Learning in Hierarchical Social Networks

Zhenliang Zhang

doi:10.1109/JSTSP.2013.2245859

Learning in Hierarchical Social Networks

2013-04-01

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DOI：10.1109/JSTSP.2013.2245859

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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 generates a message and sends it to its supervising agent, at the next level of the tree. Each supervising agent aggregates the messages 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 Type 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.

Keywords:

Bayesian learning

convergence rate

decentralized detection

tree structure

hypothesis testing

social learning

Learning in Hierarchical Social Networks

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