# FedPop: A Bayesian Approach for Personalised Federated Learning

arXiv: https://arxiv.org/abs/2206.03611 · HTML: https://mlsanity.com/paper/2206.03611/

## Key facts

- Cited by 35 papers in the map (data through 14 Oct 2026).
- Builds on 35 of its 74 references that are in the map.
- First posted on arXiv 7 Jun 2022.

## Builds on (most cited first, 30 of 35)

- [Communication-Efficient Learning of Deep Networks from Decentralized Data](https://mlsanity.com/paper/1602.05629/) (2016)
- [Advances and Open Problems in Federated Learning](https://mlsanity.com/paper/1912.04977/) (2019)
- [Federated Optimization in Heterogeneous Networks](https://mlsanity.com/paper/1812.06127/) (2018)
- [Federated Multi-Task Learning](https://mlsanity.com/paper/1705.10467/) (2017)
- [Ditto: Fair and Robust Federated Learning Through Personalization](https://mlsanity.com/paper/2012.04221/) (2020)
- [Federated Learning with Personalization Layers](https://mlsanity.com/paper/1912.00818/) (2019)
- [Exploiting Shared Representations for Personalized Federated Learning](https://mlsanity.com/paper/2102.07078/) (2021)
- [Towards Personalized Federated Learning](https://mlsanity.com/paper/2103.00710/) (2021)
- [Adaptive Personalized Federated Learning](https://mlsanity.com/paper/2003.13461/) (2020)
- [Think Locally, Act Globally: Federated Learning with Local and Global Representations](https://mlsanity.com/paper/2001.01523/) (2020)
- [Three Approaches for Personalization with Applications to Federated Learning](https://mlsanity.com/paper/2002.10619/) (2020)
- [A Field Guide to Federated Optimization](https://mlsanity.com/paper/2107.06917/) (2021)
- [Improving Federated Learning Personalization via Model Agnostic Meta Learning](https://mlsanity.com/paper/1909.12488/) (2019)
- [Federated learning with hierarchical clustering of local updates to improve training on non-IID data](https://mlsanity.com/paper/2004.11791/) (2020)
- [Federated Learning of a Mixture of Global and Local Models](https://mlsanity.com/paper/2002.05516/) (2020)
- [Theoretical guarantees for approximate sampling from smooth and log-concave densities](https://mlsanity.com/paper/1412.7392/) (2014)
- [Non-asymptotic convergence analysis for the Unadjusted Langevin Algorithm](https://mlsanity.com/paper/1507.05021/) (2015)
- [Bayesian Model-Agnostic Meta-Learning](https://mlsanity.com/paper/1806.03836/) (2018)
- [Adaptive Gradient-Based Meta-Learning Methods](https://mlsanity.com/paper/1906.02717/) (2019)
- [Recasting Gradient-Based Meta-Learning as Hierarchical Bayes](https://mlsanity.com/paper/1801.08930/) (2018)
- [FedBE: Making Bayesian Model Ensemble Applicable to Federated Learning](https://mlsanity.com/paper/2009.01974/) (2020)
- [Lower Bounds and Optimal Algorithms for Personalized Federated Learning](https://mlsanity.com/paper/2010.02372/) (2020)
- [Federated Learning with Partial Model Personalization](https://mlsanity.com/paper/2204.03809/) (2022)
- [Federated Reconstruction: Partially Local Federated Learning](https://mlsanity.com/paper/2102.03448/) (2021)
- [Variational Federated Multi-Task Learning](https://mlsanity.com/paper/1906.06268/) (2019)
- [Stochastic Distributed Learning with Gradient Quantization and Variance Reduction](https://mlsanity.com/paper/1904.05115/) (2019)
- [Bidirectional compression in heterogeneous settings for distributed or federated learning with partial participation: tight convergence guarantees](https://mlsanity.com/paper/2006.14591/) (2020)
- [Hierarchical Bayesian Bandits](https://mlsanity.com/paper/2111.06929/) (2021)
- [Personalized Federated Learning: A Unified Framework and Universal Optimization Techniques](https://mlsanity.com/paper/2102.09743/) (2021)
- [Partitioned Variational Inference: A unified framework encompassing federated and continual learning](https://mlsanity.com/paper/1811.11206/) (2018)

