Privacy with estimation guarantees
Calmon, Flávio du Pin
Duffy, Ken R.
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Citation (published version)Hao Wang, Lisa Vo, Flávio du Pin Calmon, Muriel Médard, Ken R Duffy, Mayank Varia. 2019. "Privacy With Estimation Guarantees." IEEE Transactions on Information Theory, Volume 65, Issue 12, pp. 8025 - 8042. https://doi.org./10.1109/TIT.2019.2934414
We study the central problem in data privacy: how to share data with an analyst while providing both privacy and utility guarantees to the user that owns the data. In this setting, we present an estimation-theoretic analysis of the privacy-utility trade-o (PUT). Here, an analyst is allowed to reconstruct (in a mean-squared error sense) certain functions of the data (utility), while other private functions should not be reconstructed with distortion below a certain thresh- old (privacy). We demonstrate how chi-square information captures the fundamental PUT in this case and provide bounds for the best PUT. We propose a convex program to compute privacy-assuring mappings when the functions to be disclosed and hidden are known a priori and the data distribution is known. We derive lower bounds on the minimum mean-squared error of estimating a target function from the disclosed data and evaluate the robustness of our approach when an empirical distribution is used to compute the privacy-assuring mappings in- stead of the true data distribution. We illustrate the proposed approach through two numerical experiments.