🤖 AI Summary
This paper addresses rank aggregation from pairwise preference data—e.g., in recommender systems and opinion polls—under differential privacy constraints. To mitigate model mismatch and estimation bias induced by standard randomized response mechanisms, we propose a model-agnostic adaptive debiasing framework. We establish, for the first time, a minimax lower bound on estimation error for differentially private pairwise ranking, precisely characterizing the fundamental trade-off between privacy budget ε and ranking accuracy. Theoretically, our method achieves the information-theoretically optimal convergence rate and supports both Top-K and total-order recovery. Empirical results demonstrate that, at ε = 1, our approach improves Top-10 accuracy by 37% over state-of-the-art baselines, significantly outperforming existing methods in utility–privacy trade-offs.
📝 Abstract
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.