Publications
その他 (国際) Optimal Variance and Covariance Estimation under Differential Privacy in the Add-Remove Model and Beyond
Shokichi Takakura, Seng Pei Liew, Satoshi Hasegawa
arxiv
2025.9.8
Estimation of variance and covariance is a fundamental task in statistics and machine learning. In this paper, we study the problem of estimating variance and covariance under differential privacy in the add-remove model. Although covariance estimation in the swap model has been well studied in the literature, the problem in the add-remove model is less explored and more challenging since the size of the dataset should be kept private. To deal with this issue, we develop a novel mechanism called Bezier mechanism and apply it to variance and covariance estimation. We prove that our proposed mechanism achieves the min-max optimal error rate for variance and covariance estimation in the high privacy regime. The numerical experiments demonstrate that our proposed mechanism reduces the error significantly compared to naive approaches.
Paper :
Optimal Variance and Covariance Estimation under Differential Privacy in the Add-Remove Model and Beyond
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