chl64/ml1--tennis_player_rankings

Machine Learning 1 - Rank tennis players according to their inferred skills, not their game outcomes directly.

Probabilistic Ranking of tennis players

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Given a record of 1801 game outcomes (win or lose) between 107 players, a naive approach to rank these players would be based on how many games each player won, out of all the games they played. The result is named "Empirical Ranking" and shown in the left bar chart.

The problem with Empirical Ranking is that it ignores against whom each player have played. For example, if player X was unfortunate in that he/she had to play against the world's champion in the first round of a tournament, and hence lost (all) his/her game, Empirical Ranking would suggest that X should be ranked last. However X could possibly have had the ability to defeat most players, and should possibly be ranked higher.

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Therefore, a remedy is to infer from all the game outcomes every player's "skill" (the mentioned notion of "ability"), and build a generative model for game outcome between two players. The generative model uses these skills as model parameters to predict a game outcome in the following way:

Finally the players can be ranked according to their average probability of winning, leading to "Probabilistic Ranking":

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Demo above is part of my university coursework. Details of problem statements and analysis can be found in Problems.pdf and Report.pdf respectively, while details of how skills were inferred via Gibbs Sampling and Messaging Passing can be found in the theories folder.