Private Regression via Data-Dependent Sufficient Statistic Perturbation

Cecilia Ferrando, Daniel Sheldon

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)

Previous TMLR Submission Url: https://openreview.net/forum?id=UAuexlwld1&nesting=2&sort=date-desc

Changes Since Last Submission: Removed pycache binary files and __MACOSX folder for anonymization.

Code: https://github.com/ceciliaferrando/DD-SSP

Assigned Action Editor: ~Joonas_Jälkö1

Submission Number: 4671