Contextual movement models based on normalizing flows

Abstract

Movement models predict positions of players (or objects in general) over time and are thus key to analyzing spatiotemporal data as it is often used in sports analytics. Existing movement models are either designed from physical principles or are entirely data-driven. However, the former suffers from oversimplifications to achieve feasible and interpretable models, while the latter relies on computationally costly, from a current point of view, nonparametric density estimations and require maintaining multiple estimators, each responsible for different types of movements (e.g., such as different velocities). In this paper, we propose a unified contextual probabilistic movement model based on normalizing flows. Our approach learns the desired densities by directly optimizing the likelihood and maintains only a single contextual model that can be conditioned on auxiliary variables. Training is simultaneously performed on all observed types of movements, resulting in an effective and efficient movement model. We empirically evaluate our approach on spatiotemporal data from professional soccer. Our findings show that our approach outperforms the state of the art while being orders of magnitude more efficient with respect to computation time and memory requirements.