Title: Privacy with Estimation Guarantees,
Abstract: 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-off (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 threshold (privacy). We demonstrate how $\chi^2$-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 instead of the true data distribution. We
illustrate the proposed approach through two numerical experiments.