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Inferring the causal structure of a set of random variables is a crucial problem in many disciplines of science. Over the past two decades, various approaches have been proposed for causal discovery from observational data.

Many real-world prediction problems involve modelling the dependencies between multiple different outputs across the input space. Multi-output Gaussian Processes (MOGP) are a particularly important approach to such problems. In this paper, we build on the Gaussian Process Autoregressive Regression (GPAR) model which is one of the best performing MOGP models, but which fails when observation noise is large, when there are missing data, and when non-Gaussian observation models are required.

We propose a novel ranking model that combines the Bradley-Terry-Luce probability model with a nonnegative matrix factorization framework to model and uncover the presence of latent variables that influence the performance of top tennis players.