Poster
Formal Privacy for Functional Data with Gaussian Perturbations
Ardalan Mirshani · Matthew Reimherr · Aleksandra Slavković

Tue Jun 11th 06:30 -- 09:00 PM @ Pacific Ballroom #170

Motivated by the rapid rise in statistical tools in {\it Functional Data Analysis}, we consider the Gaussian mechanism for achieving differential privacy (DP) with parameter estimates taking values in a, potentially infinite-dimensional, separable Banach space. Using classic results from probability theory, we show how densities over function spaces can be utilized to achieve the desired DP bounds. This extends prior results of Hall et al (2013) to a much broader class of statistical estimates and summaries, including path level" summaries, nonlinear functionals, and full function releases. By focusing on Banach spaces, we provide a deeper picture of the challenges for privacy with complex data, especially the role regularization plays in balancing utility and privacy. Using an application to penalized smoothing, we highlight this balance in the context of mean function estimation. Simulations and an application to {diffusion tensor imaging} are briefly presented, with extensive additions included in a supplement.

#### Author Information

##### Ardalan Mirshani (The Pennsylvania State University)

I am a 5th year PhD candidate in the Department of Statistics at the Pennsylvania State University. Regularization methods specifically on High dimensional functional data sets are the heart of my research.