{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/dynamic-ranking-with-the-btl-model-a-nearest","title":"Dynamic Ranking with the BTL Model: A Nearest Neighbor based Rank Centrality Method","arxiv_id":"2109.13743","date":"2021-09-28","proceeding":null,"authors":["Eglantine Karlé","Hemant Tyagi"],"abstract":"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 $(G_{t'})_{t' \\in \\mathcal{T}}$ on a regular grid $\\mathcal{T} \\subset [0,1]$, we aim at recovering the latent strengths of the items $w_t^* \\in \\mathbb{R}^n$ at any time $t \\in [0,1]$. 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 $(G_{t'})_{t' \\in \\mathcal{T}}$ is a sequence of Erd\\\"os-Renyi graphs, we provide non-asymptotic $\\ell_2$ and $\\ell_{\\infty}$ error bounds for estimating $w_t^*$ which in particular establishes the consistency of this method in terms of $n$, and the grid size $\\lvert\\mathcal{T}\\rvert$. We also complement our theoretical analysis with experiments on real and synthetic data.","url_abs":"https://arxiv.org/abs/2109.13743v2","url_pdf":"https://arxiv.org/pdf/2109.13743v2.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"dynamic-ranking-with-the-btl-model-a-nearest","repo_url":"https://github.com/karle-eglantine/Dynamic_Rank_Centrality","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[{"task_slug":"recommendation-systems","task_name":"Recommendation Systems"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}