On Privacy Mechanism Design Under a Bounded $α$-Lift Leakage Constraint with $χ^2$-Utility

We study the design of a statistical privacy mechanism under a bounded $α$-lift leakage constraint. An agent observes useful data $Y$, which is arbitrarily correlated with private data $X$, and releases $U$. The goal is to maximize Pearson $χ^2$-information $χ^2(Y;U)$ while satisfying the point-wise