# A State-Space Perspective on Modelling and Inference for Online Skill Rating

arXiv: https://arxiv.org/abs/2308.02414 · HTML: https://mlsanity.com/paper/2308.02414/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 66 references that are in the map.
- First posted on arXiv 4 Aug 2023.

## Builds on (most cited first, 10 of 10)

- [Expectation Propagation for approximate Bayesian inference](https://mlsanity.com/paper/1301.2294/) (2013)
- [Bayesian Workflow](https://mlsanity.com/paper/2011.01808/) (2020)
- [On Particle Methods for Parameter Estimation in State-Space Models](https://mlsanity.com/paper/1412.8695/) (2014)
- [Online Natural Gradient as a Kalman Filter](https://mlsanity.com/paper/1703.00209/) (2017)
- [On backward smoothing algorithms](https://mlsanity.com/paper/2207.00976/) (2022)
- [Modelling Competitive Sports: Bradley-Terry-'ElHo Models for Supervised and On-Line Learning of Paired Competition Outcomes](https://mlsanity.com/paper/1701.08055/) (2017)
- [Simplified Kalman filter for online rating: one-fits-all approach](https://mlsanity.com/paper/2104.14012/) (2021)
- [Exploiting locality in high-dimensional factorial hidden Markov models](https://mlsanity.com/paper/1902.01639/) (2019)
- [Approximate Smoothing and Parameter Estimation in High-Dimensional State-Space Models](https://mlsanity.com/paper/1606.08650/) (2016)
- [Online Particle Smoothing with Application to Map-matching](https://mlsanity.com/paper/2012.04602/) (2020)

## Built on by (most cited first, 2 of 2)

- [Scalable Bayesian Learning with posteriors](https://mlsanity.com/paper/2406.00104/) (2024)
- [An Analysis of Elo Rating Systems via Markov Chains](https://mlsanity.com/paper/2406.05869/) (2024)

## Abstract (arXiv)

We summarise popular methods used for skill rating in competitive sports, along with their inferential paradigms and introduce new approaches based on sequential Monte Carlo and discrete hidden Markov models. We advocate for a state-space model perspective, wherein players' skills are represented as time-varying, and match results serve as observed quantities. We explore the steps to construct the model and the three stages of inference: filtering, smoothing and parameter estimation. We examine the challenges of scaling up to numerous players and matches, highlighting the main approximations and reductions which facilitate statistical and computational efficiency. We additionally compare approaches in a realistic experimental pipeline that can be easily reproduced and extended with our open-source Python package, https://github.com/SamDuffield/abile.