Symmetric Linear Dynamical Systems are Learnable from Few Observations

Minh Vu; Andrey Y. Lokhov; Marc Vuffray

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arXiv · 2512.05337

Symmetric Linear Dynamical Systems are Learnable from Few Observations

Minh Vu·Andrey Y. Lokhov·Marc Vuffray

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Abstract

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 $T=\mathcal{O}(\log N)$ 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.

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BibTeX RIS

Minh Vu, Andrey Y. Lokhov, Marc Vuffray. 2025-12-05. Symmetric Linear Dynamical Systems are Learnable from Few Observations. https://arxiv.org/abs/2512.05337

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