High-Dimensional Differentially-Private EM Algorithm: Methods and Near-Optimal Statistical Guarantees
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Abstract (arXiv)
In this paper, we develop a general framework to design differentially private expectation-maximization (EM) algorithms in high-dimensional latent variable models, based on the noisy iterative hard-thresholding. We derive the statistical guarantees of the proposed framework and apply it to three specific models: Gaussian mixture, mixture of regression, and regression with missing covariates. In each model, we establish the near-optimal rate of convergence with differential privacy constraints, and show the proposed algorithm is minimax rate optimal up to logarithm factors. The technical tools developed for the high-dimensional setting are then extended to the classic low-dimensional latent variable models, and we propose a near rate-optimal EM algorithm with differential privacy guarantees in this setting. Simulation studies and real data analysis are conducted to support our results.
Key facts. Cited by 2 papers in the map (data through 7 Oct 2026). Builds on 27 of its 60 references that are in the map. First posted on arXiv 1 Apr 2021.
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27 of 60 references.
References · 27
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- 2014Statistical guarantees for the EM algorithm: From population to sample-based analysiscited by 131
- 2014Differentially Private Empirical Risk Minimization: Efficient Algorithms and Tight Error Boundscited by 104
- 2018Privately Learning High-Dimensional Distributionscited by 103
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- 2020Private Mean Estimation of Heavy-Tailed Distributionscited by 73
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- 2015Between Pure and Approximate Differential Privacycited by 55
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- 2016Ten Steps of EM Suffice for Mixtures of Two Gaussianscited by 40
15 more
- 2018Singularity, Misspecification, and the Convergence Rate of EMcited by 38
- 2016Global analysis of Expectation Maximization for mixtures of two Gaussianscited by 31
- 2019Differentially Private Algorithms for Learning Mixtures of Separated Gaussianscited by 27
- 2020Evading Curse of Dimensionality in Unconstrained Private GLMs via Private Gradient Descentcited by 27
- 2018Global Convergence of EM Algorithm for Mixtures of Two Component Linear Regressioncited by 25
- 2020On the Minimax Optimality of the EM Algorithm for Learning Two-Component Mixed Linear Regressioncited by 24
- 2015Regularized EM Algorithms: A Unified Framework and Statistical Guaranteescited by 19
- 2019Privacy-preserving parametric inference: a case for robust statisticscited by 17
- 2020The Cost of Privacy in Generalized Linear Models: Algorithms and Minimax Lower Boundscited by 15
- 2018Differentially Private False Discovery Rate Controlcited by 14
- 2020Guidelines for Implementing and Auditing Differentially Private Systemscited by 10
- 2017The Price of Selection in Differential Privacycited by 7
- 2020Estimation, Confidence Intervals, and Large-Scale Hypotheses Testing for High-Dimensional Mixed Linear Regressioncited by 5
- 2019Differentially Private Inference for Binomial Datacited by 4
- 2013High-dimensional cluster analysis with the Masked EM Algorithmcited by 3
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