• Corpus ID: 239050145

The Performance of the MLE in the Bradley-Terry-Luce Model in $\ell_{\infty}$-Loss and under General Graph Topologies

@inproceedings{Li2021ThePO,
  title={The Performance of the MLE in the Bradley-Terry-Luce Model in \$\ell\_\{\infty\}\$-Loss and under General Graph Topologies},
  author={Wanshan Li and Shamindra Shrotriya and Alessandro Rinaldo},
  year={2021}
}
The Bradley-Terry-Luce (BTL) model is a popular statistical approach for estimating the global ranking of a collection of items of interest using pairwise comparisons. To ensure accurate ranking, it is essential to obtain precise estimates of the model parameters in the `∞-loss. The difficulty of this task depends crucially on the topology of the pairwise comparison graph over the given items. However, beyond very few well-studied cases, such as the complete and Erdös-Rényi comparison graphs… 

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References

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Estimation from Pairwise Comparisons: Sharp Minimax Bounds with Topology Dependence
TLDR
This work considers parametric ordinal models for pairwise comparison data involving a latent vector w* e Rd that represents the "qualities" of the d items being compared; this class of models includes the two most widely used parametric models|the Bradley-Terry-Luce (BTL) and the Thurstone models.
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Given partially observed pairwise comparison data generated by the Bradley-Terry-Luce (BTL) model, we study the problem of top-$k$ ranking. That is, to optimally identify the set of top-$k$ players.
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TLDR
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TLDR
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TLDR
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TLDR
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TLDR
This paper designs a provably faster spectral ranking algorithm, which it is called accelerated spectral ranking (ASR), that is also consistent under the MNL/BTL models, and gives the first general sample complexity bounds for recovering the parameters of theMNL model from multiway comparisons under any (connected) comparison graph.
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TLDR
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MM algorithms for generalized Bradley-Terry models
The Bradley-Terry model for paired comparisons is a simple and muchstudied means to describe the probabilities of the possible outcomes when individuals are judged against one another in pairs. Among
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