Confidence Sets for the Source of a Diffusion in Regular Trees
Confidence Sets for the Source of a Diffusion in Regular Trees
复制标题
常规树中扩散源的置信集
DOI：
10.1109/tnse.2016.2627502
复制
发表时间：
2015
影响因子：
6.6
通讯作者：
Po
中科院分区：
文献类型：
--
作者：
Justin Khim;Po
我们研究的问题，确定的扩散的源在一个正常的树。当每个节点的度至少为3时，我们证明了可以为扩散源构造置信集，其大小与感染节点的数量无关。我们的估计的动机类似的结果在文献中关于识别的根节点在优先附件和均匀附件树。在我们的证明的核心是一个概率分析Pólya瓮对应的数量未感染的邻居在特定的子树的感染树。我们还提供了一个例子，说明源估计技术的缺点，在设置的基础图形是不对称的。
We study the problem of identifying the source of a diffusion spreading over a regular tree. When the degree of each node is at least three, we show that it is possible to construct confidence sets for the diffusion source with size independent of the number of infected nodes. Our estimators are motivated by analogous results in the literature concerning identification of the root node in preferential attachment and uniform attachment trees. At the core of our proofs is a probabilistic analysis of Pólya urns corresponding to the number of uninfected neighbors in specific subtrees of the infection tree. We also provide an example illustrating the shortcomings of source estimation techniques in settings where the underlying graph is asymmetric.
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DOI：
10.1214/16-aap1212
发表时间：
2017
期刊：
The Annals of Applied Probability
影响因子：
--
作者：
Frieze, Alan;Pegden, Wesley
通讯作者：
Pegden, Wesley