We seek a computationally efficient model for a collection of time series arising from multiple interacting entities (a.k.a. "agents"). Recent models of spatiotemporal 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.

翻译：本文旨在为多交互实体（亦称“智能体”）产生的时间序列集合构建计算高效的模型。现有针对个体间时空模式的建模方法未能纳入显式的系统级集体行为，而此类行为可能影响个体实体的轨迹。为弥补这一空白，我们提出一种新的分层切换状态模型，该模型可通过无监督训练同时学习系统级与个体级动态。我们采用一个潜在系统级离散状态马尔可夫链，该链对潜在实体级链施加自上而下的影响，进而控制每个观测时间序列的生成。观测值在实体与系统两个层面向潜在链的循环反馈，使得近期情境信息能以自下而上的方式影响所有层级的动态演化。我们假设，在群体动态中同时纳入自上而下与自下而上的影响将提升所学动态的可解释性，并降低预测误差。所提出的分层切换循环动态模型可通过闭式变分坐标上升更新进行学习，其计算复杂度随实体数量线性增长，渐近计算成本不高于为每个实体单独拟合模型。对合成数据及真实篮球队伍移动轨迹的分析表明，与需要更多计算资源的大型神经网络模型相比，我们提出的精简参数模型能够实现具有竞争力的预测性能。在士兵数据及包含64个协作实体的合成任务上的进一步实验证明，该方法能够随时间推移产生对团队动态的可解释性洞察。