# Federated Bayesian Deep Learning: The Application of Statistical Aggregation Methods to Bayesian Models

arXiv: https://arxiv.org/abs/2403.15263 · HTML: https://mlsanity.com/paper/2403.15263/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 31 of its 64 references that are in the map.
- First posted on arXiv 22 Mar 2024.

## Builds on (most cited first, 30 of 31)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Communication-Efficient Learning of Deep Networks from Decentralized Data](https://mlsanity.com/paper/1602.05629/) (2016)
- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [Federated Optimization in Heterogeneous Networks](https://mlsanity.com/paper/1812.06127/) (2018)
- [What Uncertainties Do We Need in Bayesian Deep Learning for Computer Vision?](https://mlsanity.com/paper/1703.04977/) (2017)
- [Federated Learning: Strategies for Improving Communication Efficiency](https://mlsanity.com/paper/1610.05492/) (2016)
- [Variational Inference: A Review for Statisticians](https://mlsanity.com/paper/1601.00670/) (2016)
- [Federated Learning with Non-IID Data](https://mlsanity.com/paper/1806.00582/) (2018)
- [Measuring the Effects of Non-Identical Data Distribution for Federated Visual Classification](https://mlsanity.com/paper/1909.06335/) (2019)
- [Deep Bayesian Active Learning with Image Data](https://mlsanity.com/paper/1703.02910/) (2017)
- [Personalized Federated Learning with Moreau Envelopes](https://mlsanity.com/paper/2006.08848/) (2020)
- [Federated Learning on Non-IID Data Silos: An Experimental Study](https://mlsanity.com/paper/2102.02079/) (2021)
- [Weight Uncertainty in Neural Networks](https://mlsanity.com/paper/1505.05424/) (2015)
- [Variational Dropout and the Local Reparameterization Trick](https://mlsanity.com/paper/1506.02557/) (2015)
- [Differentially Private Federated Learning: A Client Level Perspective](https://mlsanity.com/paper/1712.07557/) (2017)
- [Flower: A Friendly Federated Learning Research Framework](https://mlsanity.com/paper/2007.14390/) (2020)
- [Robust and Communication-Efficient Federated Learning from Non-IID Data](https://mlsanity.com/paper/1903.02891/) (2019)
- [Variational Continual Learning](https://mlsanity.com/paper/1710.10628/) (2017)
- [FedBE: Making Bayesian Model Ensemble Applicable to Federated Learning](https://mlsanity.com/paper/2009.01974/) (2020)
- [RSA: Byzantine-Robust Stochastic Aggregation Methods for Distributed Learning from Heterogeneous Datasets](https://mlsanity.com/paper/1811.03761/) (2018)
- [Flipout: Efficient Pseudo-Independent Weight Perturbations on Mini-Batches](https://mlsanity.com/paper/1803.04386/) (2018)
- [Protection Against Reconstruction and Its Applications in Private Federated Learning](https://mlsanity.com/paper/1812.00984/) (2018)
- [Personalized Federated Learning via Variational Bayesian Inference](https://mlsanity.com/paper/2206.07977/) (2022)
- [A Systematic Comparison of Bayesian Deep Learning Robustness in Diabetic Retinopathy Tasks](https://mlsanity.com/paper/1912.10481/) (2019)
- [Multi-objective Evolutionary Federated Learning](https://mlsanity.com/paper/1812.07478/) (2018)
- [A Bayesian Federated Learning Framework with Online Laplace Approximation](https://mlsanity.com/paper/2102.01936/) (2021)
- [Fusion of Probability Density Functions](https://mlsanity.com/paper/2202.11633/) (2022)
- [Distributed Weight Consolidation: A Brain Segmentation Case Study](https://mlsanity.com/paper/1805.10863/) (2018)
- [Bayesian Incremental Learning for Deep Neural Networks](https://mlsanity.com/paper/1802.07329/) (2018)

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

- [Federated Learning with Uncertainty and Personalization via Efficient Second-order Optimization](https://mlsanity.com/paper/2411.18385/) (2024)
- [Information-Geometric Barycenters for Bayesian Federated Learning](https://mlsanity.com/paper/2412.11646/) (2024)
- [Cost-Free Personalization via Information-Geometric Projection in Bayesian Federated Learning](https://mlsanity.com/paper/2509.10132/) (2025)

## Abstract (arXiv)

Federated learning (FL) is an approach to training machine learning models that takes advantage of multiple distributed datasets while maintaining data privacy and reducing communication costs associated with sharing local datasets. Aggregation strategies have been developed to pool or fuse the weights and biases of distributed deterministic models; however, modern deterministic deep learning (DL) models are often poorly calibrated and lack the ability to communicate a measure of epistemic uncertainty in prediction, which is desirable for remote sensing platforms and safety-critical applications. Conversely, Bayesian DL models are often well calibrated and capable of quantifying and communicating a measure of epistemic uncertainty along with a competitive prediction accuracy. Unfortunately, because the weights and biases in Bayesian DL models are defined by a probability distribution, simple application of the aggregation methods associated with FL schemes for deterministic models is either impossible or results in sub-optimal performance. In this work, we use independent and identically distributed (IID) and non-IID partitions of the CIFAR-10 dataset and a fully variational ResNet-20 architecture to analyze six different aggregation strategies for Bayesian DL models. Additionally, we analyze the traditional federated averaging approach applied to an approximate Bayesian Monte Carlo dropout model as a lightweight alternative to more complex variational inference methods in FL. We show that aggregation strategy is a key hyperparameter in the design of a Bayesian FL system with downstream effects on accuracy, calibration, uncertainty quantification, training stability, and client compute requirements.