Fast and Robust Rank Aggregation against Model Misspecification
This work addresses robustness in rank aggregation for applications like recommendation systems, but it is incremental as it builds on existing models with neighborhood-based modifications.
The paper tackles the problem of rank aggregation under model misspecification, where existing methods fail with agnostic noise, by proposing CoarsenRank, which performs regular rank aggregation over a neighborhood of preferences and shows robustness in experiments on four real-world datasets.
In rank aggregation (RA), a collection of preferences from different users are summarized into a total order under the assumption of homogeneity of users. Model misspecification in RA arises since the homogeneity assumption fails to be satisfied in the complex real-world situation. Existing robust RAs usually resort to an augmentation of the ranking model to account for additional noises, where the collected preferences can be treated as a noisy perturbation of idealized preferences. Since the majority of robust RAs rely on certain perturbation assumptions, they cannot generalize well to agnostic noise-corrupted preferences in the real world. In this paper, we propose CoarsenRank, which possesses robustness against model misspecification. Specifically, the properties of our CoarsenRank are summarized as follows: (1) CoarsenRank is designed for mild model misspecification, which assumes there exist the ideal preferences (consistent with model assumption) that locates in a neighborhood of the actual preferences. (2) CoarsenRank then performs regular RAs over a neighborhood of the preferences instead of the original dataset directly. Therefore, CoarsenRank enjoys robustness against model misspecification within a neighborhood. (3) The neighborhood of the dataset is defined via their empirical data distributions. Further, we put an exponential prior on the unknown size of the neighborhood, and derive a much-simplified posterior formula for CoarsenRank under particular divergence measures. (4) CoarsenRank is further instantiated to Coarsened Thurstone, Coarsened Bradly-Terry, and Coarsened Plackett-Luce with three popular probability ranking models. Meanwhile, tractable optimization strategies are introduced with regards to each instantiation respectively. In the end, we apply CoarsenRank on four real-world datasets.