# Symmetric Linear Dynamical Systems are Learnable from Few Observations

arXiv: https://arxiv.org/abs/2512.05337 · HTML: https://mlsanity.com/paper/2512.05337/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 15 of its 32 references that are in the map.
- First posted on arXiv 5 Dec 2025.

## Builds on (most cited first, 15 of 15)

- [Learning Without Mixing: Towards A Sharp Analysis of Linear System Identification](https://mlsanity.com/paper/1802.08334/) (2018)
- [Near optimal finite time identification of arbitrary linear dynamical systems](https://mlsanity.com/paper/1812.01251/) (2018)
- [Finite Sample Analysis of Stochastic System Identification](https://mlsanity.com/paper/1903.09122/) (2019)
- [Finite Time Identification in Unstable Linear Systems](https://mlsanity.com/paper/1710.01852/) (2017)
- [Learning Linear Dynamical Systems with Semi-Parametric Least Squares](https://mlsanity.com/paper/1902.00768/) (2019)
- [Learning Graphical Models Using Multiplicative Weights](https://mlsanity.com/paper/1706.06274/) (2017)
- [Finite-time Identification of Stable Linear Systems: Optimality of the Least-Squares Estimator](https://mlsanity.com/paper/2003.07937/) (2020)
- [A New Approach to Learning Linear Dynamical Systems](https://mlsanity.com/paper/2301.09519/) (2023)
- [Efficient Learning of Discrete Graphical Models](https://mlsanity.com/paper/1902.00600/) (2019)
- [Sample Complexity Lower Bounds for Linear System Identification](https://mlsanity.com/paper/1903.10343/) (2019)
- [Learning Sparse Dynamical Systems from a Single Sample Trajectory](https://mlsanity.com/paper/1904.09396/) (2019)
- [Oracle Inequalities for High Dimensional Vector Autoregressions](https://mlsanity.com/paper/1311.0811/) (2013)
- [A Direct Estimation of High Dimensional Stationary Vector Autoregressions](https://mlsanity.com/paper/1307.0293/) (2013)
- [Learning linear dynamical systems under convex constraints](https://mlsanity.com/paper/2303.15121/) (2023)
- [Real-time Anomaly Detection and Classification in Streaming PMU Data](https://mlsanity.com/paper/1911.06316/) (2019)

## Abstract (arXiv)

We consider the problem of learning the parameters of a N-dimensional stochastic linear dynamics under both full and partial observations from a single trajectory of time T. We introduce and analyze a new estimator that achieves a small maximum element-wise error on the recovery of symmetric dynamic matrices using only T=O(log N) observations, irrespective of whether the matrix is sparse or dense. This estimator is based on the method of moments and does not rely on problem-specific regularization. This is especially important for applications such as structure discovery.