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

TL;DR

This paper develops a theoretical framework for understanding the privacy-utility trade-offs in Graph Convolutional Networks under differential privacy, focusing on subsampling stability and misclassification bounds.

Contribution

It introduces the first rigorous analysis linking subsampling stability to differential privacy guarantees in GCNs, with explicit bounds on misclassification rates.

Findings

Derived upper bounds on misclassification rate based on subsampling probability

Characterized feasible ranges of subsampling probability for privacy guarantees

Provided insights into the privacy-utility trade-off in GCNs under differential privacy

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.