# Robust Federated Personalised Mean Estimation for the Gaussian Mixture Model

arXiv: https://arxiv.org/abs/2504.19955 · HTML: https://mlsanity.com/paper/2504.19955/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 18 references that are in the map.
- First posted on arXiv 28 Apr 2025.

## Builds on (most cited first, 10 of 10)

- [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)
- [Robust Estimators in High Dimensions without the Computational Intractability](https://mlsanity.com/paper/1604.06443/) (2016)
- [Agnostic Estimation of Mean and Covariance](https://mlsanity.com/paper/1604.06968/) (2016)
- [Learning from Untrusted Data](https://mlsanity.com/paper/1611.02315/) (2016)
- [Robust Federated Learning in a Heterogeneous Environment](https://mlsanity.com/paper/1906.06629/) (2019)
- [Byzantine-Resilient High-Dimensional Federated Learning](https://mlsanity.com/paper/2006.13041/) (2020)
- [Learning Discrete Distributions from Untrusted Batches](https://mlsanity.com/paper/1711.08113/) (2017)
- [Optimal Robust Learning of Discrete Distributions from Batches](https://mlsanity.com/paper/1911.08532/) (2019)
- [Learning Structured Distributions From Untrusted Batches: Faster and Simpler](https://mlsanity.com/paper/2002.10435/) (2020)

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

- [Federated Soft Clustering via Generalized Total Variation Minimization](https://mlsanity.com/paper/2609.19202/) (2026)

## Abstract (arXiv)

Federated learning with heterogeneous data and personalization has received significant recent attention. Separately, robustness to corrupted data in the context of federated learning has also been studied. In this paper we explore combining personalization for heterogeneous data with robustness, where a constant fraction of the clients are corrupted. Motivated by this broad problem, we formulate a simple instantiation which captures some of its difficulty. We focus on the specific problem of personalized mean estimation where the data is drawn from a Gaussian mixture model. We give an algorithm whose error depends almost linearly on the ratio of corrupted to uncorrupted samples, and show a lower bound with the same behavior, albeit with a gap of a constant factor.