标题： 置信匹配：类别数据的差分隐私推理 显示英文标题

标题： Fiducial Matching: Differentially Private Inference for Categorical Data

摘要： 统计推断的任务，包括为研究人员感兴趣的参数和效应构建置信区间和检验，在差分隐私（DP）环境下仍然是一个有待研究的领域。 确实，除了数据抽样带来的随机性外，DP还通过添加噪声来保护个体数据不被潜在攻击者泄露，从而提供另一种随机性来源。 由于这些噪声的卷积，在许多情况下很难确定从DP过程中产生的统计量和参数的随机行为。 在本工作中，我们通过采用基于模拟的匹配方法，借助似然框架中的工具来解决这个问题，该方法旨在复制数据生成流程（包括DP步骤），并获取由此流程产生的估计值的近似分布。 为此，我们专注于分析在国家调查中常见的分类（名义）数据，这些数据的敏感性是自然定义的，并关注加性隐私机制。 我们在覆盖率方面证明了所提出方法的有效性，并强调了其在模拟和实际数据设置中不同推断任务中的良好计算和统计性能。 显示英文摘要

摘要： The task of statistical inference, which includes the building of confidence intervals and tests for parameters and effects of interest to a researcher, is still an open area of investigation in a differentially private (DP) setting. Indeed, in addition to the randomness due to data sampling, DP delivers another source of randomness consisting of the noise added to protect an individual's data from being disclosed to a potential attacker. As a result of this convolution of noises, in many cases it is too complicated to determine the stochastic behavior of the statistics and parameters resulting from a DP procedure. In this work, we contribute to this line of investigation by employing a simulation-based matching approach, solved through tools from the fiducial framework, which aims to replicate the data generation pipeline (including the DP step) and retrieve an approximate distribution of the estimates resulting from this pipeline. For this purpose, we focus on the analysis of categorical (nominal) data that is common in national surveys, for which sensitivity is naturally defined, and on additive privacy mechanisms. We prove the validity of the proposed approach in terms of coverage and highlight its good computational and statistical performance for different inferential tasks in simulated and applied data settings.