Leszek Szczecinski - Real-time ranking (in sports)

In this talk, we will discuss the problem of ranking from pairwise comparisons, and our target application is ranking in sport competitions.

We will

i) give an overview of the ranking problem, its mathematical formalism, and links to the ranking in sports,

ii) Explain the various modeling strategies used in ranking, especially the modeling of ordinal variables.

iii) Discuss in more detail the problem of approximate statistical inference in the hidden Markov models where the observation equations are non-linear.

iv) Show the Bayesian formulation and its versions suitable for the "large" problems which will lead to an approximate Kalman filter that is generic (applicable irrespectively of the model).

v) Show how the Kalman filter can be used in the context of sport ranking, where the skills of the players/teams are inferred from the observed outcomes of the games. We will also explain how the popular and popular algorithms (such as the Elo, the Glicko, and the TrueSkill algorithms) may be seen as instances of the approach we develop.

vi) We critically compare the known and the new algorithms by means of numerical examples using synthetic as well as empirical data.