# On the Arithmetic and Geometric Fusion of Beliefs for Distributed Inference

arXiv: https://arxiv.org/abs/2204.13741 · HTML: https://mlsanity.com/paper/2204.13741/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Apr 2022.

## Built on by (most cited first, 7 of 7)

- [Distributed Bayesian Learning of Dynamic States](https://mlsanity.com/paper/2212.02565/) (2022)
- [Policy Evaluation in Decentralized POMDPs with Belief Sharing](https://mlsanity.com/paper/2302.04151/) (2023)
- [On the Fusion Strategies for Federated Decision Making](https://mlsanity.com/paper/2303.06109/) (2023)
- [Non-Asymptotic Performance of Social Machine Learning Under Limited Data](https://mlsanity.com/paper/2306.09397/) (2023)
- [Distributed Bayesian Estimation in Sensor Networks: Consensus on Marginal Densities](https://mlsanity.com/paper/2312.01227/) (2023)
- [Causal Influence in Federated Edge Inference](https://mlsanity.com/paper/2405.01260/) (2024)
- [On the dynamics of multi agent nonlinear filtering and learning](https://mlsanity.com/paper/2309.03557/) (2023)

## Abstract (arXiv)

We study the asymptotic learning rates under linear and log-linear combination rules of belief vectors in a distributed hypothesis testing problem. We show that under both combination strategies, agents are able to learn the truth exponentially fast, with a faster rate under log-linear fusion. We examine the gap between the rates in terms of network connectivity and information diversity. We also provide closed-form expressions for special cases involving federated architectures and exchangeable networks.