Weng and Lin 2011 - Bayesian Approximation for Online Ranking
Routing Summary
Full capture of Weng & Lin (JMLR 2011): closed-form online Bayesian skill updates under Bradley-Terry, Thurstone-Mosteller and Plackett-Luce, the Glicko derivation, and Halo 2 results. 7 notes.
- Need the paper on a page or the section map? → Weng and Lin 2011 - Bayesian Online Ranking Overview
- Need ranking models, Elo, the W-Stein identity? → Weng and Lin 2011 - Ranking Models and the W-Stein Approximation
- Need the derivation, error correction, team skills? → Weng and Lin 2011 - Update Rules Derivation and Error Correction
- Need the BT full-pair/partial-pair algorithm and code? → Weng and Lin 2011 - Bradley-Terry Update Algorithms
- Need TM (TrueSkill) or PL rules? → Weng and Lin 2011 - Thurstone-Mosteller and Plackett-Luce Update Rules
- Need Glicko step-by-step? → Weng and Lin 2011 - Glicko Derivation and Comparison with Elo
- Need Tables 2-5? → Weng and Lin 2011 - Halo 2 Experiments and Results
Concept Map
| Concept | Note | Type | Depends On | Key Result |
|---|---|---|---|---|
| W-Stein identity | Weng and Lin 2011 - Ranking Models and the W-Stein Approximation | theorem | Overview | posterior moments from |
| update | Weng and Lin 2011 - Update Rules Derivation and Error Correction | definition | W-Stein | , |
| BT full/partial | Weng and Lin 2011 - Bradley-Terry Update Algorithms | theorem | Elo with uncertain step size | |
| TM / PL | Weng and Lin 2011 - Thurstone-Mosteller and Plackett-Luce Update Rules | theorem | BT | TM k=2 = TrueSkill |
| Glicko | Weng and Lin 2011 - Glicko Derivation and Comparison with Elo | theorem | BT | 5-step approximation |
| Experiments | Weng and Lin 2011 - Halo 2 Experiments and Results | example | all | BT-full ~ TrueSkill, 10x faster |
Notes
- Weng and Lin 2011 - Bayesian Online Ranking Overview — CONTAINS: summary, source map, comparison table.
- Weng and Lin 2011 - Ranking Models and the W-Stein Approximation — CONTAINS: rank notation, TM/BT/PL/Elo definitions, Fig. 1, Lemma 1, Cor. 2.
- Weng and Lin 2011 - Update Rules Derivation and Error Correction — CONTAINS: Eqs. 25-30, error analysis, factorizations, team skill updates.
- Weng and Lin 2011 - Bradley-Terry Update Algorithms — CONTAINS: Algorithms 1-2, worked update, Python.
- Weng and Lin 2011 - Thurstone-Mosteller and Plackett-Luce Update Rules — CONTAINS: Algorithms 3-4, draw margin, safeguards.
- Weng and Lin 2011 - Glicko Derivation and Comparison with Elo — CONTAINS: Glicko steps I-V, Algorithm 5, worked example.
- Weng and Lin 2011 - Halo 2 Experiments and Results — CONTAINS: Tables 2-5, runtime, discussion.
Sources
Weng and Lin 2011 - A Bayesian Approximation Method for Online Ranking