# Non-Bayesian Social Learning with Uncertain Models

arXiv: https://arxiv.org/abs/1909.09228 · HTML: https://mlsanity.com/paper/1909.09228/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Sep 2019.

## Built on by (most cited first, 4 of 4)

- [Learning from Heterogeneous Data Based on Social Interactions over Graphs](https://mlsanity.com/paper/2112.09483/) (2021)
- [Distributed Bayesian Learning of Dynamic States](https://mlsanity.com/paper/2212.02565/) (2022)
- [Distributed Bayesian Estimation in Sensor Networks: Consensus on Marginal Densities](https://mlsanity.com/paper/2312.01227/) (2023)
- [Doubly Adaptive Social Learning](https://mlsanity.com/paper/2504.17370/) (2025)

## Abstract (arXiv)

Non-Bayesian social learning theory provides a framework that models distributed inference for a group of agents interacting over a social network. In this framework, each agent iteratively forms and communicates beliefs about an unknown state of the world with their neighbors using a learning rule. Existing approaches assume agents have access to precise statistical models (in the form of likelihoods) for the state of the world. However in many situations, such models must be learned from finite data. We propose a social learning rule that takes into account uncertainty in the statistical models using second-order probabilities. Therefore, beliefs derived from uncertain models are sensitive to the amount of past evidence collected for each hypothesis. We characterize how well the hypotheses can be tested on a social network, as consistent or not with the state of the world. We explicitly show the dependency of the generated beliefs with respect to the amount of prior evidence. Moreover, as the amount of prior evidence goes to infinity, learning occurs and is consistent with traditional social learning theory.