Nonparametric Estimation in the Dynamic Bradley-Terry Model

Heejong Bong, Wanshan Li, Shamindra Shrotriya, Alessandro Rinaldo
Proceedings of the Twenty Third International Conference on Artificial Intelligence and Statistics, PMLR 108:3317-3326, 2020.

Abstract

We propose a time-varying generalization of the Bradley-Terry model that allows for nonparametric modeling of dynamic global rankings of distinct teams. We develop a novel estimator that relies on kernel smoothing to pre-process the pairwise comparisons over time and is applicable in sparse settings where the Bradley-Terry may not be fit. We obtain necessary and sufficient conditions for the existence and uniqueness of our estimator. We also derive time-varying oracle bounds for both the estimation error and the excess risk in the model-agnostic setting where the Bradley-Terry model is not necessarily the true data generating process. We thoroughly test the practical effectiveness of our model using both simulated and real world data and suggest an efficient data-driven approach for bandwidth tuning.

Cite this Paper

BibTeX
@InProceedings{pmlr-v108-bong20a, title = {Nonparametric Estimation in the Dynamic Bradley-Terry Model}, author = {Bong, Heejong and Li, Wanshan and Shrotriya, Shamindra and Rinaldo, Alessandro}, booktitle = {Proceedings of the Twenty Third International Conference on Artificial Intelligence and Statistics}, pages = {3317--3326}, year = {2020}, editor = {Chiappa, Silvia and Calandra, Roberto}, volume = {108}, series = {Proceedings of Machine Learning Research}, month = {26--28 Aug}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v108/bong20a/bong20a.pdf}, url = {https://proceedings.mlr.press/v108/bong20a.html}, abstract = {We propose a time-varying generalization of the Bradley-Terry model that allows for nonparametric modeling of dynamic global rankings of distinct teams. We develop a novel estimator that relies on kernel smoothing to pre-process the pairwise comparisons over time and is applicable in sparse settings where the Bradley-Terry may not be fit. We obtain necessary and sufficient conditions for the existence and uniqueness of our estimator. We also derive time-varying oracle bounds for both the estimation error and the excess risk in the model-agnostic setting where the Bradley-Terry model is not necessarily the true data generating process. We thoroughly test the practical effectiveness of our model using both simulated and real world data and suggest an efficient data-driven approach for bandwidth tuning.} }
Endnote
%0 Conference Paper %T Nonparametric Estimation in the Dynamic Bradley-Terry Model %A Heejong Bong %A Wanshan Li %A Shamindra Shrotriya %A Alessandro Rinaldo %B Proceedings of the Twenty Third International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2020 %E Silvia Chiappa %E Roberto Calandra %F pmlr-v108-bong20a %I PMLR %P 3317--3326 %U https://proceedings.mlr.press/v108/bong20a.html %V 108 %X We propose a time-varying generalization of the Bradley-Terry model that allows for nonparametric modeling of dynamic global rankings of distinct teams. We develop a novel estimator that relies on kernel smoothing to pre-process the pairwise comparisons over time and is applicable in sparse settings where the Bradley-Terry may not be fit. We obtain necessary and sufficient conditions for the existence and uniqueness of our estimator. We also derive time-varying oracle bounds for both the estimation error and the excess risk in the model-agnostic setting where the Bradley-Terry model is not necessarily the true data generating process. We thoroughly test the practical effectiveness of our model using both simulated and real world data and suggest an efficient data-driven approach for bandwidth tuning.
APA
Bong, H., Li, W., Shrotriya, S. & Rinaldo, A.. (2020). Nonparametric Estimation in the Dynamic Bradley-Terry Model. Proceedings of the Twenty Third International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 108:3317-3326 Available from https://proceedings.mlr.press/v108/bong20a.html.

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