Learning Mixtures of Linear Dynamical Systems
ICML• 2022
Abstract
We study the problem of learning a mixture of multiple linear dynamical
systems (LDSs) from unlabeled short sample trajectories, each generated by one
of the LDS models. Despite the wide applicability of mixture models for
time-series data, learning algorithms that come with end-to-end performance
guarantees are largely absent from existing literature. There are multiple
sources of technical challenges, including but not limited to (1) the presence
of latent variables (i.e. the unknown labels of trajectories); (2) the
possibility that the sample trajectories might have lengths much smaller than
the dimension of the LDS models; and (3) the complicated temporal
dependence inherent to time-series data. To tackle these challenges, we develop
a two-stage meta-algorithm, which is guaranteed to efficiently recover each
ground-truth LDS model up to error , where is the
total sample size. We validate our theoretical studies with numerical
experiments, confirming the efficacy of the proposed algorithm.