Asymmetric Local Information Privacy and the Watchdog Mechanism

This paper proposes a novel watchdog privatization scheme by generalizing local information privacy (LIP) to enhance data utility. To protect the sensitive features $S$ correlated with some useful data $X$, LIP restricts the lift, the ratio of the posterior belief to the prior on $S$ after and before accessing $X$. For each $x$, both maximum and minimum lift over sensitive features are measures of the privacy risk of publishing this symbol and should be restricted for the privacy-preserving purpose. Previous works enforce the same bound for both max-lift and min-lift. However, empirical observations show that the min-lift is usually much smaller than the max-lift. In this work, we generalize the LIP definition to consider the unequal values of max and min lift, i.e., considering different bounds for max-lift and min-lift. This new definition is applied to the watchdog privacy mechanism. We demonstrate that the utility is enhanced under a given privacy constraint on local differential privacy. At the same time, the resulting max-lift is lower and, therefore, tightly restricts other privacy leakages, e.g., mutual information, maximal leakage, and $\alpha$-leakage.