mlsanityData to 14 Oct 2026

Time varying regression with hidden linear dynamics

arXiv 2112.14862 ↗First posted 29 Dec 2021math.ST math.OC stat.MLcited by 4

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Abstract (arXiv)

We revisit a model for time-varying linear regression that assumes the unknown parameters evolve according to a linear dynamical system. Counterintuitively, we show that when the underlying dynamics are stable the parameters of this model can be estimated from data by combining just two ordinary least squares estimates. We offer a finite sample guarantee on the estimation error of our method and discuss certain advantages it has over Expectation-Maximization (EM), which is the main approach proposed by prior work.

Key facts. Cited by 4 papers in the map (data through 14 Oct 2026). Builds on 14 of its 38 references that are in the map. First posted on arXiv 29 Dec 2021.

Builds on

14 of 38 references.

References · 14

  1. 2015An Introduction to Matrix Concentration Inequalitiescited by 397
  2. 2018Learning Without Mixing: Towards A Sharp Analysis of Linear System Identificationcited by 158
  3. 2014Statistical guarantees for the EM algorithm: From population to sample-based analysiscited by 133
  4. 2018Near optimal finite time identification of arbitrary linear dynamical systemscited by 89
  5. 2016Gradient Descent Learns Linear Dynamical Systemscited by 79
  6. 2019Finite Sample Analysis of Stochastic System Identificationcited by 67
  7. 2019Learning Linear Dynamical Systems with Semi-Parametric Least Squarescited by 58
  8. 2017Learning Linear Dynamical Systems via Spectral Filteringcited by 46
  9. 2018Spectral Filtering for General Linear Dynamical Systemscited by 37
  10. 2020Active Learning for Identification of Linear Dynamical Systemscited by 33
  11. 2017Non-Asymptotic Analysis of Robust Control from Coarse-Grained Identificationcited by 16
  12. 2019Algorithms for Heavy-Tailed Statistics: Regression, Covariance Estimation, and Beyondcited by 14
2 more
  1. 2019Sample Complexity of Kalman Filtering for Unknown Systemscited by 12
  2. 2020A spectral algorithm for robust regression with subgaussian ratescited by 8

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2022: 1; 2023: 1; 2024: 1; 2025: 0; 2026: 1.

4 papers.

  1. 2023A Stability Principle for Learning under Non-Stationaritycited by 10
  2. 2024Learning Linear Dynamics from Bilinear Observationscited by 6
  3. 2022Cost-Driven Representation Learning for Linear Quadratic Gaussian Control: Part Icited by 3
  4. 2026Cost-Driven Representation Learning for Linear Quadratic Gaussian Control: Part IIcited by 0