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Differentially Private Sparse Covariance Matrix Estimation under Lower-Bounded Moment Assumption

Author

Listed:
  • Huimin Li

    (Department of Mathematics, Beijing University of Technology, Beijing 100124, China)

  • Jinru Wang

    (Department of Mathematics, Beijing University of Technology, Beijing 100124, China)

Abstract

This paper investigates the problem of sparse covariance matrix estimation while the sampling set contains sensitive information, and both the differentially private algorithm and locally differentially private algorithm are adopted to preserve privacy. It is worth noting that the requirement of the distribution assumption in our work is only the existing bounded 4 + ε ( ε > 0 ) moment. Meanwhile, we reduce the error bounds by modifying the threshold of the existing differentially private algorithms. Finally, the numerical simulations and results from a real data application are presented to support our theoretical claims.

Suggested Citation

  • Huimin Li & Jinru Wang, 2023. "Differentially Private Sparse Covariance Matrix Estimation under Lower-Bounded Moment Assumption," Mathematics, MDPI, vol. 11(17), pages 1-16, August.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:17:p:3670-:d:1225205
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    References listed on IDEAS

    as
    1. Sanjay Chaudhuri & Mathias Drton & Thomas S. Richardson, 2007. "Estimation of a covariance matrix with zeros," Biometrika, Biometrika Trust, vol. 94(1), pages 199-216.
    2. Cai, Tony & Liu, Weidong, 2011. "Adaptive Thresholding for Sparse Covariance Matrix Estimation," Journal of the American Statistical Association, American Statistical Association, vol. 106(494), pages 672-684.
    Full references (including those not matched with items on IDEAS)

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