# Time varying regression with hidden linear dynamics

arXiv: https://arxiv.org/abs/2112.14862 · HTML: https://mlsanity.com/paper/2112.14862/

## 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 (most cited first, 14 of 14)

- [An Introduction to Matrix Concentration Inequalities](https://mlsanity.com/paper/1501.01571/) (2015)
- [Learning Without Mixing: Towards A Sharp Analysis of Linear System Identification](https://mlsanity.com/paper/1802.08334/) (2018)
- [Statistical guarantees for the EM algorithm: From population to sample-based analysis](https://mlsanity.com/paper/1408.2156/) (2014)
- [Near optimal finite time identification of arbitrary linear dynamical systems](https://mlsanity.com/paper/1812.01251/) (2018)
- [Gradient Descent Learns Linear Dynamical Systems](https://mlsanity.com/paper/1609.05191/) (2016)
- [Finite Sample Analysis of Stochastic System Identification](https://mlsanity.com/paper/1903.09122/) (2019)
- [Learning Linear Dynamical Systems with Semi-Parametric Least Squares](https://mlsanity.com/paper/1902.00768/) (2019)
- [Learning Linear Dynamical Systems via Spectral Filtering](https://mlsanity.com/paper/1711.00946/) (2017)
- [Spectral Filtering for General Linear Dynamical Systems](https://mlsanity.com/paper/1802.03981/) (2018)
- [Active Learning for Identification of Linear Dynamical Systems](https://mlsanity.com/paper/2002.00495/) (2020)
- [Non-Asymptotic Analysis of Robust Control from Coarse-Grained Identification](https://mlsanity.com/paper/1707.04791/) (2017)
- [Algorithms for Heavy-Tailed Statistics: Regression, Covariance Estimation, and Beyond](https://mlsanity.com/paper/1912.11071/) (2019)
- [Sample Complexity of Kalman Filtering for Unknown Systems](https://mlsanity.com/paper/1912.12309/) (2019)
- [A spectral algorithm for robust regression with subgaussian rates](https://mlsanity.com/paper/2007.06072/) (2020)

## Built on by (most cited first, 4 of 4)

- [A Stability Principle for Learning under Non-Stationarity](https://mlsanity.com/paper/2310.18304/) (2023)
- [Learning Linear Dynamics from Bilinear Observations](https://mlsanity.com/paper/2409.16499/) (2024)
- [Cost-Driven Representation Learning for Linear Quadratic Gaussian Control: Part I](https://mlsanity.com/paper/2212.14511/) (2022)
- [Cost-Driven Representation Learning for Linear Quadratic Gaussian Control: Part II](https://mlsanity.com/paper/2603.07437/) (2026)

## 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.