# Bayesian Federated Inference for estimating Statistical Models based on Non-shared Multicenter Data sets

arXiv: https://arxiv.org/abs/2302.07677 · HTML: https://mlsanity.com/paper/2302.07677/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 20 references that are in the map.
- First posted on arXiv 15 Feb 2023.

## Builds on (most cited first, 13 of 13)

- [Communication-Efficient Learning of Deep Networks from Decentralized Data](https://mlsanity.com/paper/1602.05629/) (2016)
- [Federated Optimization in Heterogeneous Networks](https://mlsanity.com/paper/1812.06127/) (2018)
- [The Future of Digital Health with Federated Learning](https://mlsanity.com/paper/2003.08119/) (2020)
- [A Simple Baseline for Bayesian Uncertainty in Deep Learning](https://mlsanity.com/paper/1902.02476/) (2019)
- [Data-Free Knowledge Distillation for Heterogeneous Federated Learning](https://mlsanity.com/paper/2105.10056/) (2021)
- [What Are Bayesian Neural Network Posteriors Really Like?](https://mlsanity.com/paper/2104.14421/) (2021)
- [Advances in Variational Inference](https://mlsanity.com/paper/1711.05597/) (2017)
- [Cyclical Stochastic Gradient MCMC for Bayesian Deep Learning](https://mlsanity.com/paper/1902.03932/) (2019)
- [FedBE: Making Bayesian Model Ensemble Applicable to Federated Learning](https://mlsanity.com/paper/2009.01974/) (2020)
- [Federated Learning via Posterior Averaging: A New Perspective and Practical Algorithms](https://mlsanity.com/paper/2010.05273/) (2020)
- [Federated Learning: A Signal Processing Perspective](https://mlsanity.com/paper/2103.17150/) (2021)
- [A Bayesian Federated Learning Framework with Online Laplace Approximation](https://mlsanity.com/paper/2102.01936/) (2021)
- [The unified maximum a posteriori (MAP) framework for neuronal system identification](https://mlsanity.com/paper/1811.01043/) (2018)

## Built on by (most cited first, 5 of 5)

- [Bayesian Federated Inference for Survival Models](https://mlsanity.com/paper/2404.17464/) (2024)
- [Federated Generalised Variational Inference: A Robust Probabilistic Federated Learning Framework](https://mlsanity.com/paper/2502.00846/) (2025)
- [Bayesian Federated Inference for regression models based on non-shared multicenter data sets from heterogeneous populations](https://mlsanity.com/paper/2402.02898/) (2024)
- [Federated Rule Ensemble Method in Medical Data](https://mlsanity.com/paper/2604.17956/) (2026)
- [An Accurate and Single-Communication Federated Inference Algorithm](https://mlsanity.com/paper/2608.27063/) (2026)

## Abstract (arXiv)

Identifying predictive factors for an outcome of interest via a multivariable analysis is often difficult when the data set is small. Combining data from different medical centers into a single (larger) database would alleviate this problem, but is in practice challenging due to regulatory and logistic problems. Federated Learning (FL) is a machine learning approach that aims to construct from local inferences in separate data centers what would have been inferred had the data sets been merged. It seeks to harvest the statistical power of larger data sets without actually creating them. The FL strategy is not always efficient and precise. Therefore, in this paper we refine and implement an alternative Bayesian Federated Inference (BFI) framework for multicenter data with the same aim as FL. The BFI framework is designed to cope with small data sets by inferring locally not only the optimal parameter values, but also additional features of the posterior parameter distribution, capturing information beyond what is used in FL. BFI has the additional benefit that a single inference cycle across the centers is sufficient, whereas FL needs multiple cycles. We quantify the performance of the proposed methodology on simulated and real life data.