mlsanityData to 14 Oct 2026

Learning Linear Dynamical Systems via Spectral Filtering

arXiv 1711.00946 ↗First posted 2 Nov 2017cs.LG cs.SY eess.SYcited by 46

Not on the map. Why?

Abstract (arXiv)

We present an efficient and practical algorithm for the online prediction of discrete-time linear dynamical systems with a symmetric transition matrix. We circumvent the non-convex optimization problem using improper learning: carefully overparameterize the class of LDSs by a polylogarithmic factor, in exchange for convexity of the loss functions. From this arises a polynomial-time algorithm with a near-optimal regret guarantee, with an analogous sample complexity bound for agnostic learning. Our algorithm is based on a novel filtering technique, which may be of independent interest: we convolve the time series with the eigenvectors of a certain Hankel matrix.

Key facts. Cited by 46 papers in the map (data through 14 Oct 2026). First posted on arXiv 2 Nov 2017.

Builds on

No reference list yet.

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2021: 5; 2022: 4; 2023: 7; 2024: 10; 2025: 11; 2026: 9.

46 papers.

Sort:

  1. 2023Long-term Forecasting with TiDE: Time-series Dense Encodercited by 332
  2. 2023A New Approach to Learning Linear Dynamical Systemscited by 23
  3. 2023Spectral State Space Modelscited by 21
  4. 2021Streaming Linear System Identification with Reverse Experience Replaycited by 17
  5. 2022Finite Sample Identification of Bilinear Dynamical Systemscited by 12
  6. 2023Tensor Decompositions Meet Control Theory: Learning General Mixtures of Linear Dynamical Systemscited by 10
  7. 2024Online Linear Regression in Dynamic Environments via Discountingcited by 10
  8. 2023Smoothed Online Learning for Prediction in Piecewise Affine Systemscited by 9
  9. 2024Flash STU: Fast Spectral Transform Unitscited by 7
  10. 2024FutureFill: Fast Generation from Convolutional Sequence Modelscited by 7
  11. 2021Regret Analysis of Distributed Online LQR Control for Unknown LTI Systemscited by 6
  12. 2024Learning Linear Dynamics from Bilinear Observationscited by 6
34 more
  1. 2025Universal Sequence Preconditioningcited by 6
  2. 2023Oracle-Efficient Smoothed Online Learning for Piecewise Continuous Decision Makingcited by 5
  3. 2025Finite Sample Identification of Partially Observed Bilinear Dynamical Systemscited by 5
  4. 2025Universal Learning of Nonlinear Dynamicscited by 5
  5. 2025Research Program: Theory of Learning in Dynamical Systemscited by 5
  6. 2021Time varying regression with hidden linear dynamicscited by 4
  7. 2022Fairness in Forecasting of Observations of Linear Dynamical Systemscited by 4
  8. 2025Model-free Online Learning for the Kalman Filter: Forgetting Factor and Logarithmic Regretcited by 4
  9. 2024Online Control in Population Dynamicscited by 3
  10. 2024Combining Federated Learning and Control: A Surveycited by 3
  11. 2024Long-Context Linear System Identificationcited by 3
  12. 2024Provable Length Generalization in Sequence Prediction via Spectral Filteringcited by 3
  13. 2025UnHiPPO: Uncertainty-aware Initialization for State Space Modelscited by 3
  14. 2026Continuous Latent Contexts Enable Efficient Online Learning in Transformerscited by 3
  15. 2025A New Approach to Controlling Linear Dynamical Systemscited by 2
  16. 2026Spectral Filtering for Complex Linear Dynamical Systemscited by 2
  17. 2026Elastic Spectral State Space Models for Train-Once Budgeted Inferencecited by 2
  18. 2021Scalable Balanced Training of Conditional Generative Adversarial Neural Networks on Image Datacited by 1
  19. 2024The Complexity of Sequential Prediction in Dynamical Systemscited by 1
  20. 2025SpectraLDS: Provable Distillation for Linear Dynamical Systemscited by 1
  21. 2025Logarithmic Regret and Polynomial Scaling in Online Multi-step-ahead Predictioncited by 1
  22. 2026The Power of Second Order Methods for Sequence Preconditioningcited by 1
  23. 2021ast2vec: Utilizing Recursive Neural Encodings of Python Programscited by 0
  24. 2022Stable Parallel Training of Wasserstein Conditional Generative Adversarial Neural Networkscited by 0
  25. 2022Linear RNNs Provably Learn Linear Dynamic Systemscited by 0
  26. 2023Spectral learning of Bernoulli linear dynamical systems modelscited by 0
  27. 2024Approximated Orthogonal Projection Unit: Stabilizing Regression Network Training Using Natural Gradientcited by 0
  28. 2025Efficient Spectral Control of Partially Observed Linear Dynamical Systemscited by 0
  29. 2025Transductive and Learning-Augmented Online Regressioncited by 0
  30. 2026SFO: Learning PDE Operators via Spectral Filteringcited by 0
  31. 2026Online Nonstochastic Prediction: Logarithmic Regret via Predictive Online Least Squarescited by 0
  32. 2026A Memory Efficient Unified Algorithm for Online Learning of Linear Dynamical Systemscited by 0
  33. 2026A Spectral Filtering Approach to Regret Analysis of Distributed Online Control for Linear Dynamical Systemscited by 0
  34. 2026Spectral Distillation: From Nonlinear Dynamics to Linear State-Space Modelscited by 0