Interpreting Epsilon of Differential Privacy in Terms of Advantage in Guessing or Approximating Sensitive Attributes

Differential privacy is a privacy technique with provable guarantees which is typically achieved by introducing noise to statistics before releasing them. The level of privacy is characterized by a certain numeric parameter E > 0, where smaller E means more privacy. However, there is no common agreement on how small E should be, and the actual likelihood of data leakage for the same E may vary for different released statistics and different datasets. In this paper, we show how to relate E to the increase in the probability of attacker's success in guessing something about the private data. The attacker's goal is stated as a Boolean expression over guessing particular categorical and numerical attributes, where numeric attributes can be guessed with some precision. The paper is built upon the definition of d-privacy, which is a gencralization of E-differential privacy.