# Enhancing Trajectory Prediction using Sparse Outputs: Application to Team Sports

arXiv: https://arxiv.org/abs/2106.00173 · HTML: https://mlsanity.com/paper/2106.00173/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 46 references that are in the map.
- First posted on arXiv 1 Jun 2021.

## Builds on (most cited first, 20 of 20)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [Sequence to Sequence Learning with Neural Networks](https://mlsanity.com/paper/1409.3215/) (2014)
- [Neural Machine Translation of Rare Words with Subword Units](https://mlsanity.com/paper/1508.07909/) (2015)
- [Identity Mappings in Deep Residual Networks](https://mlsanity.com/paper/1603.05027/) (2016)
- [WaveNet: A Generative Model for Raw Audio](https://mlsanity.com/paper/1609.03499/) (2016)
- [Relational inductive biases, deep learning, and graph networks](https://mlsanity.com/paper/1806.01261/) (2018)
- [Social GAN: Socially Acceptable Trajectories with Generative Adversarial Networks](https://mlsanity.com/paper/1803.10892/) (2018)
- [Bidirectional LSTM-CRF Models for Sequence Tagging](https://mlsanity.com/paper/1508.01991/) (2015)
- [A Recurrent Latent Variable Model for Sequential Data](https://mlsanity.com/paper/1506.02216/) (2015)
- [DESIRE: Distant Future Prediction in Dynamic Scenes with Interacting Agents](https://mlsanity.com/paper/1704.04394/) (2017)
- [An LSTM Network for Highway Trajectory Prediction](https://mlsanity.com/paper/1801.07962/) (2018)
- [What the Constant Velocity Model Can Teach Us About Pedestrian Motion Prediction](https://mlsanity.com/paper/1903.07933/) (2019)
- [Coordinated Multi-Agent Imitation Learning](https://mlsanity.com/paper/1703.03121/) (2017)
- [Generating Multi-Agent Trajectories using Programmatic Weak Supervision](https://mlsanity.com/paper/1803.07612/) (2018)
- [Particle-based pedestrian path prediction using LSTM-MDL models](https://mlsanity.com/paper/1804.05546/) (2018)

## Built on by (most cited first, 1 of 1)

- [A Comprehensive Review of Computer Vision in Sports: Open Issues, Future Trends and Research Directions](https://mlsanity.com/paper/2203.02281/) (2022)

## Abstract (arXiv)

Sophisticated trajectory prediction models that effectively mimic team dynamics have many potential uses for sports coaches, broadcasters and spectators. However, through experiments on soccer data we found that it can be surprisingly challenging to train a deep learning model for player trajectory prediction which outperforms linear extrapolation on average distance between predicted and true future trajectories. We propose and test a novel method for improving training by predicting a sparse trajectory and interpolating using constant acceleration, which improves performance for several models. This interpolation can also be used on models that aren't trained with sparse outputs, and we find that this consistently improves performance for all tested models. Additionally, we find that the accuracy of predicted trajectories for a subset of players can be improved by conditioning on the full trajectories of the other players, and that this is further improved when combined with sparse predictions. We also propose a novel architecture using graph networks and multi-head attention (GraN-MA) which achieves better performance than other tested state-of-the-art models on our dataset and is trivially adapted for both sparse trajectories and full-trajectory conditioned trajectory prediction.