Equation Chapter 1 Section 1 Differentially Private High-Dimensional Binary Data Publication via Adaptive Bayesian Network

Algorithm 4

SDG Algorithm.

Input: data set , Bayesian network , privacy budget

Output: synthetic data set

1: Initialize ;

2: for to do

3:   Calculate the joint distribution and the marginal distribution ;

4:   Calculate conditional distribution ;

5:   Add Laplace noise to to get ;

6:   Reset the negative value in to 0, normalize other values, and then add;

7: end for

8: Traverse the node according to the topological order of the Bayesian network ;

9: Obtain the noisy conditional distribution from , and update the value of each record attribute in according to the conditional distribution;

10: return .