Shape and Structure Preserving Differential Privacy on Manifolds

• Activity Number: 483 - Privacy and Work Force
• Type: Contributed
• Date/Time: Wednesday, August 10, 2022 : 2:00 PM to 3:50 PM
• Sponsor: Government Statistics Section
• Author(s): Carlos J Soto*
• Companies: The Pennsylvania State University
• Keywords: Differential Privacy; Machine Learning; Statistical Theory; Shape Analysis

Abstract

This work considers the problem of producing sanitized differentially private estimates through the K-norm Gradient Mechanism (KNG) of data on a Riemannian manifold. Traditionally KNG requires an objective function and produces a sanitized estimate by favoring values which nearly minimize the function. This work extends KNG to consider objective functions which take on manifold-value data. Respecting the nature of the data leads to utility gains when compared to sanitization in an ambient space, as well as removes the need for post processing. Specifically, this work considers sanitizing the Frechet mean for the sphere, symmetric positive definite matrices, and Kendall’s 2D shape space.