# Decentralized Bayesian Learning over Graphs

arXiv: https://arxiv.org/abs/1905.10466 · HTML: https://mlsanity.com/paper/1905.10466/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 May 2019.

## Built on by (most cited first, 9 of 9)

- [The effect of network topologies on fully decentralized learning: a preliminary investigation](https://mlsanity.com/paper/2307.15947/) (2023)
- [Impact of network topology on the performance of Decentralized Federated Learning](https://mlsanity.com/paper/2402.18606/) (2024)
- [Coordination-free Decentralised Federated Learning on Complex Networks: Overcoming Heterogeneity](https://mlsanity.com/paper/2312.04504/) (2023)
- [Decentralized Bayesian Learning with Metropolis-Adjusted Hamiltonian Monte Carlo](https://mlsanity.com/paper/2107.07211/) (2021)
- [Bristle: Decentralized Federated Learning in Byzantine, Non-i.i.d. Environments](https://mlsanity.com/paper/2110.11006/) (2021)
- [Joint Signal Recovery and Graph Learning from Incomplete Time-Series](https://mlsanity.com/paper/2312.16940/) (2023)
- [Distributed Markov Chain Monte Carlo Sampling based on the Alternating Direction Method of Multipliers](https://mlsanity.com/paper/2401.15838/) (2024)
- [Decentralized Federated Learning of Probabilistic Generative Classifiers](https://mlsanity.com/paper/2507.17285/) (2025)
- [DecHW: Heterogeneous Decentralized Federated Learning Exploiting Second-Order Information](https://mlsanity.com/paper/2601.19938/) (2026)

## Abstract (arXiv)

We propose a decentralized learning algorithm over a general social network. The algorithm leaves the training data distributed on the mobile devices while utilizing a peer to peer model aggregation method. The proposed algorithm allows agents with local data to learn a shared model explaining the global training data in a decentralized fashion. The proposed algorithm can be viewed as a Bayesian and peer-to-peer variant of federated learning in which each agent keeps a "posterior probability distribution" over a global model parameters. The agent update its "posterior" based on 1) the local training data and 2) the asynchronous communication and model aggregation with their 1-hop neighbors. This Bayesian formulation allows for a systematic treatment of model aggregation over any arbitrary connected graph. Furthermore, it provides strong analytic guarantees on converge in the realizable case as well as a closed form characterization of the rate of convergence. We also show that our methodology can be combined with efficient Bayesian inference techniques to train Bayesian neural networks in a decentralized manner. By empirical studies we show that our theoretical analysis can guide the design of network/social interactions and data partitioning to achieve convergence.