一种基于图的框架，用于扩展度量差分隐私机制
A Graph-Based Framework for Extending Metric Differential Privacy Mechanisms
- University of North Texas（北德克萨斯大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文提出一种基于图的扩展框架，用于度量差分隐私机制，通过种子记录扩展至大域，满足正确性要求并保持ε-mDP，实验显示良好效用与可扩展性权衡。
AI中文摘要：
度量差分隐私（mDP）非常适合结构化秘密域，但在大型或细粒度域上直接构建效用感知机制通常在计算上是不可行的。我们研究基于扩展的mDP设计，其中机制首先在有限的种子记录集合上指定，然后扩展到更大的目标域。据我们所知，这是第一项将扩展系统地表述为mDP的通用设计范式而非特定方法构造的工作。我们提出了一种基于图的扩展框架，确定了正确性的三个要求：局部mDP约束、重叠一致性和后继级mDP保持，并表明在这些条件下，诱导的全局机制是良定义的，并在目标域上满足ε-mDP。我们进一步用基于树的扩展算法实例化该框架，用于多分辨率网格，其中多维扩展通过一维插值和维度级组合实现。在路线图数据集上的实验表明，我们的方法在保持精确mDP保证的同时，实现了强大的效用-可扩展性权衡。
英文摘要：
Metric differential privacy (mDP) is well suited to structured secret domains, but directly constructing utility-aware mechanisms over large or fine-grained domains is often computationally prohibitive. We study extension-based mDP design, where a mechanism is first specified on a finite set of seed records and then extended to a larger target domain. To our knowledge, this is the first work to systematically formulate extension as a general design paradigm for mDP rather than a method-specific construction. We present a graph-based extension framework, identify three requirements for correctness, local mDP constraints, overlap consistency, and successor-level mDP preservation, and show that, under these conditions, the induced global mechanism is well defined and satisfies $ε$-mDP on the target domain. We further instantiate the framework with a tree-based extension algorithm for multi-resolution grids, where multi-dimensional extension is realized through one-dimensional interpolation and dimension-wise composition. Experiments on road-map datasets demonstrate that our approach achieves a strong utility-scalability trade-off while preserving exact mDP guarantees.
