2026-07-21T11:24:03Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:23150 2025-10-02T12:35:21Z ddc:004 open_access

The Correlated Gaussian Sparse Histogram Mechanism Lebeda, Christian Janos Retschmeier, Lukas differential privacy correlated noise sparse gaussian histograms We consider the problem of releasing a sparse histogram under (ε, δ)-differential privacy. The stability histogram independently adds noise from a Laplace or Gaussian distribution to the non-zero entries and removes those noisy counts below a threshold. Thereby, the introduction of new non-zero values between neighboring histograms is only revealed with probability at most δ, and typically, the value of the threshold dominates the error of the mechanism. We consider the variant of the stability histogram with Gaussian noise. Recent works ([Joseph and Yu, COLT '24] and [Lebeda, SOSA '25]) reduced the error for private histograms using correlated Gaussian noise. However, these techniques can not be directly applied in the very sparse setting. Instead, we adopt Lebeda’s technique and show that adding correlated noise to the non-zero counts only allows us to reduce the magnitude of noise when we have a sparsity bound. This, in turn, allows us to use a lower threshold by up to a factor of 1/2 compared to the non-correlated noise mechanism. We then extend our mechanism to a setting without a known bound on sparsity. Additionally, we show that correlated noise can give a similar improvement for the more practical discrete Gaussian mechanism. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Christian Janos Lebeda and Lukas Retschmeier 2025 Is Part Of LIPIcs, Volume 329, 6th Symposium on Foundations of Responsible Computing (FORC 2025) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.FORC.2025.23 urn:nbn:de:0030-drops-231503 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FORC.2025.23 eng https://creativecommons.org/licenses/by/4.0/legalcode