PageRank and the Bradley-Terry model
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866913231711240192 |
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| author | Selby, David Antony |
| author_facet | Selby, David Antony |
| contents | PageRank and the Bradley-Terry model are competing approaches to ranking entities such as teams in sports tournaments or journals in citation networks. The Bradley-Terry model is a classical statistical method for ranking based on paired comparisons. The PageRank algorithm ranks nodes according to their importance in a network. Whereas Bradley-Terry scores are computed via maximum likelihood estimation, PageRanks are derived from the stationary distribution of a Markov chain. More recent work has shown maximum likelihood estimates for the Bradley-Terry model may be approximated from such a limiting distribution, an interesting connection that has been discovered and rediscovered over the decades. Here we show - through relatively simple mathematics - a connection between paired comparisons and PageRank that exploits the quasi-symmetry property of the Bradley-Terry model. This motivates a novel interpretation of Bradley-Terry scores as 'scaled' PageRanks, and vice versa, with direct implications for citation-based journal ranking metrics. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_07811 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | PageRank and the Bradley-Terry model Selby, David Antony Methodology PageRank and the Bradley-Terry model are competing approaches to ranking entities such as teams in sports tournaments or journals in citation networks. The Bradley-Terry model is a classical statistical method for ranking based on paired comparisons. The PageRank algorithm ranks nodes according to their importance in a network. Whereas Bradley-Terry scores are computed via maximum likelihood estimation, PageRanks are derived from the stationary distribution of a Markov chain. More recent work has shown maximum likelihood estimates for the Bradley-Terry model may be approximated from such a limiting distribution, an interesting connection that has been discovered and rediscovered over the decades. Here we show - through relatively simple mathematics - a connection between paired comparisons and PageRank that exploits the quasi-symmetry property of the Bradley-Terry model. This motivates a novel interpretation of Bradley-Terry scores as 'scaled' PageRanks, and vice versa, with direct implications for citation-based journal ranking metrics. |
| title | PageRank and the Bradley-Terry model |
| topic | Methodology |
| url | https://arxiv.org/abs/2402.07811 |