# Discovering group dynamics in coordinated time series via hierarchical recurrent switching-state models

arXiv: https://arxiv.org/abs/2401.14973 · HTML: https://mlsanity.com/paper/2401.14973/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 22 of its 65 references that are in the map.
- First posted on arXiv 26 Jan 2024.

## Builds on (most cited first, 22 of 22)

- [Efficiently Modeling Long Sequences with Structured State Spaces](https://mlsanity.com/paper/2111.00396/) (2021)
- [Variational Inference: A Review for Statisticians](https://mlsanity.com/paper/1601.00670/) (2016)
- [Learning to Simulate Complex Physics with Graph Networks](https://mlsanity.com/paper/2002.09405/) (2020)
- [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)
- [Structured Inference Networks for Nonlinear State Space Models](https://mlsanity.com/paper/1609.09869/) (2016)
- [GroupNet: Multiscale Hypergraph Neural Networks for Trajectory Prediction with Relational Reasoning](https://mlsanity.com/paper/2204.08770/) (2022)
- [Amortized Causal Discovery: Learning to Infer Causal Graphs from Time-Series Data](https://mlsanity.com/paper/2006.10833/) (2020)
- [Generating Multi-Agent Trajectories using Programmatic Weak Supervision](https://mlsanity.com/paper/1803.07612/) (2018)
- [The Multi-Agent Behavior Dataset: Mouse Dyadic Social Interactions](https://mlsanity.com/paper/2104.02710/) (2021)
- [Tree-Structured Recurrent Switching Linear Dynamical Systems for Multi-Scale Modeling](https://mlsanity.com/paper/1811.12386/) (2018)
- [Collapsed Amortized Variational Inference for Switching Nonlinear Dynamical Systems](https://mlsanity.com/paper/1910.09588/) (2019)
- [Deep Explicit Duration Switching Models for Time Series](https://mlsanity.com/paper/2110.13878/) (2021)
- [Discovering Nonlinear Relations with Minimum Predictive Information Regularization](https://mlsanity.com/paper/2001.01885/) (2020)
- [Factorised Neural Relational Inference for Multi-Interaction Systems](https://mlsanity.com/paper/1905.08721/) (2019)
- [Deep Switching Auto-Regressive Factorization:Application to Time Series Forecasting](https://mlsanity.com/paper/2009.05135/) (2020)
- [Stochastic Variational Inference for Hidden Markov Models](https://mlsanity.com/paper/1411.1670/) (2014)
- [baller2vec++: A Look-Ahead Multi-Entity Transformer For Modeling Coordinated Agents](https://mlsanity.com/paper/2104.11980/) (2021)
- [Graph Switching Dynamical Systems](https://mlsanity.com/paper/2306.00370/) (2023)
- [Variational Inference and Learning of Piecewise-linear Dynamical Systems](https://mlsanity.com/paper/2006.01668/) (2020)
- [Joint modeling of multiple time series via the beta process with application to motion capture segmentation](https://mlsanity.com/paper/1308.4747/) (2013)
- [Deep Switching State Space Model (DS3M) for Nonlinear Time Series Forecasting with Regime Switching](https://mlsanity.com/paper/2106.02329/) (2021)

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

- [Locating acts of mechanistic reasoning in student team conversations with mechanistic machine learning](https://mlsanity.com/paper/2604.21870/) (2026)

## Abstract (arXiv)

We seek a computationally efficient model for a collection of time series arising from multiple interacting entities (a.k.a. "agents"). Recent models of temporal patterns across individuals fail to incorporate explicit system-level collective behavior that can influence the trajectories of individual entities. To address this gap in the literature, we present a new hierarchical switching-state model that can be trained in an unsupervised fashion to simultaneously learn both system-level and individual-level dynamics. We employ a latent system-level discrete state Markov chain that provides top-down influence on latent entity-level chains which in turn govern the emission of each observed time series. Recurrent feedback from the observations to the latent chains at both entity and system levels allows recent situational context to inform how dynamics unfold at all levels in bottom-up fashion. We hypothesize that including both top-down and bottom-up influences on group dynamics will improve interpretability of the learned dynamics and reduce error when forecasting. Our hierarchical switching recurrent dynamical model can be learned via closed-form variational coordinate ascent updates to all latent chains that scale linearly in the number of entities. This is asymptotically no more costly than fitting a separate model for each entity. Analysis of both synthetic data and real basketball team movements suggests our lean parametric model can achieve competitive forecasts compared to larger neural network models that require far more computational resources. Further experiments on soldier data as well as a synthetic task with 64 cooperating entities show how our approach can yield interpretable insights about team dynamics over time.