A Generalization of the Stratonovich's Value of Information and Application to Privacy-Utility Trade-off

TL;DR

This paper generalizes the Stratonovich's value of information to broader loss functions and leakage models, providing bounds and conditions that enhance understanding of privacy-utility trade-offs in data analysis.

Contribution

It introduces a generalized VoI framework, derives an upper bound, and offers a weaker achievable condition for classical loss functions, advancing privacy-utility trade-off analysis.

Findings

Derived an upper bound for the generalized VoI.

Provided a weaker achievable condition for classical loss functions.

Interpreted the condition within the privacy-utility trade-off context.

Abstract

The Stratonovich's value of information (VoI) is quantity that measure how much inferential gain is obtained from a perturbed sample under information leakage constraint. In this paper, we introduce a generalized VoI for a general loss function and general information leakage. Then we derive an upper bound of the generalized VoI. Moreover, for a classical loss function, we provide a achievable condition of the upper bound which is weaker than that of in previous studies. Since VoI can be viewed as a formulation of a privacy-utility trade-off (PUT) problem, we provide an interpretation of the achievable condition in the PUT context.