a feasible range for the subsampling parameter but also provides both theoretical justification and practical guidance for preserving model utility while satisfying differential privacy constraints.

Abstract

We study differential privacy (DP) in Graph Convolutional Networks (GCNs) through the framework of \textit{subsampling stability}. We derive upper bounds on the misclassification rate that depend explicitly on the subsampling probability $p_s$. Furthermore, we characterize the \textit{privacy--utility trade-off} by identifying feasible ranges of $p_s$; if $p_s$ is too large, the stability-based privacy condition becomes difficult to satisfy, yielding vacuous guarantees, whereas if it is too small, accuracy deteriorates. Our results provide the first rigorous theoretical framework for understanding subsampling stability in GCNs under DP.

Problem

• differential privacy
• Graph Convolutional Networks
• privacy-utility trade-off
• subsampling stability
• misclassification rate

Innovation

• subsampling stability
• differential privacy
• Graph Convolutional Networks
• privacy-utility trade-off
• misclassification rate