Rate-Optimal Rank Aggregation with Private Pairwise Rankings
This work addresses privacy concerns in applications like recommender systems and surveys, offering a method to balance utility and protection, though it is incremental as it builds on existing randomized response techniques.
The paper tackles the problem of preserving privacy in rank aggregation from pairwise rankings, proposing an adaptive debiasing method for randomized response mechanisms to reduce bias and ensure consistent estimation, with theoretical minimax rates and validation through simulations and real-world data.
In various real-world scenarios, such as recommender systems and political surveys, pairwise rankings are commonly collected and utilized for rank aggregation to derive an overall ranking of items. However, preference rankings can reveal individuals' personal preferences, highlighting the need to protect them from exposure in downstream analysis. In this paper, we address the challenge of preserving privacy while ensuring the utility of rank aggregation based on pairwise rankings generated from a general comparison model. A common privacy protection strategy in practice is the use of the randomized response mechanism to perturb raw pairwise rankings. However, a critical challenge arises because the privatized rankings no longer adhere to the original model, resulting in significant bias in downstream rank aggregation tasks. To address this, we propose an adaptive debiasing method for rankings from the randomized response mechanism, ensuring consistent estimation of true preferences and enhancing the utility of downstream rank aggregation. Theoretically, we provide insights into the relationship between overall privacy guarantees and estimation errors in private ranking data, and establish minimax rates for estimation errors. This enables the determination of optimal privacy guarantees that balance consistency in rank aggregation with privacy protection. We also investigate convergence rates of expected ranking errors for partial and full ranking recovery, quantifying how privacy protection affects the specification of top-$K$ item sets and complete rankings. Our findings are validated through extensive simulations and a real-world application.