# Bayesian data fusion with shared priors

arXiv: https://arxiv.org/abs/2212.07311 · HTML: https://mlsanity.com/paper/2212.07311/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 58 references that are in the map.
- First posted on arXiv 14 Dec 2022.

## Builds on (most cited first, 17 of 17)

- [Communication-Efficient Learning of Deep Networks from Decentralized Data](https://mlsanity.com/paper/1602.05629/) (2016)
- [Advances and Open Problems in Federated Learning](https://mlsanity.com/paper/1912.04977/) (2019)
- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [When Gaussian Process Meets Big Data: A Review of Scalable GPs](https://mlsanity.com/paper/1807.01065/) (2018)
- [FedBE: Making Bayesian Model Ensemble Applicable to Federated Learning](https://mlsanity.com/paper/2009.01974/) (2020)
- [Bayesian Neural Network Priors Revisited](https://mlsanity.com/paper/2102.06571/) (2021)
- [Peer-to-peer Federated Learning on Graphs](https://mlsanity.com/paper/1901.11173/) (2019)
- [Distributed Gaussian Processes](https://mlsanity.com/paper/1502.02843/) (2015)
- [Personalized Federated Learning with Gaussian Processes](https://mlsanity.com/paper/2106.15482/) (2021)
- [A Bayesian Federated Learning Framework with Online Laplace Approximation](https://mlsanity.com/paper/2102.01936/) (2021)
- [Emerging Trends in Federated Learning: From Model Fusion to Federated X Learning](https://mlsanity.com/paper/2102.12920/) (2021)
- [Generalized Robust Bayesian Committee Machine for Large-scale Gaussian Process Regression](https://mlsanity.com/paper/1806.00720/) (2018)
- [Fusion of Federated Learning and Industrial Internet of Things: A Survey](https://mlsanity.com/paper/2101.00798/) (2021)
- [Fusion of Probability Density Functions](https://mlsanity.com/paper/2202.11633/) (2022)
- [A Universal Approximation Theorem for Mixture of Experts Models](https://mlsanity.com/paper/1602.03683/) (2016)
- [Personalized Federated Learning over non-IID Data for Indoor Localization](https://mlsanity.com/paper/2107.04189/) (2021)
- [Second Order Statistics Analysis and Comparison between Arithmetic and Geometric Average Fusion](https://mlsanity.com/paper/1901.08015/) (2019)

## Built on by (most cited first, 3 of 3)

- [Model Merging by Uncertainty-Based Gradient Matching](https://mlsanity.com/paper/2310.12808/) (2023)
- [Knowledge Adaptation as Posterior Correction](https://mlsanity.com/paper/2506.14262/) (2025)
- [A Bayesian Framework for Clustered Federated Learning](https://mlsanity.com/paper/2410.15473/) (2024)

## Abstract (arXiv)

The integration of data and knowledge from several sources is known as data fusion. When data is only available in a distributed fashion or when different sensors are used to infer a quantity of interest, data fusion becomes essential. In Bayesian settings, a priori information of the unknown quantities is available and, possibly, present among the different distributed estimators. When the local estimates are fused, the prior knowledge used to construct several local posteriors might be overused unless the fusion node accounts for this and corrects it. In this paper, we analyze the effects of shared priors in Bayesian data fusion contexts. Depending on different common fusion rules, our analysis helps to understand the performance behavior as a function of the number of collaborative agents and as a consequence of different types of priors. The analysis is performed by using two divergences which are common in Bayesian inference, and the generality of the results allows to analyze very generic distributions. These theoretical results are corroborated through experiments in a variety of estimation and classification problems, including linear and nonlinear models, and federated learning schemes.