Papers › Dynamic Ranking with the BTL Model: A Nearest Neighbor based Rank Centrality Method
Dynamic Ranking with the BTL Model: A Nearest Neighbor based Rank Centrality Method
Eglantine Karlé, Hemant Tyagi
Many applications such as recommendation systems or sports tournaments involve pairwise comparisons within a collection of n items, the goal being to aggregate the binary outcomes of the comparisons in order to recover the latent strength and/or global ranking of the items. In recent years, this problem has received significant interest from a theoretical perspective with a number of methods being proposed, along with associated statistical guarantees under the assumption of a suitable generative model. While these results typically collect the pairwise comparisons as one comparison graph G, however in many applications - such as the outcomes of soccer matches during a tournament - the nature of pairwise outcomes can evolve with time. Theoretical results for such a dynamic setting are relatively limited compared to the aforementioned static setting. We study in this paper an extension of the classic BTL (Bradley-Terry-Luce) model for the static setting to our dynamic setup under the assumption that the probabilities of the pairwise outcomes evolve smoothly over the time domain [0,1]. Given a sequence of comparison graphs (G_(t′))_(t′ ∈𝒯) on a regular grid 𝒯 ⊂[0,1], we aim at recovering the latent strengths of the items wₜ^* ∈ℝⁿ at any time t ∈[0,1]. To this end, we adapt the Rank Centrality method - a popular spectral approach for ranking in the static case - by locally averaging the available data on a suitable neighborhood of t. When (G_(t′))_(t′ ∈𝒯) is a sequence of Erd\"os-Renyi graphs, we provide non-asymptotic ℓ₂ and ℓ_∞ error bounds for estimating wₜ^* which in particular establishes the consistency of this method in terms of n, and the grid size |𝒯|. We also complement our theoretical analysis with experiments on real and synthetic data.
Code
Repository list and official/mentioned flags are the archive's, frozen 2025-07-28. Reachability, where shown, is from one Syntology probe window (2026-09-16 to 2026-09-18); repositories not probed show nothing. GitHub stars are not tracked.
Code Syntology ran Syntology
Not run by Syntology. Nothing on this page verifies that the listed code works.
Tasks
Results from the paper archive 2025-07-28
No leaderboard rows for this paper in the archive.
Report a problem or propose a change · a person checks every report against the paper or source before anything changes; decisions are listed on /corrections