  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.
