影响者与巨型成分：社会传染属性隐私保护的基本难点
Influencers and the Giant Component: the Fundamental Hardness in Privacy Protection for Socially Contagious Attributes
摘要：
已知相关性的存在使得隐私保护更加困难。我们调查的隐私的社会传染属性的个人网络，其中每个人拥有的属性可能会影响一些其他人采用it. We表明，以下的独立级联模型的传染存在一个巨大的连接组件的受感染的节点，包含一个常数部分的所有节点谁都收到来自同一组源的传染。我们进一步表明，这是非常难以隐藏这个巨大的连接组件的存在，如果我们想获得一个估计的激活用户在一个可接受的水平。此外，拥有这种知识的对手可以预测的真实状态（“活跃”或“不活跃”）与体面的概率为许多个人，无论隐私（扰动）机制使用。作为一个案例研究，我们表明，Wasserstein机制，一个国家的最先进的隐私机制，专门为相关数据设计的，在我们的设置中的计数估计的顺序$Ω(n)$的幅度引入噪声。在独立级联模型下，我们给出了两类随机网络：Erdos Renyi图和Chung-Lu幂律图的理论保证。实验表明，一个巨大的连接组件的感染节点可以出现在现实世界的网络，一个简单的推理攻击可以揭示一个很好的一部分节点的状态。
英文摘要：
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 $Ω(n)$ 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.
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。
