Formal privacy for functional data with Gaussian perturbations

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

Abstract

Motivated by the rapid rise in statistical tools in Functional Data Analysis, we consider the Gaussian mechanism for achieving differential privacy (DP) with parameter estimates taking values in a, potentially infinite-dimensional, separable Ba-nach 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.

Original languageEnglish (US)
Title of host publication36th International Conference on Machine Learning, ICML 2019
PublisherInternational Machine Learning Society (IMLS)
Pages8082-8091
Number of pages10
ISBN (Electronic)9781510886988
StatePublished - 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
CountryUnited 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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