Private Regression via Data-Dependent Sufficient Statistic Perturbation

• URL: http://arxiv.org/abs/2405.15002v1
• Date: Thu, 23 May 2024 19:09:50 GMT
• Title: Private Regression via Data-Dependent Sufficient Statistic Perturbation
• Authors: Cecilia Ferrando, Daniel Sheldon,
• Abstract summary: We introduce data-dependent SSP for linear regression based on post-processing privately released marginals. We extend this result to logistic regression by developing an approximate objective that can be expressed in terms of sufficient statistics.
• Score: 9.58219088613742
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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