Trajectory Imputation in Multi-Agent Sports with Derivative-Accumulating Self-Ensemble

TL;DR

This paper introduces MIDAS, a novel neural network framework that accurately imputes missing multi-agent trajectories in sports data by predicting positions, velocities, and accelerations, and combining estimates through a learnable ensemble.

Contribution

The paper presents MIDAS, a new derivative-accumulating self-ensemble method that improves trajectory imputation accuracy and physical plausibility in multi-agent sports scenarios.

Findings

MIDAS outperforms existing methods in positional accuracy.

MIDAS produces more physically plausible trajectories.

Demonstrates applicability to downstream sports analytics tasks.

Abstract

Multi-agent trajectory data collected from domains such as team sports often suffer from missing values due to various factors. While many imputation methods have been proposed for spatiotemporal data, they are not well-suited for multi-agent sports scenarios where player movements are highly dynamic and inter-agent interactions continuously evolve. To address these challenges, we propose MIDAS (Multi-agent Imputer with Derivative-Accumulating Self-ensemble), a framework that imputes multi-agent trajectories with high accuracy and physical plausibility. It jointly predicts positions, velocities, and accelerations through a Set Transformer-based neural network and generates alternative estimates by recursively accumulating predicted velocity and acceleration values. These predictions are then combined using a learnable weighted ensemble to produce final imputed trajectories. Experiments on three sports datasets demonstrate that MIDAS significantly outperforms existing baselines in both positional accuracy and physical plausibility. Lastly, we showcase use cases of MIDAS, such as approximating total distance and pass success probability, to highlight its applicability to practical downstream tasks that require complete tracking data.