The Ising model, originally developed as a spin-glass model for ferromagnetic elements, has gained popularity as a network-based model for capturing dependencies in agents' outputs. Its increasing adoption in healthcare and the social sciences has raised privacy concerns regarding the confidentiality of agents' responses. In this paper, we present a novel $(\varepsilon,\delta)$-differentially private algorithm specifically designed to protect the privacy of individual agents' outcomes. Our algorithm allows for precise estimation of the natural parameter using a single network through an objective perturbation technique. Furthermore, we establish regret bounds for this algorithm and assess its performance on synthetic datasets and two real-world networks: one involving HIV status in a social network and the other concerning the political leaning of online blogs.

翻译：伊辛模型最初作为铁磁元素的旋玻璃模型而发展，如今已作为一种基于网络的模型被广泛用于捕捉个体输出之间的依赖关系。其在医疗健康及社会科学领域的日益普及引发了关于个体响应保密性的隐私担忧。本文提出一种新颖的$(\varepsilon,\delta)$-差分隐私算法，专门用于保护个体结果的隐私。该算法通过目标扰动技术，仅需单个网络即可实现对自然参数的精确估计。此外，我们为该算法建立了遗憾界，并在合成数据集及两个真实网络（涉及社交网络中HIV状态与在线博客政治倾向）上评估了其性能。