Gaussian copulas are widely used to estimate multivariate distributions and relationships. We present algorithms for estimating Gaussian copula correlations that ensure differential privacy. We first convert data values into sets of two-way tables of counts above and below marginal medians. We then add noise to these counts to satisfy differential privacy. We utilize the one-to-one correspondence between the true counts and the copula correlation to estimate a posterior distribution of the copula correlation given the noisy counts, marginalizing over the distribution of the underlying true counts using a composite likelihood. We also present an alternative, maximum likelihood approach for point estimation. Using simulation studies, we compare these methods to extant methods in the literature for computing differentially private copula correlations.

翻译：高斯Copula被广泛用于估计多元分布及其关联关系。本文提出了确保差分隐私的高斯Copula相关性估计算法。我们首先将数据值转换为基于边缘中位数的双向计数表，随后对这些计数添加噪声以满足差分隐私要求。利用真实计数与Copula相关性之间的一一对应关系，我们通过复合似然函数对潜在真实计数的分布进行边际化处理，基于噪声计数估计Copula相关性的后验分布。同时提出了一种用于点估计的替代性最大似然方法。通过模拟研究，我们将这些方法与文献中现有的差分隐私Copula相关性计算方法进行了比较。