Universal Exact Compression of Differentially Private Mechanisms
<|reference_start|>Universal Exact Compression of Differentially Private Mechanisms: To reduce the communication cost of differential privacy mechanisms, we introduce a novel construction, called Poisson private representation (PPR), designed to compress and simulate any local randomizer while ensuring local differential privacy. Unlike previous simulation-based local differential privacy mechanisms, PPR exactly preserves the joint distribution of the data and the output of the original local randomizer. Hence, the PPR-compressed privacy mechanism retains all desirable statistical properties of the original privacy mechanism such as unbiasedness and Gaussianity. Moreover, PPR achieves a compression size within a logarithmic gap from the theoretical lower bound. Using the PPR, we give a new order-wise trade-off between communication, accuracy, central and local differential privacy for distributed mean estimation. Experiment results on distributed mean estimation show that PPR consistently gives a better trade-off between communication, accuracy and central differential privacy compared to the coordinate subsampled Gaussian mechanism, while also providing local differential privacy.<|reference_end|>
@article{liu2024universal,
    title={Universal Exact Compression of Differentially Private Mechanisms},
    author={Yanxiao Liu and Wei-Ning Chen and Ayfer "Ozg"ur and Cheuk Ting Li},
    journal={arXiv preprint arXiv:2405.20782},
    year={2024},
    archivePrefix={arXiv},
    eprint={2405.20782},
    primaryClass={cs.CR cs.IT math.IT stat.ML}
}