Differential privacy (DP) has become the gold standard for privacy-preserving data analysis, but its applicability can be limited in scenarios involving complex dependencies between sensitive information and datasets. To address this, we introduce differential confounding privacy (DCP), a specialized form of the Pufferfish privacy (PP) framework that generalizes DP by accounting for broader relationships between sensitive information and datasets. DCP adopts the$(\epsilon, \delta)$-indistinguishability framework to quantify privacy loss. We show that while DCP mechanisms retain privacy guarantees under composition, they lack the graceful compositional properties of DP. To overcome this, we propose an Inverse Composition (IC) framework, where a leader-follower model optimally designs a privacy strategy to achieve target guarantees without relying on worst-case privacy proofs, such as sensitivity calculation. Experimental results validate IC's effectiveness in managing privacy budgets and ensuring rigorous privacy guarantees under composition.

AI-driven algorithmic systems are increasingly adopted across various sectors, yet the lack of transparency can raise accountability concerns about claimed privacy protection measures. While machine-based audits offer one avenue for addressing these issues, they are often costly and time-consuming. Herd audit, on the other hand, offers a promising alternative by leveraging collective intelligence from end-users. However, the presence of epistemic disparity among auditors, resulting in varying levels of domain expertise and access to relevant knowledge, captured by the rational inattention model, may impact audit assurance. An effective herd audit must establish a credible accountability threat for algorithm developers, incentivizing them not to breach user trust. In this work, our objective is to develop a systematic framework that explores the impact of herd audits on algorithm developers through the lens of the Stackelberg game. Our analysis reveals the importance of easy access to information and the appropriate design of rewards, as they increase the auditors’ assurance in the audit process. In this context, herd audit serves as a deterrent to negligent behavior. Therefore, by enhancing herd accountability, herd audit contributes to responsible algorithm development, fostering trust between users and algorithms.

Privacy-preserving distributed machine learning becomes increasingly important due to the recent rapid growth of data. This paper focuses on a class of regularized empirical risk minimization machine learning problems, and develops two methods to provide differential privacy to distributed learning algorithms over a network. We first decentralize the learning algorithm using the alternating direction method of multipliers, and propose the methods of dual variable perturbation and primal variable perturbation to provide dynamic differential privacy. The two mechanisms lead to algorithms that can provide privacy guarantees under mild conditions of the convexity and differentiability of the loss function and the regularizer. We study the performance of the algorithms, and show that the dual variable perturbation outperforms its primal counterpart. To design an optimal privacy mechanism, we analyze the fundamental tradeoff between privacy and accuracy, and provide guidelines to choose privacy parameters. Numerical experiments using customer information database are performed to corroborate the results on privacy and utility tradeoffs and design.