Differentially Private Vine Copulas for Preserving Higher-Order Dependence Structures

Generating high-utility synthetic data under differential privacy (DP) remains challenging when complex dependence and higher-order interactions are present. Traditional marginal and graph-based DP methods can preserve low-dimensional structure, such as univariate marginals and pairwise correlations, but often fail to recover higher-order interactions. While DP deep generative models such as GANs can, in principle, capture complex dependence, they are often unstable and difficult to tune. We propose Differentially Private Vine Copulas (DPRIVVE), an end-to-end differentially private synthetic data generator that models higher-order dependence via conditional propagation. DPRIVVE combines differentially private marginal transformations to construct DP pseudo-observations without data leakage, private D-vine ordering, and private copula family and parameter estimation. Notably, DPRIVVE more accurately captures higher-order interactions relative to competing DP baselines. Moreover, these improvements consistently hold over varying privacy budgets and dependence structures while preserving standard utility metrics.