Differentially Private (Gradient) Expectation Maximization Algorithm with Statistical Guarantees
This addresses privacy concerns for sensitive data in statistical estimation, offering a novel solution with theoretical backing, though it builds incrementally on existing DP methods.
The authors tackled the problem of preserving privacy in (Gradient) Expectation Maximization algorithms by proposing the first differentially private version with finite sample statistical guarantees, achieving near-optimal estimation error for Gaussian Mixture Models and providing first guarantees for Mixture of Regressions and Linear Regression with Missing Covariates.
(Gradient) Expectation Maximization (EM) is a widely used algorithm for estimating the maximum likelihood of mixture models or incomplete data problems. A major challenge facing this popular technique is how to effectively preserve the privacy of sensitive data. Previous research on this problem has already lead to the discovery of some Differentially Private (DP) algorithms for (Gradient) EM. However, unlike in the non-private case, existing techniques are not yet able to provide finite sample statistical guarantees. To address this issue, we propose in this paper the first DP version of (Gradient) EM algorithm with statistical guarantees. Moreover, we apply our general framework to three canonical models: Gaussian Mixture Model (GMM), Mixture of Regressions Model (MRM) and Linear Regression with Missing Covariates (RMC). Specifically, for GMM in the DP model, our estimation error is near optimal in some cases. For the other two models, we provide the first finite sample statistical guarantees. Our theory is supported by thorough numerical experiments.