Data-driven Rank Breaking for Efficient Rank Aggregation
This work addresses a computational efficiency issue in rank aggregation systems for applications like social choice or recommendation systems, but it is incremental as it builds on existing rank-breaking approaches.
The paper tackles the problem of inconsistent estimates in rank aggregation due to naive rank-breaking methods by introducing an optimal rank-breaking estimator that achieves consistency and the best error bound, characterizing the tradeoff between accuracy and complexity.
Rank aggregation systems collect ordinal preferences from individuals to produce a global ranking that represents the social preference. Rank-breaking is a common practice to reduce the computational complexity of learning the global ranking. The individual preferences are broken into pairwise comparisons and applied to efficient algorithms tailored for independent paired comparisons. However, due to the ignored dependencies in the data, naive rank-breaking approaches can result in inconsistent estimates. The key idea to produce accurate and consistent estimates is to treat the pairwise comparisons unequally, depending on the topology of the collected data. In this paper, we provide the optimal rank-breaking estimator, which not only achieves consistency but also achieves the best error bound. This allows us to characterize the fundamental tradeoff between accuracy and complexity. Further, the analysis identifies how the accuracy depends on the spectral gap of a corresponding comparison graph.