Learning Mixtures of Linear Dynamical Systems

Yanxi Chen, H. Vincent Poor

Research output: Contribution to journalConference articlepeer-review

5 Scopus citations

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 d 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 Oe(pd/T), where T is the total sample size. We validate our theoretical studies with numerical experiments, confirming the efficacy of the proposed algorithm.

Original languageEnglish (US)
Pages (from-to)3507-3557
Number of pages51
JournalProceedings of Machine Learning Research
Volume162
StatePublished - 2022
Externally publishedYes
Event39th International Conference on Machine Learning, ICML 2022 - Baltimore, United States
Duration: Jul 17 2022Jul 23 2022

All Science Journal Classification (ASJC) codes

  • Artificial Intelligence
  • Software
  • Control and Systems Engineering
  • Statistics and Probability

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