2024/05/23 by Cecilia Ferrando, Daniel Sheldon, Ferrando, Cecilia +1 · 1 citation
Economics, Econometrics and Finance · Mathematics · #Census and Population Estimation #Economic and Environmental Valuation #FOS: Computer and information sciences #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Statistical Methods and Bayesian Inference
paper · pdf · doi:10.48550/arxiv.2405.15002
openalex publication_date 2024/05/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.