Learning Algorithms for Mixtures of Linear Dynamical Systems: A Practical Approach

Abstract

In this work, we give the first implementation of an algorithm to learn a mixture of linear dynamical systems (LDS’s), and an analysis of algorithms to learn a single linear dynamical system. Following the work of Bakshi et al. ([1]), we implement a recent polynomial-time algorithm based on a tensor decomposition with learning guarantees in a general setting, with some simplifications and minor optimizations. Our largest contribution is giving the first expectation-maximization (E-M) algorithm for learning a mixture of LDS’s, and an experimental evaluation against the Tensor Decomposition algorithm. We find that the E-M algorithm performs extremely well, and much better than the Tensor Decomposition algorithm. We analyze performance of these and other algorithms to learn both a single LDS and a mixture of LDS’s under various conditions (such as how much noise is present) and algorithm settings.