Bayesian data fusion with shared priors

TL;DR

This paper analyzes how shared priors affect Bayesian data fusion performance across various models and fusion rules, providing theoretical insights and experimental validation in estimation, classification, and federated learning contexts.

Contribution

It offers a theoretical framework for understanding the impact of shared priors in Bayesian data fusion, applicable to diverse models and fusion strategies.

Findings

Shared priors can lead to overconfidence in fused estimates.

Performance varies with the number of agents and the type of prior used.

Theoretical results are validated through experiments in multiple scenarios.

Abstract

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.