Local Differential Privacy for Belief Functions

TL;DR

This paper introduces two novel local differential privacy definitions for belief functions, analyzing their properties and impact on privacy-utility trade-offs in distribution estimation.

Contribution

It presents new privacy definitions for belief functions, extending differential privacy concepts to imprecise probabilities and belief semantics.

Findings

Both definitions satisfy composition and post-processing properties.

The framework assesses the impact of 'don't know' on privacy and utility.

Experimental results demonstrate the effectiveness of the proposed approaches.

Abstract

In this paper, we propose two new definitions of local differential privacy for belief functions. One is based on Shafer's semantics of randomly coded messages and the other from the perspective of imprecise probabilities. We show that such basic properties as composition and post-processing also hold for our new definitions. Moreover, we provide a hypothesis testing framework for these definitions and study the effect of "don't know" in the trade-off between privacy and utility in discrete distribution estimation.