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Simulation-based, Finite-sample Inference for Privatized Data

J Awan, Z Wang - arXiv preprint arXiv:2303.05328, 2023 - arxiv.org
Mathematics paper math.ST Suggest

… In Section 3.2, we show that, using simulation-based inference, we can construct valid confidence sets with guaranteed coverage, even accounting for the randomness in the simulation. …

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BibTeX

@article{2303.05328v7,
Author        = {Jordan Awan and Zhanyu Wang},
Title         = {Simulation-based, Finite-sample Inference for Privatized Data},
Eprint        = {2303.05328v7},
ArchivePrefix = {arXiv},
PrimaryClass  = {math.ST},
Abstract      = {Privacy protection methods, such as differentially private mechanisms, introduce noise into resulting statistics which often produces complex and intractable sampling distributions. In this paper, we propose a simulation-based "repro sample" approach to produce statistically valid confidence intervals and hypothesis tests, which builds on the work of Xie and Wang (2022). We show that this methodology is applicable to a wide variety of private inference problems, appropriately accounts for biases introduced by privacy mechanisms (such as by clamping), and improves over other state-of-the-art inference methods such as the parametric bootstrap in terms of the coverage and type I error of the private inference. We also develop significant improvements and extensions for the repro sample methodology for general models (not necessarily related to privacy), including 1) modifying the procedure to ensure guaranteed coverage and type I errors, even accounting for Monte Carlo error, and 2) proposing efficient numerical algorithms to implement the confidence intervals and $p$-values.},
Year          = {2023},
Month         = {Mar},
Url           = {http://arxiv.org/abs/2303.05328v7},
File          = {2303.05328v7.pdf}
}

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