Privacy protection with heavy-tailed noise for linear dynamical systems

Abstract Privacy protection in linear dynamical systems is investigated in this paper. A standard mechanism employed in systems and control literature is to mask private data by adding Gaussian noise . A shortcoming of this mechanism is that the occurrence of outliers is vulnerable. The goal of this paper is to present a novel mechanism that can hide outliers. The key idea is to utilize stably distributed noise, which has the following two preferable properties for this purpose; One is its heavy-tailed distribution that is beneficial to hide extreme values including scale-free data. The other is its closedness with respect to addition similarly to Gaussian, which enables us to design filter/controller under privacy requirements based on linear control theory. From a theoretical point of view, we quantify the privacy level of the proposed mechanism in terms of differential privacy. The derivation is nontrivial because the density function of the stable distribution has no analytic expression.