Optimal Utility-Privacy Trade-off with Total Variation Distance as a Privacy Measure

The total variation distance is proposed as a privacy measure in an information disclosure scenario when the goal is to reveal some information about available data in order to receive utility, while preserving the privacy of sensitive data from the legitimate receiver. The total variation distance is motivated as a measure of privacy-leakage by showing that: i) it satisfies the post-processing and linkage inequalities, which makes it consistent with an intuitive notion of a privacy measure; ii) the optimal utility-privacy trade-off can be solved through a standard linear program when total variation distance is employed as the privacy measure; iii) it provides a bound on the privacy-leakage measured by mutual information, maximal leakage, or the improvement in an inference attack with an arbitrary bounded cost function.