2019/01/30 by Jordan Awan, Awan, Jordan, Ana Kenney +5
Computer Science · Mathematics · #46E22 #46S50 #60G15 #62H25 #Cryptography and Security (cs.CR) #FOS: Computer and information sciences #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Privacy-Preserving Technologies in Data #Statistical Methods and Bayesian Inference #Statistical Methods and Inference
paper · pdf · doi:10.48550/arxiv.1901.10864
openalex publication_date 2019/01/30 · openalex created_date 2019/07/12 · openalex updated_date 2026/07/28
The exponential mechanism is a fundamental tool of Differential Privacy (DP)\ndue to its strong privacy guarantees and flexibility. We study its extension to\nsettings with summaries based on infinite dimensional outputs such as with\nfunctional data analysis, shape analysis, and nonparametric statistics. We show\nthat one can design the mechanism with respect to a specific base measure over\nthe output space, such as a Guassian process. We provide a positive result that\nestablishes a Central Limit Theorem for the exponential mechanism quite\nbroadly. We also provide an apparent negative result, showing that the\nmagnitude of the noise introduced for privacy is asymptotically non-negligible\nrelative to the statistical estimation error. We develop an ep-DP mechanism\nfor functional principal component analysis, applicable in separable Hilbert\nspaces. We demonstrate its performance via simulations and applications to two\ndatasets.\n