Recently Chen and Poor initiated the study of learning mixtures of linear dynamical systems. While linear dynamical systems already have wide-ranging applications in modeling time-series data, using mixture models can lead to a better fit or even a richer understanding of underlying subpopulations represented in the data. In this work we give a new approach to learning mixtures of linear dynamical systems that is based on tensor decompositions. As a result, our algorithm succeeds without strong separation conditions on the components, and can be used to compete with the Bayes optimal clustering of the trajectories. Moreover our algorithm works in the challenging partially-observed setting. Our starting point is the simple but powerful observation that the classic Ho-Kalman algorithm is a close relative of modern tensor decomposition methods for learning latent variable models. This gives us a playbook for how to extend it to work with more complicated generative models.

翻译：近期Chen与Poor开创了线性动力系统混合模型的学习研究。尽管线性动力系统已广泛用于时间序列数据建模，但采用混合模型不仅能提升拟合效果，更能深入理解数据中潜在子群体的结构特征。本研究提出基于张量分解的线性动力系统混合模型学习新方法。该方法无需对组件设置严格分离条件，即可实现轨迹的贝叶斯最优聚类，且能应用于部分观测的复杂场景。我们的出发点是基于一个简洁而有力的观察：经典Ho-Kalman算法与现代用于隐变量模型学习的张量分解方法存在密切关联。这种关联为我们提供了如何将该算法拓展至更复杂生成模型的研究范式。