A Spectral Approach for the Dynamic Bradley-Terry Model Article Swipe
Xinyu Tian
,
Jian Shi
,
Xiaotong Shen
,
Kai Song
·
YOU?
·
· 2023
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2307.16642
YOU?
·
· 2023
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2307.16642
The dynamic ranking, due to its increasing importance in many applications, is becoming crucial, especially with the collection of voluminous time-dependent data. One such application is sports statistics, where dynamic ranking aids in forecasting the performance of competitive teams, drawing on historical and current data. Despite its usefulness, predicting and inferring rankings pose challenges in environments necessitating time-dependent modeling. This paper introduces a spectral ranker called Kernel Rank Centrality, designed to rank items based on pairwise comparisons over time. The ranker operates via kernel smoothing in the Bradley-Terry model, utilizing a Markov chain model. Unlike the maximum likelihood approach, the spectral ranker is nonparametric, demands fewer model assumptions and computations, and allows for real-time ranking. We establish the asymptotic distribution of the ranker by applying an innovative group inverse technique, resulting in a uniform and precise entrywise expansion. This result allows us to devise a new inferential method for predictive inference, previously unavailable in existing approaches. Our numerical examples showcase the ranker's utility in predictive accuracy and constructing an uncertainty measure for prediction, leveraging data from the National Basketball Association (NBA). The results underscore our method's potential compared to the gold standard in sports, the Arpad Elo rating system.
Related Topics
Concepts
Computer science
Ranking (information retrieval)
Inference
Pairwise comparison
Nonparametric statistics
Kernel (algebra)
Data mining
Machine learning
Markov chain Monte Carlo
Rank (graph theory)
Smoothing
Artificial intelligence
Econometrics
Mathematics
Bayesian probability
Combinatorics
Computer vision
Metadata
- Type
- preprint
- Language
- en
- Landing Page
- http://arxiv.org/abs/2307.16642
- https://arxiv.org/pdf/2307.16642
- OA Status
- green
- Related Works
- 10
- OpenAlex ID
- https://openalex.org/W4385474370
All OpenAlex metadata
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- OpenAlex ID
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https://openalex.org/W4385474370Canonical identifier for this work in OpenAlex
- DOI
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https://doi.org/10.48550/arxiv.2307.16642Digital Object Identifier
- Title
-
A Spectral Approach for the Dynamic Bradley-Terry ModelWork title
- Type
-
preprintOpenAlex work type
- Language
-
enPrimary language
- Publication year
-
2023Year of publication
- Publication date
-
2023-07-31Full publication date if available
- Authors
-
Xinyu Tian, Jian Shi, Xiaotong Shen, Kai SongList of authors in order
- Landing page
-
https://arxiv.org/abs/2307.16642Publisher landing page
- PDF URL
-
https://arxiv.org/pdf/2307.16642Direct link to full text PDF
- Open access
-
YesWhether a free full text is available
- OA status
-
greenOpen access status per OpenAlex
- OA URL
-
https://arxiv.org/pdf/2307.16642Direct OA link when available
- Concepts
-
Computer science, Ranking (information retrieval), Inference, Pairwise comparison, Nonparametric statistics, Kernel (algebra), Data mining, Machine learning, Markov chain Monte Carlo, Rank (graph theory), Smoothing, Artificial intelligence, Econometrics, Mathematics, Bayesian probability, Combinatorics, Computer visionTop concepts (fields/topics) attached by OpenAlex
- Cited by
-
0Total citation count in OpenAlex
- Related works (count)
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10Other works algorithmically related by OpenAlex
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| abstract_inverted_index.ranking, | 2 |
| abstract_inverted_index.ranking. | 114 |
| abstract_inverted_index.rankings | 51 |
| abstract_inverted_index.showcase | 159 |
| abstract_inverted_index.spectral | 63, 100 |
| abstract_inverted_index.standard | 191 |
| abstract_inverted_index.approach, | 98 |
| abstract_inverted_index.entrywise | 136 |
| abstract_inverted_index.establish | 116 |
| abstract_inverted_index.inferring | 50 |
| abstract_inverted_index.modeling. | 58 |
| abstract_inverted_index.numerical | 157 |
| abstract_inverted_index.potential | 186 |
| abstract_inverted_index.real-time | 113 |
| abstract_inverted_index.resulting | 130 |
| abstract_inverted_index.smoothing | 84 |
| abstract_inverted_index.utilizing | 89 |
| abstract_inverted_index.Basketball | 178 |
| abstract_inverted_index.asymptotic | 118 |
| abstract_inverted_index.challenges | 53 |
| abstract_inverted_index.collection | 17 |
| abstract_inverted_index.especially | 14 |
| abstract_inverted_index.expansion. | 137 |
| abstract_inverted_index.historical | 41 |
| abstract_inverted_index.importance | 7 |
| abstract_inverted_index.increasing | 6 |
| abstract_inverted_index.inference, | 150 |
| abstract_inverted_index.innovative | 126 |
| abstract_inverted_index.introduces | 61 |
| abstract_inverted_index.leveraging | 173 |
| abstract_inverted_index.likelihood | 97 |
| abstract_inverted_index.predicting | 48 |
| abstract_inverted_index.predictive | 149, 164 |
| abstract_inverted_index.previously | 151 |
| abstract_inverted_index.technique, | 129 |
| abstract_inverted_index.underscore | 183 |
| abstract_inverted_index.voluminous | 19 |
| abstract_inverted_index.Association | 179 |
| abstract_inverted_index.Centrality, | 68 |
| abstract_inverted_index.application | 24 |
| abstract_inverted_index.approaches. | 155 |
| abstract_inverted_index.assumptions | 107 |
| abstract_inverted_index.comparisons | 76 |
| abstract_inverted_index.competitive | 37 |
| abstract_inverted_index.forecasting | 33 |
| abstract_inverted_index.inferential | 146 |
| abstract_inverted_index.performance | 35 |
| abstract_inverted_index.prediction, | 172 |
| abstract_inverted_index.statistics, | 27 |
| abstract_inverted_index.unavailable | 152 |
| abstract_inverted_index.uncertainty | 169 |
| abstract_inverted_index.usefulness, | 47 |
| abstract_inverted_index.constructing | 167 |
| abstract_inverted_index.distribution | 119 |
| abstract_inverted_index.environments | 55 |
| abstract_inverted_index.Bradley-Terry | 87 |
| abstract_inverted_index.applications, | 10 |
| abstract_inverted_index.computations, | 109 |
| abstract_inverted_index.necessitating | 56 |
| abstract_inverted_index.nonparametric, | 103 |
| abstract_inverted_index.time-dependent | 20, 57 |
| cited_by_percentile_year | |
| countries_distinct_count | 0 |
| institutions_distinct_count | 4 |
| citation_normalized_percentile |