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：近来Chen和Poor开创了对线性动力系统混合模型的学习研究。尽管线性动力系统在时序数据建模中已有广泛应用，但采用混合模型既能实现更优的数据拟合，又能更深入地理解数据所代表的潜在子群体。本文提出了一种基于张量分解的线性动力系统混合模型学习新方法。该方法无需对组件施加严格分离条件，即可与贝叶斯最优轨迹聚类效果相媲美。此外，本算法适用于具有挑战性的部分观测场景。我们的出发点在于一个简单而有力的观察：经典Ho-Kalman算法与现代用于学习潜变量模型的张量分解方法存在密切联系。这为我们拓展该算法以处理更复杂生成模型提供了方法论框架。