  Understanding agent behaviour in Multi-Agent Systems (MAS) is an important
problem in domains such as autonomous driving, disaster response, and sports
analytics. Existing MAS problems typically use uniform timesteps with
observations for all agents. In this work, we analyse the problem of agent
location imputation, specifically posed in environments with non-uniform
timesteps and limited agent observability (~95% missing values). Our approach
uses Long Short-Term Memory and Graph Neural Network components to learn
temporal and inter-agent patterns to predict the location of all agents at
every timestep. We apply this to the domain of football (soccer) by imputing
the location of all players in a game from sparse event data (e.g., shots and
passes). Our model estimates player locations to within ~6.9m; a ~62% reduction
in error from the best performing baseline. This approach facilitates
downstream analysis tasks such as player physical metrics, player coverage, and
team pitch control. Existing solutions to these tasks often require optical
tracking data, which is expensive to obtain and only available to elite clubs.
By imputing player locations from easy to obtain event data, we increase the
accessibility of downstream tasks.
