2025/06/04 by Hang Liu, Liu, Hang, Anna Scaglione +3 · 1 citation
Computer Science · #Bayesian Methods and Mixture Models #Cryptography and Security (cs.CR) #FOS: Computer and information sciences #FOS: Electrical engineering #Information Theory (cs.IT) #Machine Learning (cs.LG) #Methodology (stat.ME) #Privacy-Preserving Technologies in Data #Signal Processing (eess.SP) #Stochastic Gradient Optimization Techniques #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.2506.03467
openalex publication_date 2025/06/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/31
Gaussian Mixture Models (GMMs) are widely used statistical models for representing multi-modal data distributions, with numerous applications in data mining, pattern recognition, data simulation, and machine learning. However, recent research has shown that releasing GMM parameters poses significant privacy risks, potentially exposing sensitive information about the underlying data. In this paper, we address the challenge of releasing GMM parameters while ensuring differential privacy (DP) guarantees. Specifically, we focus on the privacy protection of mixture weights, component means, and covariance matrices. We propose to use Kullback-Leibler (KL) divergence as a utility metric to assess the accuracy of the released GMM, as it captures the joint impact of noise perturbation on all the model parameters. To achieve privacy, we introduce a DP mechanism that adds carefully calibrated random perturbations to the GMM parameters. Through theoretical analysis, we quantify the effects of privacy budget allocation and perturbation statistics on the DP guarantee, and derive a tractable expression for evaluating KL divergence. We formulate and solve an optimization problem to minimize the KL divergence between the released and original models, subject to a given (ε, δ)-DP constraint. Extensive experiments on both synthetic and real-world datasets demonstrate that our approach achieves strong privacy guarantees while maintaining high utility.