CAREER: Differential Privacy Meets Random Geometry: Interpretation, Applications, and Trade-offs

Protecting personal data while still learning useful patterns from it is a central challenge in modern computing, especially in artificial intelligence and machine learning systems that influence health, finance, and online services. This project studies how privacy protection by noise perturbation changes accuracy, learning efficiency, and reliability. It develops new ways to understand and improve these trade-offs. The project's novelties are a geometric view of privacy protection that makes abstract privacy mechanisms more interpretable and a unified framework for analyzing how privacy, utility, convergence, and generalization interact. The project's broader significance and importance are that it strengthens the scientific foundation of trustworthy data analysis, helps make privacy-preserving learning more practical, and supports education and workforce development through course development, student research involvement, and outreach activities. The project interprets differential privacy through random geometry, random matrix methods, concentration of measure, and learning theory. It represents privacy mechanisms based on noise perturbation through geometric objects such as random triangles and their induced point clouds, which provide visual and quantitative descriptions of privacy loss and utility degradation in high dimensions. Using this framework, the project derives new characterizations and bounds for privacy loss, develops tighter analysis tools for privacy amplification and composition, and designs both isotropic and anisotropic noise mechanisms that improve the privacy-utility frontier. The project also studies how these geometric tools explain and optimize trade-offs among model accuracy, convergence speed, and learnability in privacy-preserving learning pipelines. Results from this work can improve the design of privacy-preserving data analysis and machine learning systems. The open-released code, data, and educational materials will help the overall research community. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria. NSF Award ID: 2543221 | Program: 01003031DB NSF RESEARCH & RELATED ACTIVIT,01002627DB NSF RESEARCH & RELATED ACTIVIT,01002930DB NSF RESEARCH & RELATED ACTIVIT | Principal Investigator: Tianxi Ji | Institution: Texas Tech University, LUBBOCK, TX | Award Amount: $344,417 View on NSF Award Search: https://www.nsf.gov/awardsearch/show-award/?AWD_ID=2543221 View on Research.gov: https://www.research.gov/awardapi-service/v1/awards/2543221.html