## Built on by (most cited first, 30 of 35)

- [Personalized Federated Learning under Mixture of Distributions](https://mlsanity.com/paper/2305.01068/) (2023)
- [From Risk to Uncertainty: Generating Predictive Uncertainty Measures via Bayesian Estimation](https://mlsanity.com/paper/2402.10727/) (2024)
- [One-Shot Federated Conformal Prediction](https://mlsanity.com/paper/2302.06322/) (2023)
- [Bayesian Federated Learning: A Survey](https://mlsanity.com/paper/2304.13267/) (2023)
- [Privacy Preserving Federated Learning in Medical Imaging with Uncertainty Estimation](https://mlsanity.com/paper/2406.12815/) (2024)
- [FedHB: Hierarchical Bayesian Federated Learning](https://mlsanity.com/paper/2305.04979/) (2023)
- [Dirichlet-based Uncertainty Quantification for Personalized Federated Learning with Improved Posterior Networks](https://mlsanity.com/paper/2312.11230/) (2023)
- [Federated Variational Inference Methods for Structured Latent Variable Models](https://mlsanity.com/paper/2302.03314/) (2023)
- [FedSI: Federated Subnetwork Inference for Efficient Uncertainty Quantification](https://mlsanity.com/paper/2404.15657/) (2024)
- [Marginal and training-conditional guarantees in one-shot federated conformal prediction](https://mlsanity.com/paper/2405.12567/) (2024)
- [Federated Automatic Latent Variable Selection in Multi-output Gaussian Processes](https://mlsanity.com/paper/2407.16935/) (2024)
- [Federated ADMM from Bayesian Duality](https://mlsanity.com/paper/2506.13150/) (2025)
- [Federated Variational Inference: Towards Improved Personalization and Generalization](https://mlsanity.com/paper/2305.13672/) (2023)
- [Bayesian Personalized Federated Learning with Shared and Personalized Uncertainty Representations](https://mlsanity.com/paper/2309.15499/) (2023)
- [Federated Learning with Nonvacuous Generalisation Bounds](https://mlsanity.com/paper/2310.11203/) (2023)
- [Scalable Vertical Federated Learning via Data Augmentation and Amortized Inference](https://mlsanity.com/paper/2405.04043/) (2024)
- [Future-Proofing Medical Imaging with Privacy-Preserving Federated Learning and Uncertainty Quantification: A Review](https://mlsanity.com/paper/2409.16340/) (2024)
- [Personalized Federated Learning via Amortized Bayesian Meta-Learning](https://mlsanity.com/paper/2307.02222/) (2023)
- [A Comprehensive View of Personalized Federated Learning on Heterogeneous Clinical Datasets](https://mlsanity.com/paper/2309.16825/) (2023)
- [PPFL: A Personalized Federated Learning Framework for Heterogeneous Population](https://mlsanity.com/paper/2310.14337/) (2023)
- [ADEPT: Hierarchical Bayes Approach to Personalized Federated Unsupervised Learning](https://mlsanity.com/paper/2402.12537/) (2024)
- [Trustworthy Personalized Bayesian Federated Learning via Posterior Fine-Tune](https://mlsanity.com/paper/2402.16911/) (2024)
- [Information-Geometric Barycenters for Bayesian Federated Learning](https://mlsanity.com/paper/2412.11646/) (2024)
- [Federated Generalised Variational Inference: A Robust Probabilistic Federated Learning Framework](https://mlsanity.com/paper/2502.00846/) (2025)
- [Towards Instance-wise Personalized Federated Learning via Semi-Implicit Bayesian Prompt Tuning](https://mlsanity.com/paper/2508.19621/) (2025)
- [Who to Trust? Aggregating Client Predictions in Federated Distillation](https://mlsanity.com/paper/2509.15147/) (2025)
- [Federated Learning via Meta-Variational Dropout](https://mlsanity.com/paper/2510.20225/) (2025)
- [Federated Learning for Non-factorizable Models using Deep Generative Prior Approximations](https://mlsanity.com/paper/2405.16055/) (2024)
- [Personalizing Low-Rank Bayesian Neural Networks Via Federated Learning](https://mlsanity.com/paper/2410.14390/) (2024)
- [Bayesian Federated Cause-of-Death Classification and Quantification Under Distribution Shift](https://mlsanity.com/paper/2505.02257/) (2025)

## Abstract (arXiv)

Personalised federated learning (FL) aims at collaboratively learning a machine learning model taylored for each client. Albeit promising advances have been made in this direction, most of existing approaches works do not allow for uncertainty quantification which is crucial in many applications. In addition, personalisation in the cross-device setting still involves important issues, especially for new clients or those having small number of observations. This paper aims at filling these gaps. To this end, we propose a novel methodology coined FedPop by recasting personalised FL into the population modeling paradigm where clients' models involve fixed common population parameters and random effects, aiming at explaining data heterogeneity. To derive convergence guarantees for our scheme, we introduce a new class of federated stochastic optimisation algorithms which relies on Markov chain Monte Carlo methods. Compared to existing personalised FL methods, the proposed methodology has important benefits: it is robust to client drift, practical for inference on new clients, and above all, enables uncertainty quantification under mild computational and memory overheads. We provide non-asymptotic convergence guarantees for the proposed algorithms and illustrate their performances on various personalised federated learning tasks.