Joint UConn/UMass
STATISTICS COLLOQUIUM
Carlos Soto, Assistant Professor
Department of Mathematics and Statistics
University of Massachusetts, Amherst
Differential Privacy over Riemannian Manifolds
In this work we consider the problem of releasing a differentially private statistical summary that resides on a Riemannian manifold. We present an extension of the Laplace or K-norm mechanism that utilizes intrinsic distances and volumes on the manifold. We also consider in detail the specific case where the summary is the Fr'echet mean of data residing on a manifold. We demonstrate that our mechanism is rate optimal and depends only on the dimension of the manifold, not on the dimension of any ambient space, while also showing how ignoring the manifold structure can decrease the utility of the sanitized summary. We illustrate our framework in two examples of particular interest in statistics: the space of symmetric positive definite matrices, which is used for covariance matrices, and the sphere, which can be used as a space for modeling discrete distributions.
Bio: Carlos Soto is an assistant professor at UMass Amherst. He received his PhD at Florida State University where he focused on Statistical Shape Analysis. His research includes statistics on manifolds, shape analysis, functional data analysis, and differential privacy.
DATE: March 26, 2025, 4:00 pm, AUST 202
WebEx:
Coffee will be served at 3:30 and pizza after the colloquium in AUST 326
For more information, contact: Tracy Burke at tracy.burke@uconn.edu