2021/07/15 by Amirreza Zamani, Zamani, Amirreza, Tobias J. Oechtering +3 · 5 citations
Computer Science · #Adversarial Robustness in Machine Learning #Cryptography and Data Security #FOS: Computer and information sciences #Information Theory (cs.IT) #Privacy-Preserving Technologies in Data
paper · pdf · doi:10.48550/arxiv.2107.07484
openalex publication_date 2021/07/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study a statistical signal processing privacy problem, where an agent observes useful data Y and wants to reveal the information to a user. Since the useful data is correlated with the private data X, the agent employs a privacy mechanism to generate data U that can be released. We study the privacy mechanism design that maximizes the revealed information about Y while satisfying a strong ℓ1-privacy criterion. When a sufficiently small leakage is allowed, we show that the optimizer vectors of the privacy mechanism design problem have a specific geometry, i.e., they are perturbations of fixed vector distributions. This geometrical structure allows us to use a local approximation of the conditional entropy. By using this approximation the original optimization problem can be reduced to a linear program so that an approximate solution for privacy mechanism can be easily obtained. The main contribution of this work is to consider non-zero leakage with a non-invertible leakage matrix. In an example inspired by water mark application, we first investigate the accuracy of the approximation. Then, we employ different measures for utility and privacy leakage to compare the privacy-utility trade-off using our approach with other methods. In particular, it has been shown that by allowing small leakage, significant utility can be achieved using our method compared to the case where no leakage is allowed.