mlsanityData to 14 Oct 2026

Learning Mixtures of Linear Dynamical Systems

arXiv 2201.11211 ↗First posted 26 Jan 2022stat.ML cs.LG cs.SYcited by 15

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Abstract (arXiv)

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

Key facts. Cited by 15 papers in the map (data through 14 Oct 2026). Builds on 54 of its 101 references that are in the map. First posted on arXiv 26 Jan 2022.

Builds on

54 of 101 references.

References · 54

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2022: 2; 2023: 4; 2024: 4; 2025: 3; 2026: 2.

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  1. 2022Learning Mixtures of Markov Chains and MDPscited by 12
  2. 2023Tensor Decompositions Meet Control Theory: Learning General Mixtures of Linear Dynamical Systemscited by 10
  3. 2023An Interventional Perspective on Identifiability in Gaussian LTI Systems with Independent Component Analysiscited by 9
  4. 2022Efficient List-Decodable Regression using Batchescited by 5
  5. 2025Conformal Prediction for Time-series Forecasting with Change Pointscited by 5
  6. 2023Linear Regression using Heterogeneous Data Batchescited by 3
  7. 2024Interventional Causal Discovery in a Mixture of DAGscited by 3
  8. 2025A New Approach to Controlling Linear Dynamical Systemscited by 2
  9. 2023Joint Problems in Learning Multiple Dynamical Systemscited by 1
  10. 2024Learning the Topology and Behavior of Discrete Dynamical Systemscited by 1
  11. 2024Finite Sample Analysis of Tensor Decomposition for Learning Mixtures of Linear Systemscited by 1
  12. 2024Efficient PAC Learnability of Dynamical Systems Over Multilayer Networkscited by 0
3 more
  1. 2025Learning Mixtures of Linear Dynamical Systems via Hybrid Tensor-EM Methodcited by 0
  2. 2026Uniform error bounds for quantized dynamical modelscited by 0
  3. 2026Modeling Dynamic Mixtures of Time-Delay Systems from Streaming Time Seriescited by 0