A Generalized Leakage Interpretation of Alpha-Mutual Information

TL;DR

This paper offers a unified interpretation of alpha-mutual information through generalized g-leakage, linking it to adversarial decision problems and risk aversion, advancing the theoretical understanding of information flow measures.

Contribution

It introduces a novel interpretation of alpha-MI within a generalized decision framework using Kolmogorov-Nagumo means and q-logarithms, connecting it to adversarial risk preferences.

Findings

Alpha-MI can be interpreted as adversarial gain in a generalized decision framework.

The parameter alpha reflects the adversary's risk aversion.

The framework unifies various information leakage measures under a common interpretation.

Abstract

This paper presents a unified interpretation of $\alpha$-mutual information ($\alpha$-MI) in terms of generalized $g$-leakage. Specifically, we present a novel interpretation of $\alpha$-MI within an extended framework for quantitative information flow based on adversarial generalized decision problems. This framework employs the Kolmogorov-Nagumo mean and the $q$-logarithm to characterize adversarial gain. Furthermore, we demonstrate that, within this framework, the parameter $\alpha$ can be interpreted as a measure of the adversary's risk aversion.