Year: 2022
Type: preprint
Abstract: The goal of community detection over graphs is to recover underlying labels/attributes of users (e.g., political affiliation) given the connectivity between users (represented by adjacency matrix of a graph). There has been significant recent progress on understanding the fundamental limits of community detection when the graph is generated from a stochastic block model (SBM). Specifically, sharp information theoretic limits and efficient algorithms have been obtained for SBMs as a function of $p$ and $q$, which represent the intra-community and inter-community connection probabilities. In this paper, we study the community detection problem while preserving the privacy of the individual connections (edges) between the vertices. Focusing on the notion of $(ε, δ)$-edge differential privacy (DP), we seek to understand the fundamental tradeoffs between $(p, q)$, DP budget $(ε, δ)$, and computational efficiency for exact recovery of the community labels. To this end, we present and analyze the associated information-theoretic tradeoffs for three broad classes of differentially private community recovery mechanisms: a) stability based mechanism; b) sampling based mechanisms; and c) graph perturbation mechanisms. Our main findings are that stability and sampling based mechanisms lead to a superior tradeoff between $(p,q)$ and the privacy budget $(ε, δ)$; however this comes at the expense of higher computational complexity. On the other hand, albeit low complexity, graph perturbation mechanisms require the privacy budget $ε$ to scale as $Ω(\log(n))$ for exact recovery. To the best of our knowledge, this is the first work to study the impact of privacy constraints on the fundamental limits for community detection.
Source: arXiv (Cornell University)
Institutions: University of Arizona, University of Virginia
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
Awards: III: Medium: Collaborative Research: Detecting and Controlling Network-based Spread of Hospital Acquired Infections, G5248879451, G5260964573, CAREER: Communication- Efficient Distributed Computation: Information- Theoretic Foundations and Algorithms, BIGDATA: Collaborative Research: F: Efficient Distributed Computation of Large-Scale Graph Problems in Epidemiology and Contagion Dynamics, G6671297155, EAGER: DCL: SaTC: Enabling Interdisciplinary Collab: Impact-aware Machine Learning for Fair and Private Decision Making: Algorithms and Applications in Juvenile Justice Systems, CIF: Small: Learning To Correct Errors, Detection and characterization of critical under-immunized hotspots, Expeditions: Collaborative Research: Global Pervasive Computational Epidemiology, SaTC: CORE: Small: Robust Physical Layer Security with Channel Knowledge Uncertainty
OpenAlex ID: W4221146012