Influencers and the Giant Component: the Fundamental Hardness in Privacy Protection for Socially Contagious Attributes

TL;DR

This paper explores the fundamental difficulty of protecting privacy for contagious attributes in networks, showing that large connected infected groups are hard to hide and can be exploited to infer individual statuses, even with advanced privacy mechanisms.

Contribution

It demonstrates the existence of giant infected components in social contagion models and analyzes the limitations of current privacy mechanisms in hiding this information.

Findings

Giant connected components of infected nodes are common in social contagion networks.

State-of-the-art privacy mechanisms like Wasserstein introduce large noise, reducing effectiveness.

Simple inference attacks can accurately predict individual statuses despite privacy protections.

Abstract

The presence of correlation is known to make privacy protection more difficult. We investigate the privacy of socially contagious attributes on a network of individuals, where each individual possessing that attribute may influence a number of others into adopting it. We show that for contagions following the Independent Cascade model there exists a giant connected component of infected nodes, containing a constant fraction of all the nodes who all receive the contagion from the same set of sources. We further show that it is extremely hard to hide the existence of this giant connected component if we want to obtain an estimate of the activated users at an acceptable level. Moreover, an adversary possessing this knowledge can predict the real status ("active" or "inactive") with decent probability for many of the individuals regardless of the privacy (perturbation) mechanism used. As a case study, we show that the Wasserstein mechanism, a state-of-the-art privacy mechanism designed specifically for correlated data, introduces a noise with magnitude of order $\Omega(n)$ in the count estimation in our setting. We provide theoretical guarantees for two classes of random networks: Erdos Renyi graphs and Chung-Lu power-law graphs under the Independent Cascade model. Experiments demonstrate that a giant connected component of infected nodes can and does appear in real-world networks and that a simple inference attack can reveal the status of a good fraction of nodes.