Algorithm 1.

DPCopula-MLE algorithm

Input: Original data vector D = (X1, …, Xm), and privacy budget ε.

Output: Differentially private synthetic data D̃ Create a differentially private marginal histogram with privacy budget $\frac{{\epsilon }_1}{m}$ for each dimension Xj, j = 1, …, m, in the original data vector to obtain DP empirical marginal distribution (Ũ1, …, Ũm) by equation (2); Use DP MLE to estimate the DP correlation matrix P̃ with privacy budget $\frac{{\epsilon }_2}{\left(\begin{array}{c}\hfill m\hfill \\ \hfill 2\hfill \end{array}\right)}$ for each correlation coefficient and ε2 = ε − ε1; Sample DP synthetic dataset D̃ by algorithm 3.