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

arXiv: https://arxiv.org/abs/2408.10878 · HTML: https://mlsanity.com/paper/2408.10878/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 32 references that are in the map.
- First posted on arXiv 20 Aug 2024.

## Builds on (most cited first, 18 of 18)

- [Relational inductive biases, deep learning, and graph networks](https://mlsanity.com/paper/1806.01261/) (2018)
- [TimesNet: Temporal 2D-Variation Modeling for General Time Series Analysis](https://mlsanity.com/paper/2210.02186/) (2022)
- [Social GAN: Socially Acceptable Trajectories with Generative Adversarial Networks](https://mlsanity.com/paper/1803.10892/) (2018)
- [CSDI: Conditional Score-based Diffusion Models for Probabilistic Time Series Imputation](https://mlsanity.com/paper/2107.03502/) (2021)
- [Recurrent Neural Networks for Multivariate Time Series with Missing Values](https://mlsanity.com/paper/1606.01865/) (2016)
- [Neural Relational Inference for Interacting Systems](https://mlsanity.com/paper/1802.04687/) (2018)
- [AgentFormer: Agent-Aware Transformers for Socio-Temporal Multi-Agent Forecasting](https://mlsanity.com/paper/2103.14023/) (2021)
- [BRITS: Bidirectional Recurrent Imputation for Time Series](https://mlsanity.com/paper/1805.10572/) (2018)
- [SAITS: Self-Attention-based Imputation for Time Series](https://mlsanity.com/paper/2202.08516/) (2022)
- [Filling the G_ap_s: Multivariate Time Series Imputation by Graph Neural Networks](https://mlsanity.com/paper/2108.00298/) (2021)
- [Estimating Missing Data in Temporal Data Streams Using Multi-directional Recurrent Neural Networks](https://mlsanity.com/paper/1711.08742/) (2017)
- [Learning to Reconstruct Missing Data from Spatiotemporal Graphs with Sparse Observations](https://mlsanity.com/paper/2205.13479/) (2022)
- [NAOMI: Non-Autoregressive Multiresolution Sequence Imputation](https://mlsanity.com/paper/1901.10946/) (2019)
- [ImputeFormer: Low Rankness-Induced Transformers for Generalizable Spatiotemporal Imputation](https://mlsanity.com/paper/2312.01728/) (2023)
- [Uncovering the Missing Pattern: Unified Framework Towards Trajectory Imputation and Prediction](https://mlsanity.com/paper/2303.16005/) (2023)
- [NRTSI: Non-Recurrent Time Series Imputation](https://mlsanity.com/paper/2102.03340/) (2021)
- [Interaction Modeling with Multiplex Attention](https://mlsanity.com/paper/2208.10660/) (2022)
- [Ball Trajectory Inference from Multi-Agent Sports Contexts Using Set Transformer and Hierarchical Bi-LSTM](https://mlsanity.com/paper/2306.08206/) (2023)

## Built on by (most cited first, 3 of 3)

- [Multi-Modal Soccer Scene Analysis with Masked Pre-Training](https://mlsanity.com/paper/2512.19528/) (2025)
- [Training-Free Off-Screen Player Imputation for Broadcast-Based Spatial Football Analytics](https://mlsanity.com/paper/2607.11548/) (2026)
- [PathCRF: Ball-Free Soccer Event Detection via Possession Path Inference from Player Trajectories](https://mlsanity.com/paper/2602.12080/) (2026)

## Abstract (arXiv)

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.