Ranking Differential Privacy

TL;DR

This paper introduces a new concept called epsilon-ranking differential privacy to protect ranking data, develops a multistage algorithm for generating private synthetic rankings, and analyzes its utility and privacy trade-offs through theoretical and empirical studies.

Contribution

It proposes epsilon-ranking differential privacy, connects it with the Mallows model, and develops a multistage ranking algorithm with theoretical utility guarantees.

Findings

The synthetic rankings preserve utility in downstream tasks.

Privacy parameter epsilon influences estimation accuracy.

The algorithm effectively balances privacy and utility.

Abstract

Rankings are widely collected in various real-life scenarios, leading to the leakage of personal information such as users' preferences on videos or news. To protect rankings, existing works mainly develop privacy protection on a single ranking within a set of ranking or pairwise comparisons of a ranking under the $\epsilon$-differential privacy. This paper proposes a novel notion called $\epsilon$-ranking differential privacy for protecting ranks. We establish the connection between the Mallows model (Mallows, 1957) and the proposed $\epsilon$-ranking differential privacy. This allows us to develop a multistage ranking algorithm to generate synthetic rankings while satisfying the developed $\epsilon$-ranking differential privacy. Theoretical results regarding the utility of synthetic rankings in the downstream tasks, including the inference attack and the personalized ranking tasks, are established. For the inference attack, we quantify how $\epsilon$ affects the estimation of the true ranking based on synthetic rankings. For the personalized ranking task, we consider varying privacy preferences among users and quantify how their privacy preferences affect the consistency in estimating the optimal ranking function. Extensive numerical experiments are carried out to verify the theoretical results and demonstrate the effectiveness of the proposed synthetic ranking algorithm.