从犯罪嫌疑人身上铲除谣言文化
Rooting out the Rumor Culprit from Suspects
摘要：
假设一个谣言来源于一组嫌疑人中的一个来源，在网络中传播，如何根除这个谣言来源？利用可疑节点的先验知识和感染节点的观测值，我们构造了一个最大后验概率（MAP）估计器来识别谣言源。先验的嫌疑人集及其相关的连接带来了新的成分的问题，因此，我们建议使用本地的谣言中心，一个广义的概念，基于谣言中心，从嫌疑人识别来源。对于节点度为δ的正则树型网络，我们刻画了Pc（n），即在有限和渐近状态下观察到n个感染节点时估计器的正确检测概率。首先，当每个被感染的节点都是可疑节点时，Pc（n）从0.25渐近增长到0.307，δ从3到无穷大，这是Shah和Zaman（2011，2012）通过不同的方法首次建立的结果;并且它随着n单调下降，随着δ单调增加。其次，当嫌疑人形成网络的连通子图时，如果δ>2，Pc（n）渐近显著超过先验概率，并且随着δ变大而实现可靠检测;此外，它随着n单调减小，随着δ单调增加。第三，当只有两个嫌疑人时，若δ>2，Pc（n）渐近至少为0.75，并且它随两个嫌疑人之间的距离而增大。第四，当存在多个嫌疑人时，在所有可能的连接模式中，它们形成网络的连通子图实现了最小的检测概率。我们的分析利用了概率论中波利亚瓮模型的思想，不仅在渐近制度，而且在一般的有限n制度的谣言传播过程中的行为洞察。
英文摘要：
Suppose that a rumor originating from a single source among a set of suspects spreads in a network, how to root out this rumor source? With the a priori knowledge of suspect nodes and an observation of infected nodes, we construct a maximum a posteriori (MAP) estimator to identify the rumor source using the susceptible-infected (SI) model. The a priori suspect set and its associated connectivity bring about new ingredients to the problem, and thus we propose to use local rumor center, a generalized concept based on rumor centrality, to identify the source from suspects. For regular tree-type networks of node degree δ, we characterize Pc(n), the correct detection probability of the estimator upon observing n infected nodes, in both the finite and asymptotic regimes. First, when every infected node is a suspect, Pc(n) asymptotically grows from 0.25 to 0.307 with δ from 3 to infinity, a result first established in Shah and Zaman (2011, 2012) via a different approach; and it monotonically decreases with n and increases with δ. Second, when the suspects form a connected subgraph of the network, Pc(n) asymptotically significantly exceeds the a priori probability if δ>2, and reliable detection is achieved as δ becomes large; furthermore, it monotonically decreases with n and increases with δ. Third, when there are only two suspects, Pc(n) is asymptotically at least 0.75 if δ>2; and it increases with the distance between the two suspects. Fourth, when there are multiple suspects, among all possible connection patterns, that they form a connected subgraph of the network achieves the smallest detection probability. Our analysis leverages ideas from the Polya's urn model in probability theory and sheds insight into the behavior of the rumor spreading process not only in the asymptotic regime but also for the general finite-n regime.
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