# Privacy-Preserving Distributed Expectation Maximization for Gaussian Mixture Model using Subspace Perturbation

arXiv: https://arxiv.org/abs/2209.07833 · HTML: https://mlsanity.com/paper/2209.07833/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 31 references that are in the map.
- First posted on arXiv 16 Sep 2022.

## Builds on (most cited first, 7 of 7)

- [Communication-Efficient Learning of Deep Networks from Decentralized Data](https://mlsanity.com/paper/1602.05629/) (2016)
- [Deep Learning with Differential Privacy](https://mlsanity.com/paper/1607.00133/) (2016)
- [Deep Models Under the GAN: Information Leakage from Collaborative Deep Learning](https://mlsanity.com/paper/1702.07464/) (2017)
- [Privacy Preserving Machine Learning: Threats and Solutions](https://mlsanity.com/paper/1804.11238/) (2018)
- [Distributed Optimization Using the Primal-Dual Method of Multipliers](https://mlsanity.com/paper/1702.00841/) (2017)
- [Privacy-Preserving Distributed Optimization via Subspace Perturbation: A General Framework](https://mlsanity.com/paper/2004.13999/) (2020)
- [Privacy-Preserving Distributed Processing: Metrics, Bounds, and Algorithms](https://mlsanity.com/paper/2009.01098/) (2020)

## Built on by (most cited first, 2 of 2)

- [From Centralized to Decentralized Federated Learning: Theoretical Insights, Privacy Preservation, and Robustness Challenges](https://mlsanity.com/paper/2503.07505/) (2025)
- [Improving the Utility of Differentially Private Clustering through Dynamical Processing](https://mlsanity.com/paper/2304.13886/) (2023)

## Abstract (arXiv)

Privacy has become a major concern in machine learning. In fact, the federated learning is motivated by the privacy concern as it does not allow to transmit the private data but only intermediate updates. However, federated learning does not always guarantee privacy-preservation as the intermediate updates may also reveal sensitive information. In this paper, we give an explicit information-theoretical analysis of a federated expectation maximization algorithm for Gaussian mixture model and prove that the intermediate updates can cause severe privacy leakage. To address the privacy issue, we propose a fully decentralized privacy-preserving solution, which is able to securely compute the updates in each maximization step. Additionally, we consider two different types of security attacks: the honest-but-curious and eavesdropping adversary models. Numerical validation shows that the proposed approach has superior performance compared to the existing approach in terms of both the accuracy and privacy level.