Dynamic Ranking : Extensions of the BTL and the Translation Synchronization model.
112 (Bât Braconnier, La doua)
Bât Braconnier, La doua
Many applications, such as recommendation systems or sports tournaments, involve pairwise comparisons within a collection of n items, the goal being to use this data in order to infer the latent strength and/or global ranking of the items. Existing results for this problem predominantly focus on the setting consisting of a single comparison graph G. However, there exist scenarios (e.g., sports tournaments) where the the pairwise comparison data evolves with time but theoretical results for this dynamic setting are relatively limited.
Given a sequence of comparison graphs (G_t)_t on a regular grid, the aim is to recover the latent strength of each item i for each time t. We study an extension of the classic BTL (Bradley-Terry-Luce) model under a Lipschitz-type smoothness assumption, and the Translation Synchronization problem in this dynamic setting under a more global smoothness assumption. We discuss theoretical error bounds for each proposed estimators. Experiments on synthetic and real datasets complement these findings.