Utility Optimal Model for Differential Privacy Based on the Rate Distortion

Privacy leakage has become a widely concerned issue and a major restricting factor for data releasing and sharing in the era of big data. This issue urgently needs effective privacy preserving mechanism to protect individual's private information while preserving the accuracy of released data. Commonly, the privacy-preserving data release is achieved by data distortion disturbance. Indeed, this will raise a problem of tradeoff between privacy protection intensity and the degree of data distortion, that is known as the problem of privacy-utility tradeoff. Recently years, the issue of privacy-utility tradeoff has become a hot topic in the field of privacy. Additionally, differential privacy (DP) as a strict privacy protection technology has been widely studied by researchers. The basic idea of DP is randomized perturbation for the purpose to release noisy data. Thus, the privacy-utility tradeoff is still the key research of differential privacy. In this paper, we mainly focus on the scenario of differential privacy offline data release. Based on Shannon's communication theory, we adopt privacy spread communication model to simulate data releasing and model the randomized perturbation of differential privacy as a noisy channel model, i.e., a randomized probability mapping. Further, we adopt mutual information and expected distortion measure function to quantify privacy leakage and data usability. Thus, the problem of tradeoff between privacy and utility can be formalized as mutual information privacy optimization problem, which can be solved by celebrated rate-distortion theory. In this regard, Wang et al presented the mutual information privacy (PD-MIP), and utilized Karush-Kuhn-Tucker (KKT) condition to illustrate optimality criterion of mutual information privacy. And then, they proved that the optimal mutual information privacy also is close to the optimal differential privacy level when given a distortion constraint. Besides, Kalantari also pointed out that differential privacy leakage is the upper bound of mutual information privacy leakage. These researches establish a fundamental relation between mutual information privacy and differential privacy. However, they do not consider that how to obtain the optimal mutual information privacy mechanism, and the impact of related data on mutual information privacy leakage. That is, the data association of auxiliary background knowledge can help to obtain more private information, thus leading to the inference of individual's privacy with higher probability. Therefore, it is meaningful to study the impact of related data on mutual information privacy leakage. To address the problem mentioned above, we consider the influence of auxiliary background knowledge on the mutual information privacy leakage, and propose mutual information privacy metric based on joint events. Furthermore, we modify the current rate-distortion function, and propose a minimized mutual information privacy disclosure model. Finally, for the difficult problem of computing rate-distortion by using the Lagrange approach, we propose an approximate algorithm of differential privacy optimization channel mechanism based on the principle of Blahut-Arimoto algorithm. We verify the effectiveness of the proposed iterative approximate computation. The experimental results show that the amount of mutual information privacy disclosure is 21.7% which is lower than that in symmetric discrete channel mechanism under the condition of limited distortion. Meanwhile, the data utility improves 38.3% under the same privacy tolerance. © 2020, Science Press. All right reserved.