Private Regression via Data-Dependent Sufficient Statistic Perturbation
<|reference_start|>Private Regression via Data-Dependent Sufficient Statistic Perturbation: Sufficient statistic perturbation (SSP) is a widely used method for differentially private linear regression. SSP adopts a data-independent approach where privacy noise from a simple distribution is added to sufficient statistics. However, sufficient statistics can often be expressed as linear queries and better approximated by data-dependent mechanisms. In this paper we introduce data-dependent SSP for linear regression based on post-processing privately released marginals, and find that it outperforms state-of-the-art data-independent SSP. We extend this result to logistic regression by developing an approximate objective that can be expressed in terms of sufficient statistics, resulting in a novel and highly competitive SSP approach for logistic regression. We also make a connection to synthetic data for machine learning: for models with sufficient statistics, training on synthetic data corresponds to data-dependent SSP, with the overall utility determined by how well the mechanism answers these linear queries.<|reference_end|>
@article{ferrando2024private,
    title={Private Regression via Data-Dependent Sufficient Statistic Perturbation},
    author={Cecilia Ferrando, Daniel Sheldon},
    journal={arXiv preprint arXiv:2405.15002},
    year={2024},
    archivePrefix={arXiv},
    eprint={2405.15002},
    primaryClass={cs.LG stat.ML}
}