TY - JOUR

T1 - Contextual movement models based on normalizing flows

AU - Fadel, Samuel

AU - Mair, Sebastian

AU - da Silva Torres, Ricardo

AU - Brefeld, Ulf

N1 - Funding Information: The authors would like to thank Hendrik Weber, Deutsche Fußball Liga (DFL), and Sportcast GmbH for providing positional data. This research was funded in part by the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES), Brazil, Finance Code 001 and by FAPESP (grants #2018/19350-5, #2017/20945-0, #2016/50250-1, #2017/24005-2, #2019/17729-0, #2015/24494-8). This research was partially funded by the RFF PastOPol project. Publisher Copyright: © 2021, The Author(s).

PY - 2023/3

Y1 - 2023/3

N2 - 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.

AB - 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.

KW - Density estimation

KW - Movement models

KW - Normalizing flows

KW - Soccer data

KW - Spatiotemporal data

KW - Sports analytics

KW - Business informatics

UR - http://www.scopus.com/inward/record.url?scp=85112411875&partnerID=8YFLogxK

UR - https://www.mendeley.com/catalogue/5106630b-09f6-335c-b742-231b1d6e4834/

U2 - 10.1007/s10182-021-00412-w

DO - 10.1007/s10182-021-00412-w

M3 - Journal articles

VL - 107

SP - 51

EP - 72

JO - AStA Advances in Statistical Analysis

JF - AStA Advances in Statistical Analysis

SN - 1863-8171

IS - 1-2

ER -