Data Disclosure With Non-Zero Leakage and Non-Invertible Leakage Matrix

We study a statistical signal processing privacy problem, where an agent observes useful data $Y$ and wants to reveal the information user. Since is correlated with private notation="LaTeX">$X$ , employs mechanism generate notation="LaTeX">$U$ that can be released. design maximizes revealed about while satisfying strong notation="LaTeX">$\ell _{1}$ -privacy criterion. When sufficiently small leakage allowed, we show optimizer distributions of problem have specific geometry, i.e., they are perturbations fixed vector distributions. This geometrical structure allows us use local approximation conditional entropy. By using this original optimization reduced linear program so approximate solution for optimal easily obtained. The main contribution work consider non-invertible matrix non-zero leakage. In our first example, inspired by watermark application, demonstrate accuracy approximation. Then, employ different measures utility compare privacy-utility trade-off approach other methods. particular, allowing leakage, significant achieved method compared case no allowed. second third examples which based on MNIST set medical applications, illustrate suggested disclosed . It has been shown letters disclosing more combined (randomized) produce new letter