# Social Learning and Distributed Hypothesis Testing

arXiv: https://arxiv.org/abs/1410.4307 · HTML: https://mlsanity.com/paper/1410.4307/

## Key facts

- Cited by 20 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Oct 2014.

## Built on by (most cited first, 20 of 20)

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- [The Query/Hit Model for Sequential Hypothesis Testing](https://mlsanity.com/paper/2502.00605/) (2025)
- [Robust Information Selection for Hypothesis Testing with Misclassification Penalties](https://mlsanity.com/paper/2502.14738/) (2025)
- [Doubly Adaptive Social Learning](https://mlsanity.com/paper/2504.17370/) (2025)
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## Abstract (arXiv)

This paper considers a problem of distributed hypothesis testing and social learning. Individual nodes in a network receive noisy local (private) observations whose distribution is parameterized by a discrete parameter (hypotheses). The conditional distributions are known locally at the nodes, but the true parameter/hypothesis is not known. An update rule is analyzed in which nodes 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. In this paper we show that under mild assumptions, the belief of any node in any incorrect hypothesis converges to zero exponentially fast, and we characterize the exponential rate of learning which is given in terms of the network structure and the divergences between the observations' distributions. Our main result is the concentration property established on the rate of convergence.