On the Relation Between Identifiability, Differential Privacy and Mutual-Information Privacy
It addresses foundational privacy theory for researchers in data privacy and machine learning, establishing theoretical links between key privacy metrics.
This paper investigates the relationships between three privacy notions—identifiability, differential privacy, and mutual-information privacy—under a unified privacy-distortion framework, proving fundamental connections such as bounds between identifiability and differential privacy levels and consistency between identifiability and mutual-information privacy.
This paper investigates the relation between three different notions of privacy: identifiability, differential privacy and mutual-information privacy. Under a unified privacy-distortion framework, where the distortion is defined to be the Hamming distance of the input and output databases, we establish some fundamental connections between these three privacy notions. Given a distortion level $D$, define $ε_{\mathrm{i}}^*(D)$ to be the smallest (best) identifiability level, and $ε_{\mathrm{d}}^*(D)$ to be the smallest differential privacy level. We characterize $ε_{\mathrm{i}}^*(D)$ and $ε_{\mathrm{d}}^*(D)$, and prove that $ε_{\mathrm{i}}^*(D)-ε_X\leε_{\mathrm{d}}^*(D)\leε_{\mathrm{i}}^*(D)$ for $D$ in some range, where $ε_X$ is a constant depending on the distribution of the original database $X$, and diminishes to zero when the distribution of $X$ is uniform. Furthermore, we show that identifiability and mutual-information privacy are consistent in the sense that given distortion level $D$, the mechanism that optimizes the mutual-information privacy also minimizes the identifiability level.