Symmetric Linear Dynamical Systems are Learnable from Few Observations

• URL: http://arxiv.org/abs/2512.05337v1
• Date: Fri, 05 Dec 2025 00:33:31 GMT
• Title: Symmetric Linear Dynamical Systems are Learnable from Few Observations
• Authors: Minh Vu, Andrey Y. Lokhov, Marc Vuffray,
• Abstract summary: We introduce and analyze a new estimator that achieves a small maximum element-wise error on the recovery of symmetric dynamic matrices.<n>This estimator is based on the method of moments and does not rely on problem-specific regularization.
• Score: 3.7910294046839845
• License: http://creativecommons.org/licenses/by/4.0/
• 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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