Optimizing Differentially Private Linear Gaussian Mechanisms
Open Access
- Author:
- Xiao, Yingtai
- Graduate Program:
- Computer Science and Engineering
- Degree:
- Doctor of Philosophy
- Document Type:
- Dissertation
- Date of Defense:
- February 13, 2024
- Committee Members:
- John Sampson, Professor in Charge/Director of Graduate Studies
Mehrdad Mahdavi, Major Field Member
Aleksandra Slavkovic, Outside Unit & Field Member
Kiwan Maeng, Special Signatory
Kiwan Maeng, Major Field Member
Daniel Kifer, Chair & Dissertation Advisor
Danfeng Zhang, Special Member
Member Committee, Special Member - Keywords:
- Differential Privacy
Linear Query
Database
Optimization - Abstract:
- Differential Privacy (DP) has become the standard for protecting confidentiality in publicly available data. One crucial use of DP is in differentially private linear queries, which play a fundamental role in various fields including database searches, creating synthetic data, sharing statistics, and deep learning. To optimize the performance of differentially private linear queries with Gaussian noise—referred to as linear Gaussian Mechanisms, we first introduce ResidualPlanner, a scalable matrix mechanism for generating noisy marginals with Gaussian noise. It optimizes for multiple loss functions, facilitating efficient computation of marginal variances even in large-scale settings and advancing differentially private data release mechanisms' capabilities. Secondly, we propose Common Mechanism to allocate privacy budgets optimally between competing mechanisms. By dissecting mechanisms into shared and mechanism-specific components, it aids analysts in selecting mechanisms without compromising privacy budgets. Lastly, we present SM-II, which enhances accuracy in differentially private data releases by controlling accuracy at the per-query level. It employs privacy-preserving Gaussian noise with an optimized covariance structure to meet accuracy requirements for each query efficiently.