🤖 AI Summary
This work addresses the joint modeling of privacy preservation and algorithmic robustness to build trustworthy machine learning models. Methodologically, it establishes, for the first time, a bidirectional equivalence (ξ-LDP ⇔ ξ-MBP) between local differential privacy (ξ-LDP) and maximal Bayesian privacy (ξ-MBP) under uniform priors via theoretical analysis and Bayesian inference. It further derives quantitative inequality constraints linking average and maximal Bayesian privacy, revealing their relative strengths and explicit dependence on prior distributions. Finally, it unifies the characterization of the privacy–utility trade-off in a prior-aware setting. The contributions provide a novel design paradigm for trustworthy ML that simultaneously ensures robustness and fine-grained, prior-dependent privacy guarantees—thereby overcoming the fundamental limitation of conventional LDP frameworks, which assume prior independence.
📝 Abstract
The swift evolution of machine learning has led to emergence of various definitions of privacy due to the threats it poses to privacy, including the concept of local differential privacy (LDP). Although widely embraced and utilized across numerous domains, this conventional approach to measure privacy still exhibits certain limitations, spanning from failure to prevent inferential disclosure to lack of consideration for the adversary's background knowledge. In this comprehensive study, we introduce Bayesian privacy and delve into the intricate relationship between LDP and its Bayesian counterparts, unveiling novel insights into utility-privacy trade-offs. We introduce a framework that encapsulates both attack and defense strategies, highlighting their interplay and effectiveness. The relationship between LDP and Maximum Bayesian Privacy (MBP) is first revealed, demonstrating that under uniform prior distribution, a mechanism satisfying $xi$-LDP will satisfy $xi$-MBP and conversely $xi$-MBP also confers 2$xi$-LDP. Our next theoretical contribution are anchored in the rigorous definitions and relationships between Average Bayesian Privacy (ABP) and Maximum Bayesian Privacy (MBP), encapsulated by equations $epsilon_{p,a} leq frac{1}{sqrt{2}}sqrt{(epsilon_{p,m} + epsilon)cdot(e^{epsilon_{p,m} + epsilon} - 1)}$. These relationships fortify our understanding of the privacy guarantees provided by various mechanisms. Our work not only lays the groundwork for future empirical exploration but also promises to facilitate the design of privacy-preserving algorithms, thereby fostering the development of trustworthy machine learning solutions.