A Generalized Leakage Interpretation of Alpha-Mutual Information

2026-01-14

AI Summary

This work proposes a unified interpretation of α-mutual information in the context of quantitative information flow and its connection to privacy leakage. By constructing an adversarial generalized decision model and employing Kolmogorov–Nagumo averages together with q-logarithms to characterize the adversary’s gain, the study establishes α-mutual information as a specific instance of generalized g-leakage for the first time. The theoretical link between α-mutual information and generalized g-leakage reveals that the parameter α precisely corresponds to the adversary’s degree of risk aversion. This insight yields a cohesive framework for interpreting privacy leakage through the lens of information-theoretic measures, thereby deepening the understanding of the relationship between information metrics and adversarial behavior.

Technology Category

• Machine Learning: Information Theory
• Game Theory and Economic Paradigms: Adversarial Learning
• Multiagent Systems: Adversarial Agents

Application Category

• Security and Privacy: Large-scale security measurements
• User Modeling, Personalization and Recommendation: User privacy protection in personalized systems
• Web Mining and Content Analysis: Content-based information diffusion

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.

Problem

• alpha-mutual information
• generalized leakage
• quantitative information flow
• adversarial decision problems
• risk aversion

Innovation

• alpha-mutual information
• generalized g-leakage
• quantitative information flow
• adversarial decision problems
• risk aversion