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

Abstract

When using differential privacy to publish high-dimensional data, the huge dimensionality leads to greater noise. Especially for high-dimensional binary data, it is easy to be covered by excessive noise. Most existing methods cannot address real high-dimensional data problems appropriately because they suffer from high time complexity. Therefore, in response to the problems above, we propose the differential privacy adaptive Bayesian network algorithm PrivABN to publish high-dimensional binary data. This algorithm uses a new greedy algorithm to accelerate the construction of Bayesian networks, which reduces the time complexity of the GreedyBayes algorithm from $O\left({nkC}_{m+1}^{k+2}\right)$ to $O\left({nm}^4\right)$ . In addition, it uses an adaptive algorithm to adjust the structure and uses a differential privacy Exponential mechanism to preserve the privacy, so as to generate a high-quality protected Bayesian network. Moreover, we use the Bayesian network to calculate the conditional distribution with noise and generate a synthetic dataset for publication. This synthetic dataset satisfies $\epsilon$ -differential privacy. Lastly, we carry out experiments against three real-life high-dimensional binary datasets to evaluate the functional performance.