Private Regression via Data-Dependent Sufficient Statistic Perturbation

TMLR Paper4671 Authors

Abstract: 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.

Submission Length: Regular submission (no more than 12 pages of main content)

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Removed pycache binary files and __MACOSX folder for anonymization.

Assigned Action Editor: Joonas Jälkö

Submission Number: 4671