Tunable Measures for Information Leakage and Applications to Privacy-Utility Tradeoffs

Jiachun Liao, Oliver Kosut, Lalitha Sankar, Flavio Du Pin Calmon

Research output: Contribution to journalArticlepeer-review

48 Scopus citations


We introduce a tunable measure for information leakage called maximal α -leakage. This measure quantifies the maximal gain of an adversary in inferring any (potentially random) function of a dataset from a release of the data. The inferential capability of the adversary is, in turn, quantified by a class of adversarial loss functions that we introduce as α -loss, α in [1,∞) cup ∞ . The choice of α determines the specific adversarial action and ranges from refining a belief (about any function of the data) for α =1 to guessing the most likely value for α = ∞ while refining the α th moment of the belief for α in between. Maximal α -leakage then quantifies the adversarial gain under α -loss over all possible functions of the data. In particular, for the extremal values of α =1and α =∞ , maximal α -leakage simplifies to mutual information and maximal leakage, respectively. For α in (1,∞) this measure is shown to be the Arimoto channel capacity of order α . We show that maximal α -leakage satisfies data processing inequalities and a sub-additivity property thereby allowing for a weak composition result. Building upon these properties, we use maximal α -leakage as the privacy measure and study the problem of data publishing with privacy guarantees, wherein the utility of the released data is ensured via a hard distortion constraint. Unlike average distortion, hard distortion provides a deterministic guarantee of fidelity. We show that under a hard distortion constraint, for α >1 the optimal mechanism is independent of α , and therefore, the resulting optimal tradeoff is the same for all values of α >1. Finally, the tunability of maximal α -leakage as a privacy measure is also illustrated for binary data with average Hamming distortion as the utility measure.

Original languageEnglish (US)
Article number8804205
Pages (from-to)8043-8066
Number of pages24
JournalIEEE Transactions on Information Theory
Issue number12
StatePublished - Dec 2019


  • Arimoto mutual information
  • Mutual information
  • Sibson mutual information
  • f -divergence
  • hard distortion
  • maximal a-leakage
  • maximal leakage
  • privacy-utility tradeoff

ASJC Scopus subject areas

  • Information Systems
  • Computer Science Applications
  • Library and Information Sciences


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