Post-Processing Large-Scale Differentially Private Data with Known Constraints

• Activity Number: 287 - Contributed Poster Presentations: Government Statistics Section
• Type: Contributed
• Date/Time: Tuesday, August 9, 2022 : 10:30 AM to 12:20 PM
• Sponsor: Government Statistics Section
• Author(s): Paul Bartholomew* and Adam Michael Edwards and Jordan Alexander Awan and Philip Leclerc and Rohan Rele and Andrew Sillers and David Zhou
• Companies: The MITRE Corporation and The MITRE Corporation and Purdue University and U.S. Census Bureau and The MITRE Corporation and The MITRE Corporation and The MITRE Corporation
• Keywords: Formal-privacy post-processing; Differential Privacy; Algorithms; uniform-minimum-variance-unbiased-estimates (UMVUE); Confidence Intervals

Abstract

The U.S. decennial census publishes statistics for geographic units ranging from the 8 million census blocks to the national level. To meet their privacy and confidentiality mandates the U.S. Census Bureau uses a Differential Privacy (DP) framework to inject Discrete Gaussian noise into each of these statistics, with the exception of a limited number of designated invariants, which it calls "noisy measurements." The current post-processing methodology used to restore hierarchical and cross-table consistency relationships relies on a non-negative least squares (NNLS) framework to produce the published estimates. The research reported here seeks to enforce the known hierarchical and linear/affine relationships of the dataset to produce the uniformly-minimum-variance-unbiased-estimator (UMVUE) and confidence intervals. The proposed algorithm combines existing theory related to UMVUE, constrained ordinary least squares (OLS), and optimization decomposition methodologies. This study proposes an algorithm that exploits the hierarchical and affine nature of the constraints to produce the UMVUE and confidence intervals in a computationally efficient manner. © 2022 MITRE|#22-1280