Algorithm 2.

DP MLE

Input: Original data vector D = (X1, …, Xm), privacy budget ε2, and k ∈ N+.

Output: Differentially private correlation matrix estimator P̃ Divide D horizontally into l disjoint partitions D1, …, Dl with each partition having $b=\frac{n}{l}$ tuples; For each partition Dt, t ∈ 1, …, l: $${\mathbf{P̃}}^t=\underset{P_{ij}\in \mathrm{\Theta }}{\text{arg max}}\sum _{r=(i-1)b+1}^{rb}\mathit{\text{log}}{\mathrm{C}}_{\mathbf{P}}^{Ga}(x_1^r,\dots ,x_m^r)$$ where ${\mathrm{C}}_{\mathbf{P}}^{Ga}$ represents the density of Gaussian copula. For each Pij ∈ [−1, 1], i, j ∈ 1, …, m Compute the average value through ${\mathrm{P̄}}_{ij}=\frac{1}{l}{\sum }_l^{t=1}{P}_{ij}^t$, Then inject Laplace noise to P̄ij and obtain DP P̃ij as $${\mathrm{P̃}}_{ij}={\mathrm{P̄}}_{ij}+\mathit{\text{Lap}}[\frac{\left(\begin{array}{c}\hfill m\hfill \\ \hfill 2\hfill \end{array}\right)\mathrm{\Lambda }}{l{\epsilon }_2}]$$ where Λ is the diameter of each correlation coefficient space Θ with a value of 2; Collect all P̃ij to constitute the DP correlation matrix estimator P̃