Benefits and pitfalls of the exponential mechanism with applications to Hilbert spaces and functional PCA

Jordan Awan, Ana Kenney, Matthew Reimherr, Aleksandra Slavković

Research output: Chapter in Book/Report/Conference proceedingConference contribution

4 Scopus citations

Abstract

The exponential mechanism is a fundamental tool of Differential Privacy (DP) due to its strong privacy guarantees and flexibility. We study its extension to settings with summaries based on infinite dimensional outputs such as with functional data analysis, shape analysis, and nonparametric statistics. We show that the mechanism must be designed with respect to a specific base measure over the output space, such as a Gaussian process. We provide a positive result that establishes a Central Limit Theorem for the exponential mechanism quite broadly. We also provide a negative result, showing that the magnitude of noise introduced for privacy is asymptotically non-negligible relative to the statistical estimation error. We develop an e-DP mechanism for functional principal component analysis, applicable in separable Hilbert spaces, and demonstrate its performance via simulations and applications to two datasets.

Original languageEnglish (US)
Title of host publication36th International Conference on Machine Learning, ICML 2019
PublisherInternational Machine Learning Society (IMLS)
Pages577-587
Number of pages11
ISBN (Electronic)9781510886988
StatePublished - Jan 1 2019
Event36th International Conference on Machine Learning, ICML 2019 - Long Beach, United States
Duration: Jun 9 2019Jun 15 2019

Publication series

Name36th International Conference on Machine Learning, ICML 2019
Volume2019-June

Conference

Conference36th International Conference on Machine Learning, ICML 2019
Country/TerritoryUnited States
CityLong Beach
Period6/9/196/15/19

All Science Journal Classification (ASJC) codes

  • Education
  • Computer Science Applications
  • Human-Computer Interaction

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