arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 2202.00636cs.SIcs.CRcs.ITcs.LGmath.IT
收藏

随机块模型的差分隐私社区检测

Differentially Private Community Detection for Stochastic Block Models

University of Arizona(亚利桑那大学);University of Virginia(弗吉尼亚大学)

Mohamed Seif, Dung Nguyen, Anil Vullikanti, Ravi Tandon

AI总结:

本文研究SBM中边差分隐私下的社区精确恢复,分析稳定性、采样与图扰动三类机制,揭示隐私预算、连接概率和计算复杂度之间的权衡。

摘要:

图上社区检测的目标是在给定用户之间连接性(由图的邻接矩阵表示)的情况下,恢复用户的潜在标签/属性(例如政治派别)。近年来,在理解当图由随机块模型(SBM)生成时社区检测的基本极限方面取得了重大进展。具体而言,人们已经获得了SBM的精确信息论极限和高效算法,这些结果是$p$和$q$的函数,其中$p$和$q$分别表示社区内和社区间的连接概率。在本文中,我们研究社区检测问题,同时保护顶点之间个体连接(边)的隐私。聚焦于$(ε, δ)$-边差分隐私(DP)这一概念,我们寻求理解在$(p, q)$、DP预算$(ε, δ)$与精确恢复社区标签的计算效率之间的基本权衡。为此,我们提出并分析了三大类差分隐私社区恢复机制的相关信息论权衡:a)基于稳定性的机制;b)基于采样的机制;以及c)图扰动机制。我们的主要发现是,基于稳定性和采样的机制在$(p,q)$与隐私预算$(ε, δ)$之间带来更优的权衡;然而,这是以更高的计算复杂度为代价的。另一方面,图扰动机制尽管复杂度较低,但为了精确恢复,要求隐私预算$ε$按$Ω(\log(n))$缩放。据我们所知,这是首个研究隐私约束对社区检测基本极限影响的工作。

英文摘要:

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.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

↑