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This arXiv paper treats differentially private release of Gaussian mixture model parameters as a constrained optimization problem, using KL divergence to balance privacy-budget allocation against model fidelity. It is a theory-heavy contribution to privacy-preserving statistical learning rather than a deployed system, so its practical value depends on whether the privacy-utility tradeoffs hold up on real workloads. Readers working on private model release should note that it addresses mixture weights, means, and covariances jointly, not just one parameter at a time.
Differentially Private Distribution Release of Gaussian Mixture Models via KL-Divergence Minimization
arXiv:2506.03467v4 Announce Type: replace-cross Abstract: 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. We develop a KL-divergence-driven optimization framework for differentially private GMM release that jointly designs privacy-budget allocation and parameter perturbations. 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 fitted non-private models, subject to a given $(\epsilon, \delta)$-DP constraint. Extensive experiments on both synthetic and real-world datasets demonstrate that our approach achieves strong privacy guarantees while maintaining high utility.
Abstract: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. We develop a KL-divergence-driven optimization framework for differentially private GMM release that jointly designs privacy-budget allocation and parameter perturbations. 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 fitted non-private models, subject to a given $(\epsilon, \delta)$-DP constraint. Extensive experiments on both synthetic and real-world datasets demonstrate that our approach achieves strong privacy guarantees while maintaining high utility.
Information Theory (cs.IT); Cryptography and Security (cs.CR); Machine Learning (cs.LG); Signal Processing (eess.SP); Methodology (stat.ME)
arXiv:2506.03467 [cs.IT]
(or arXiv:2506.03467v4 [cs.IT] for this version)
https://doi.org/10.48550/arXiv.2506.03467 Focus to learn more arXiv-issued DOI via DataCite
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