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Differentially private histogram with valid statistics

Author

Listed:
  • Cao, Zilong
  • Wu, Shisong
  • Li, Xuanang
  • Zhang, Hai

Abstract

Differentially private histograms (DP-Histograms) are integral to data publication and privacy preservation efforts. However, conventional DP-Histograms often fail to preserve valid statistical information and the essential characteristics of the original data. This paper shows the invalidity of variance is the inherent shortcomings in general DP-Histograms, and introduces a novel algorithm called the Differentially Private Histogram with Valid Statistics (VSDPH) to overcome the problem. The VSDPH, grounded in linear programming and bounded Lipschitz distance, efficiently generates DP histograms while preserving the valid statistics of the original data. Our theoretical analysis demonstrates that histograms produced by VSDPH maintain asymptotically valid variance, and we establish an upper bound based on the 1-Wasserstein distance. Through experiments, we validate that VSDPH can accurately hold the statistical characteristics of the original data. This capability brings the resulting histograms closer to the originals.

Suggested Citation

  • Cao, Zilong & Wu, Shisong & Li, Xuanang & Zhang, Hai, 2025. "Differentially private histogram with valid statistics," Statistics & Probability Letters, Elsevier, vol. 219(C).
    • Handle: RePEc:eee:stapro:v:219:y:2025:i:c:s0167715224003237
    DOI: 10.1016/j.spl.2024.110354
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    References listed on IDEAS

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    1. Wasserman, Larry & Zhou, Shuheng, 2010. "A Statistical Framework for Differential Privacy," Journal of the American Statistical Association, American Statistical Association, vol. 105(489), pages 375-389.
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