Algorithm 4.

DPCopula-Kendall’s τ algorithm

Input: Original data vector (X1, …, Xm) containing m attributes, privacy budget ε

Output: Differentially private synthetic data D̃ Compute a differentially private marginal histogram with the privacy budget $\frac{{\epsilon }_1}{m}$ for each Xi in D ; Compute the DP correlation matrix P̃ using algorithm 5 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 data D̃ by algorithm 3.