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Differential Privacy Over Riemannian Manifolds
Add to Calendar 2021-12-03T15:10:00 2021-12-03T16:00:00 UTC Differential Privacy Over Riemannian Manifolds 327 Thomas Building, University Park, PA
Start DateFri, Dec 03, 2021
10:10 AM
End DateFri, Dec 03, 2021
11:00 AM
Presented By
Carlos Soto
Event Series: SMAC Talks

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 further consider in detail the specific case where the summary is the Fréchet 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.