# A Federated Generalized Expectation-Maximization Algorithm for Mixture Models with an Unknown Number of Components

arXiv: https://arxiv.org/abs/2601.21160 · HTML: https://mlsanity.com/paper/2601.21160/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 42 references that are in the map.
- First posted on arXiv 29 Jan 2026.

## Builds on (most cited first, 16 of 16)

- [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)
- [Federated Optimization in Heterogeneous Networks](https://mlsanity.com/paper/1812.06127/) (2018)
- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [Tackling the Objective Inconsistency Problem in Heterogeneous Federated Optimization](https://mlsanity.com/paper/2007.07481/) (2020)
- [Federated Optimization: Distributed Machine Learning for On-Device Intelligence](https://mlsanity.com/paper/1610.02527/) (2016)
- [Federated Learning with Personalization Layers](https://mlsanity.com/paper/1912.00818/) (2019)
- [Federated Multi-Task Learning under a Mixture of Distributions](https://mlsanity.com/paper/2108.10252/) (2021)
- [Statistical guarantees for the EM algorithm: From population to sample-based analysis](https://mlsanity.com/paper/1408.2156/) (2014)
- [Heterogeneity for the Win: One-Shot Federated Clustering](https://mlsanity.com/paper/2103.00697/) (2021)
- [DeepDPM: Deep Clustering With an Unknown Number of Clusters](https://mlsanity.com/paper/2203.14309/) (2022)
- [Personalized Federated Learning under Mixture of Distributions](https://mlsanity.com/paper/2305.01068/) (2023)
- [Towards Federated Clustering: A Federated Fuzzy c-Means Algorithm (FFCM)](https://mlsanity.com/paper/2201.07316/) (2022)
- [Asynchronous Federated Clustering with Unknown Number of Clusters](https://mlsanity.com/paper/2412.20341/) (2024)
- [Making Better Use of Unlabelled Data in Bayesian Active Learning](https://mlsanity.com/paper/2404.17249/) (2024)
- [Federated K-Means Clustering via Dual Decomposition-based Distributed Optimization](https://mlsanity.com/paper/2307.13267/) (2023)

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

- [Federated Clustering with Unknown Local and Global Cluster Cardinalities](https://mlsanity.com/paper/2609.36762/) (2026)

## Abstract (arXiv)

We study the problem of federated clustering when the total number of clusters K across clients is unknown, and the clients have heterogeneous but potentially overlapping cluster sets in their local data. To that end, we develop FedGEM: a federated generalized expectation-maximization algorithm for the training of mixture models with an unknown number of components. Our proposed algorithm relies on each of the clients performing EM steps locally, and constructing an uncertainty set around the maximizer associated with each local component. The central server utilizes the uncertainty sets to learn potential cluster overlaps between clients, and infer the global number of clusters via closed-form computations. We perform a thorough theoretical study of our algorithm, presenting probabilistic convergence guarantees under common assumptions. Subsequently, we study the specific setting of isotropic GMMs, providing tractable, low-complexity computations to be performed by each client during each iteration of the algorithm, as well as rigorously verifying assumptions required for algorithm convergence. We perform various numerical experiments, where we empirically demonstrate that our proposed method achieves comparable performance to centralized EM, and that it outperforms various existing federated clustering methods.