Privacy-Preserving Correlation Coefficient

Differential privacy is a confidentiality metric and quan-titatively guarantees the confidentiality of individuals. A noise criterion, called sensitivity, must be calculated when constructing a probabilistic dis-turbance mechanism that satisfies differential privacy. Depending on the statistical process, the sensitivity may be very large or even impossible to compute. As a result, the usefulness of the constructed mechanism may be significantly low; it might even be impossible to directly construct it. In this paper, we first discuss situations in which sensitivity is difficult to calculate, and then propose a differential privacy with additional dummy data as a countermeasure. When the sensitivity in the conventional differ-ential privacy is calculable, a mechanism that satisfies the proposed metric satisfies the conventional differential privacy at the same time, and it is possible to evaluate the relationship between the respective privacy param-eters. Next, we derive sensitivity by focusing on correlation coefficients as a case study of a statistical process for which sensitivity is difficult to cal-culate, and propose a probabilistic disturbing mechanism that satisfies the proposed metric. Finally, we experimentally evaluate the effect of noise on the sensitivity of the proposed and direct methods. Experiments show that privacy-preserving correlation coefficients can be derived with less noise compared to using direct methods.