### Abstract

This paper considers a problem of distributed hypothesis testing and social learning. Individual nodes in a network receive noisy (private) observations whose distribution is parameterized by a discrete parameter (hypotheses). The distributions are known locally at the nodes, but the true parameter/hypothesis is not known. An update rule is analyzed in which agents first perform a Bayesian update of their belief (distribution estimate) of the parameter based on their local observation, communicate these updates to their neighbors, and then perform a 'non-Bayesian' linear consensus using the log-beliefs of their neighbors. The main result of this paper is that under mild assumptions, the belief of any agent in any incorrect parameter converges to zero exponentially fast, and the exponential rate of learning is a characterized by the network structure and the divergences between the observations' distributions.

Original language | English (US) |
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Title of host publication | 2014 IEEE International Symposium on Information Theory, ISIT 2014 |

Publisher | Institute of Electrical and Electronics Engineers Inc. |

Pages | 551-555 |

Number of pages | 5 |

ISBN (Print) | 9781479951864 |

DOIs | |

State | Published - Jan 1 2014 |

Event | 2014 IEEE International Symposium on Information Theory, ISIT 2014 - Honolulu, HI, United States Duration: Jun 29 2014 → Jul 4 2014 |

### Publication series

Name | IEEE International Symposium on Information Theory - Proceedings |
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ISSN (Print) | 2157-8095 |

### Other

Other | 2014 IEEE International Symposium on Information Theory, ISIT 2014 |
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Country | United States |

City | Honolulu, HI |

Period | 6/29/14 → 7/4/14 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Information Systems
- Modeling and Simulation
- Applied Mathematics

### Cite this

*2014 IEEE International Symposium on Information Theory, ISIT 2014*(pp. 551-555). [6874893] (IEEE International Symposium on Information Theory - Proceedings). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/ISIT.2014.6874893