Formal Privacy for Functional Data with Gaussian Perturbations

Ardalan Mirshani, Matthew Reimherr, Aleksandra Slavković
Proceedings of the 36th International Conference on Machine Learning, PMLR 97:4595-4604, 2019.

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 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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v97-mirshani19a, title = {Formal Privacy for Functional Data with {G}aussian Perturbations}, author = {Mirshani, Ardalan and Reimherr, Matthew and Slavkovi{\'c}, Aleksandra}, booktitle = {Proceedings of the 36th International Conference on Machine Learning}, pages = {4595--4604}, year = {2019}, editor = {Chaudhuri, Kamalika and Salakhutdinov, Ruslan}, volume = {97}, series = {Proceedings of Machine Learning Research}, month = {09--15 Jun}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v97/mirshani19a/mirshani19a.pdf}, url = {https://proceedings.mlr.press/v97/mirshani19a.html}, 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 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.} }
Endnote
%0 Conference Paper %T Formal Privacy for Functional Data with Gaussian Perturbations %A Ardalan Mirshani %A Matthew Reimherr %A Aleksandra Slavković %B Proceedings of the 36th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2019 %E Kamalika Chaudhuri %E Ruslan Salakhutdinov %F pmlr-v97-mirshani19a %I PMLR %P 4595--4604 %U https://proceedings.mlr.press/v97/mirshani19a.html %V 97 %X 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 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.
APA
Mirshani, A., Reimherr, M. & Slavković, A.. (2019). Formal Privacy for Functional Data with Gaussian Perturbations. Proceedings of the 36th International Conference on Machine Learning, in Proceedings of Machine Learning Research 97:4595-4604 Available from https://proceedings.mlr.press/v97/mirshani19a.html.

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