# Federated Generalised Variational Inference: A Robust Probabilistic Federated Learning Framework

arXiv: https://arxiv.org/abs/2502.00846 · HTML: https://mlsanity.com/paper/2502.00846/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 53 of its 84 references that are in the map.
- First posted on arXiv 2 Feb 2025.

## Builds on (most cited first, 30 of 53)

- [Communication-Efficient Learning of Deep Networks from Decentralized Data](https://mlsanity.com/paper/1602.05629/) (2016)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Advances and Open Problems in Federated Learning](https://mlsanity.com/paper/1912.04977/) (2019)
- [Variational Inference: A Review for Statisticians](https://mlsanity.com/paper/1601.00670/) (2016)
- [Adaptive Federated Optimization](https://mlsanity.com/paper/2003.00295/) (2020)
- [Deep Leakage from Gradients](https://mlsanity.com/paper/1906.08935/) (2019)
- [Generalized Cross Entropy Loss for Training Deep Neural Networks with Noisy Labels](https://mlsanity.com/paper/1805.07836/) (2018)
- [Bayesian Nonparametric Federated Learning of Neural Networks](https://mlsanity.com/paper/1905.12022/) (2019)
- [A General Framework for Updating Belief Distributions](https://mlsanity.com/paper/1306.6430/) (2013)
- [Expectation Propagation for approximate Bayesian inference](https://mlsanity.com/paper/1301.2294/) (2013)
- [On the properties of variational approximations of Gibbs posteriors](https://mlsanity.com/paper/1506.04091/) (2015)
- [Federated Learning via Posterior Averaging: A New Perspective and Practical Algorithms](https://mlsanity.com/paper/2010.05273/) (2020)
- [An elementary introduction to information geometry](https://mlsanity.com/paper/1808.08271/) (2018)
- [Personalized Federated Learning with Gaussian Processes](https://mlsanity.com/paper/2106.15482/) (2021)
- [From Local SGD to Local Fixed-Point Methods for Federated Learning](https://mlsanity.com/paper/2004.01442/) (2020)
- [Variational Federated Multi-Task Learning](https://mlsanity.com/paper/1906.06268/) (2019)
- [Personalized Federated Learning via Variational Bayesian Inference](https://mlsanity.com/paper/2206.07977/) (2022)
- [Robust Generalised Bayesian Inference for Intractable Likelihoods](https://mlsanity.com/paper/2104.07359/) (2021)
- [The Fundamental Price of Secure Aggregation in Differentially Private Federated Learning](https://mlsanity.com/paper/2203.03761/) (2022)
- [Federated Generalized Bayesian Learning via Distributed Stein Variational Gradient Descent](https://mlsanity.com/paper/2009.06419/) (2020)
- [FedPop: A Bayesian Approach for Personalised Federated Learning](https://mlsanity.com/paper/2206.03611/) (2022)
- [Partitioned Variational Inference: A unified framework encompassing federated and continual learning](https://mlsanity.com/paper/1811.11206/) (2018)
- [Gradient Masked Averaging for Federated Learning](https://mlsanity.com/paper/2201.11986/) (2022)
- [Doubly Robust Bayesian Inference for Non-Stationary Streaming Data with β-Divergences](https://mlsanity.com/paper/1806.02261/) (2018)
- [Non-exponentially weighted aggregation: regret bounds for unbounded loss functions](https://mlsanity.com/paper/2009.03017/) (2020)
- [Distributed Bayesian Learning with Stochastic Natural-gradient Expectation Propagation and the Posterior Server](https://mlsanity.com/paper/1512.09327/) (2015)
- [A General Theory for Federated Optimization with Asynchronous and Heterogeneous Clients Updates](https://mlsanity.com/paper/2206.10189/) (2022)
- [Federated Learning as Variational Inference: A Scalable Expectation Propagation Approach](https://mlsanity.com/paper/2302.04228/) (2023)
- [Federated Stochastic Gradient Langevin Dynamics](https://mlsanity.com/paper/2004.11231/) (2020)
- [Robust and Scalable Bayesian Online Changepoint Detection](https://mlsanity.com/paper/2302.04759/) (2023)

## Built on by (most cited first, 1 of 1)

- [Rates of Convergence of Generalised Variational Inference Posteriors under Prior Misspecification](https://mlsanity.com/paper/2510.03109/) (2025)

## Abstract (arXiv)

We introduce FedGVI, a probabilistic Federated Learning (FL) framework that is robust to both prior and likelihood misspecification. FedGVI addresses limitations in both frequentist and Bayesian FL by providing unbiased predictions under model misspecification, with calibrated uncertainty quantification. Our approach generalises previous FL approaches, specifically Partitioned Variational Inference (Ashman et al., 2022), by allowing robust and conjugate updates, decreasing computational complexity at the clients. We offer theoretical analysis in terms of fixed-point convergence, optimality of the cavity distribution, and provable robustness to likelihood misspecification. Further, we empirically demonstrate the effectiveness of FedGVI in terms of improved robustness and predictive performance on multiple synthetic and real world classification data sets.