We seek to model a collection of time series arising from multiple entities interacting over the same time period. Recent work focused on modeling individual time series is inadequate for our intended applications, where collective system-level behavior influences the trajectories of individual entities. To address such problems, we present a new hierarchical switching-state model that can be trained in an unsupervised fashion to simultaneously explain both system-level and individual-level dynamics. We employ a latent system-level discrete state Markov chain that drives latent entity-level chains which in turn govern the dynamics of each observed time series. Feedback from the observations to the chains at both the entity and system levels improves flexibility via context-dependent state transitions. Our hierarchical switching recurrent dynamical models can be learned via closed-form variational coordinate ascent updates to all latent chains that scale linearly in the number of individual time series. This is asymptotically no more costly than fitting separate models for each entity. Experiments on synthetic and real datasets show that our model can produce better forecasts of future entity behavior than existing methods. Moreover, the availability of latent state chains at both the entity and system level enables interpretation of group dynamics.

翻译：我们旨在对来自多个实体在同一时间段内交互产生的时间序列集合进行建模。现有研究侧重于对单个时间序列进行建模，这不足以应对我们的目标应用场景——在这些场景中，系统层面的集体行为会影响各实体的轨迹。为解决此类问题，我们提出了一种新的分层切换状态模型，该模型能够以无监督方式训练，同时解释系统层面和个体层面的动态。我们采用一个潜在的系统级离散状态马尔可夫链，驱动潜在的实体级链，进而控制每个观测时间序列的动态。观测结果对实体级和系统级链的反馈通过依赖上下文的状态转换提高了模型灵活性。我们的分层切换循环动态模型可通过闭式变分坐标上升更新所有潜在链进行学习，其计算复杂度与个体时间序列数量呈线性关系，渐近意义上与为每个实体单独拟合模型的成本相当。在合成数据集和真实数据集上的实验表明，与现有方法相比，我们的模型能更好地预测未来实体行为。此外，实体级和系统级潜在状态链的可用性使我们能够解释群体动态。