A Linear Reduction Method for Local Differential Privacy and Log-lift

Abstract

This paper considers the problem of publishing data X while protecting the correlated sensitive information S . We propose a linear method to generate the sanitized data Y with the same alphabet Y=X that attains local differential privacy (LDP) and log-lift at the same time. It is revealed that both LDP and log-lift are inversely proportional to the statistical distance between conditional probability PY|S(x|s) and marginal probability PY(x) : the closer the two probabilities are, the more private Y is. Specifying PY|S(x|s) that linearly reduces this distance |PY|S(x|s)−PY(x)|=(1−α)|PX|S(x|s)−PX(x)|,∀s,x for some α∈(0,1] , we study the problem of how to generate Y from the original data S an..