Hayk Amirkhanian, Markus Walker, Uwe D. Hanebeck, Marco F. Huber

Proceedings of the 28th International Conference on Information Fusion (FUSION 2025), pp. 1–8, Rio de Janeiro, Brazil, Bridging Bayesian Inference and Neural Network Training: Equivalence of KBNN and Statistical Linearization

Abstract:

Accurate uncertainty quantification is critical for robust and trustworthy predictions in many real-world applications. Bayesian Neural Networks (BNNs) provide a principled approach for modeling uncertainty but are often limited by the computational complexity of Bayesian inference. In this paper, we introduce a statistical linearization approach for multilayer feedforward BNNs. We demonstrate that this statistical linearization is equivalent to the Kalman Bayesian Neural Networks (KBNN) framework. This equivalence unifies these methodologies, providing a theoretical foundation for understanding the relationship between different BNN training approaches.