# Learning interaction rules from multi-animal trajectories via augmented behavioral models

arXiv: https://arxiv.org/abs/2107.05326 · HTML: https://mlsanity.com/paper/2107.05326/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 26 of its 98 references that are in the map.
- First posted on arXiv 12 Jul 2021.

## Builds on (most cited first, 26 of 26)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Social GAN: Socially Acceptable Trajectories with Generative Adversarial Networks](https://mlsanity.com/paper/1803.10892/) (2018)
- [Towards Robust Interpretability with Self-Explaining Neural Networks](https://mlsanity.com/paper/1806.07538/) (2018)
- [ChauffeurNet: Learning to Drive by Imitating the Best and Synthesizing the Worst](https://mlsanity.com/paper/1812.03079/) (2018)
- [Neural Relational Inference for Interacting Systems](https://mlsanity.com/paper/1802.04687/) (2018)
- [Markerless tracking of user-defined features with deep learning](https://mlsanity.com/paper/1804.03142/) (2018)
- [PRECOG: PREdiction Conditioned On Goals in Visual Multi-Agent Settings](https://mlsanity.com/paper/1905.01296/) (2019)
- [Multiple Futures Prediction](https://mlsanity.com/paper/1911.00997/) (2019)
- [Theory-guided Data Science: A New Paradigm for Scientific Discovery from Data](https://mlsanity.com/paper/1612.08544/) (2016)
- [Composing graphical models with neural networks for structured representations and fast inference](https://mlsanity.com/paper/1603.06277/) (2016)
- [Amortized Causal Discovery: Learning to Infer Causal Graphs from Time-Series Data](https://mlsanity.com/paper/2006.10833/) (2020)
- [Coordinated Multi-Agent Imitation Learning](https://mlsanity.com/paper/1703.03121/) (2017)
- [Economy Statistical Recurrent Units For Inferring Nonlinear Granger Causality](https://mlsanity.com/paper/1911.09879/) (2019)
- [VAIN: Attentional Multi-agent Predictive Modeling](https://mlsanity.com/paper/1706.06122/) (2017)
- [Interpretable Models for Granger Causality Using Self-explaining Neural Networks](https://mlsanity.com/paper/2101.07600/) (2021)
- [Social Attention for Autonomous Decision-Making in Dense Traffic](https://mlsanity.com/paper/1911.12250/) (2019)
- [SimGANs: Simulator-Based Generative Adversarial Networks for ECG Synthesis to Improve Deep ECG Classification](https://mlsanity.com/paper/2006.15353/) (2020)
- [Generating Long-term Trajectories Using Deep Hierarchical Networks](https://mlsanity.com/paper/1706.07138/) (2017)
- [Neural Granger Causality](https://mlsanity.com/paper/1802.05842/) (2018)
- [Learning recurrent representations for hierarchical behavior modeling](https://mlsanity.com/paper/1611.00094/) (2016)
- [Discovering Nonlinear Relations with Minimum Predictive Information Regularization](https://mlsanity.com/paper/2001.01885/) (2020)
- [In reply to Faes et al. and Barnett et al. regarding "A study of problems encountered in Granger causality analysis from a neuroscience perspective"](https://mlsanity.com/paper/1709.10248/) (2017)
- [Scalable Matrix-valued Kernel Learning for High-dimensional Nonlinear Multivariate Regression and Granger Causality](https://mlsanity.com/paper/1408.2066/) (2014)
- [Dynamic mode decomposition in vector-valued reproducing kernel Hilbert spaces for extracting dynamical structure among observables](https://mlsanity.com/paper/1808.10551/) (2018)
- [The Long Road to Computational Location Privacy: A Survey](https://mlsanity.com/paper/1810.03568/) (2018)
- [Validity of time reversal for testing Granger causality](https://mlsanity.com/paper/1509.07636/) (2015)

## Built on by (most cited first, 5 of 5)

- [Interpretable Machine Learning in Physics: A Review](https://mlsanity.com/paper/2503.23616/) (2025)
- [Estimating counterfactual treatment outcomes over time in complex multiagent scenarios](https://mlsanity.com/paper/2206.01900/) (2022)
- [Adaptive action supervision in reinforcement learning from real-world multi-agent demonstrations](https://mlsanity.com/paper/2305.13030/) (2023)
- [Learning Heterogeneous Interaction Strengths by Trajectory Prediction with Graph Neural Network](https://mlsanity.com/paper/2208.13179/) (2022)
- [Relax, it doesn't matter how you get there: A new self-supervised approach for multi-timescale behavior analysis](https://mlsanity.com/paper/2303.08811/) (2023)

## Abstract (arXiv)

Extracting the interaction rules of biological agents from movement sequences pose challenges in various domains. Granger causality is a practical framework for analyzing the interactions from observed time-series data; however, this framework ignores the structures and assumptions of the generative process in animal behaviors, which may lead to interpretational problems and sometimes erroneous assessments of causality. In this paper, we propose a new framework for learning Granger causality from multi-animal trajectories via augmented theory-based behavioral models with interpretable data-driven models. We adopt an approach for augmenting incomplete multi-agent behavioral models described by time-varying dynamical systems with neural networks. For efficient and interpretable learning, our model leverages theory-based architectures separating navigation and motion processes, and the theory-guided regularization for reliable behavioral modeling. This can provide interpretable signs of Granger-causal effects over time, i.e., when specific others cause the approach or separation. In experiments using synthetic datasets, our method achieved better performance than various baselines. We then analyzed multi-animal datasets of mice, flies, birds, and bats, which verified our method and obtained novel biological insights.