Personalized Federated Learning under Mixture of Distributions

TL;DR

This paper introduces FedGMM, a federated learning method that models diverse client data distributions with Gaussian mixtures, improving personalization, adaptability, and uncertainty quantification in federated settings.

Contribution

The paper proposes FedGMM, a novel federated learning approach using Gaussian mixture models and a federated EM algorithm to better handle distribution heterogeneity and unseen data.

Findings

FedGMM outperforms existing PFL methods on synthetic and benchmark datasets.

FedGMM effectively adapts to new clients with minimal overhead.

FedGMM enables uncertainty quantification in federated models.

Abstract

The recent trend towards Personalized Federated Learning (PFL) has garnered significant attention as it allows for the training of models that are tailored to each client while maintaining data privacy. However, current PFL techniques primarily focus on modeling the conditional distribution heterogeneity (i.e. concept shift), which can result in suboptimal performance when the distribution of input data across clients diverges (i.e. covariate shift). Additionally, these techniques often lack the ability to adapt to unseen data, further limiting their effectiveness in real-world scenarios. To address these limitations, we propose a novel approach, FedGMM, which utilizes Gaussian mixture models (GMM) to effectively fit the input data distributions across diverse clients. The model parameters are estimated by maximum likelihood estimation utilizing a federated Expectation-Maximization algorithm, which is solved in closed form and does not assume gradient similarity. Furthermore, FedGMM possesses an additional advantage of adapting to new clients with minimal overhead, and it also enables uncertainty quantification. Empirical evaluations on synthetic and benchmark datasets demonstrate the superior performance of our method in both PFL classification and novel sample detection.