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arXiv 1206.0652cs.SIcs.ITcs.LGmath.IT
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分层社交网络中的学习

Learning in Hierarchical Social Networks

Colorado State University(科罗拉多州立大学);The University of Melbourne(墨尔本大学);Defence Science and Technology Organisation(国防科学技术组织)

Zhenliang Zhang, Edwin K. P. Chong, Ali Pezeshki, William Moran, Stephen D. Howard

摘要:

我们研究了一个社会网络组成的代理组织为一个层次的M元根树,常见的企业和军事组织结构。目标是聚合信息以解决二元假设检验问题。每一个在树的一片叶子上的主体,也只有这样一个主体,对潜在的真实假设进行直接测量。然后,叶代理做出决定,并将其发送到树的下一级的监督代理。每个监督代理汇总来自其组的M个成员的决策,生成摘要消息,并将其发送给下一级的监督者,等等。我们推导出与此决定相关的第一和第二类错误概率的上限和下限相对于叶代理的数量,这反过来又表征了第一类,第二类和总错误概率的收敛速度。我们还提供了一个消息传递计划,涉及非二进制消息字母表和表征的错误概率的指数相对于消息字母表的大小。

英文摘要:

We study a social network consisting of agents organized as a hierarchical M-ary rooted tree, common in enterprise and military organizational structures. The goal is to aggregate information to solve a binary hypothesis testing problem. Each agent at a leaf of the tree, and only such an agent, makes a direct measurement of the underlying true hypothesis. The leaf agent then makes a decision and sends it to its supervising agent, at the next level of the tree. Each supervising agent aggregates the decisions from the M members of its group, produces a summary message, and sends it to its supervisor at the next level, and so on. Ultimately, the agent at the root of the tree makes an overall decision. We derive upper and lower bounds for the Type I and II error probabilities associated with this decision with respect to the number of leaf agents, which in turn characterize the converge rates of the Type I, Type II, and total error probabilities. We also provide a message-passing scheme involving non-binary message alphabets and characterize the exponent of the error probability with respect to the message alphabet size.

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。

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