Title: Statistical disclosure control for functional PCA
Authors: Jordan Awan - Penn State University (United States)
Matthew Reimherr - Pennsylvania State University (United States)
Aleksandra Slavkovic - Penn State University (United States)
Ana Kenney - Pennsylvania State University (United States) [presenting]
Abstract: Differential Privacy (DP) is a common and rigorous approach to quantify the disclosure risk of statistical procedures performed on sensitive data. Much work has been done on count and multivariate data, however the functional setting remains relatively unexplored even though large amounts of identifying information may be present. In functional data analysis (FDA), principal components are widely used for interpretation and as a dimension reduction technique for further study. It is therefore important to design a method that can still retain these properties while guaranteeing some level of DP. However, simply adding noise can result in very poor output due to the structure of principal components. In past literature, the exponential mechanism was utilized for PCA on multivariate data, and here we extend this approach to the functional setting. We demonstrate through a simulation study that the output of our method results in components comparable to the non-private ones for even moderate sample size.