Optimal Local Differentially Private Quantization

Abstract

Information sanitization to suppress sensitive information expressed through diverse sensor measurements is investigated in this work. Specifically, this work aims to integrate privacy preservation into the data compression phase of the sensing system streamline. The problem is posed as finding an optimal mapping from a collection of underlying raw distributions that reveal sensitive information for the data to another collection of distributions which are local differentially private and with minimum distortion. The optimal sanitization operation are transformed to convex optimization problems. In particular, a parallel is drawn to a “biased” quantization method and an efficient sub-gradient method is proposed to derive the optimal transformation, and a generalized version of the classical Lloyd Max iterative algorithm is proposed to derive the optimal biased quantizers that achieve required inference privacy. In the real time framework, an algorithm is proposed that achieves asymptotically the same distortion as if the source distribution were known apriori.