Symmetric Linear Dynamical Systems are Learnable from Few Observations
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866909945665945600 |
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| author | Vu, Minh Lokhov, Andrey Y. Vuffray, Marc |
| author_facet | Vu, Minh Lokhov, Andrey Y. Vuffray, Marc |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2512_05337 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Symmetric Linear Dynamical Systems are Learnable from Few Observations Vu, Minh Lokhov, Andrey Y. Vuffray, Marc Machine Learning Systems and Control Optimization and Control 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. |
| title | Symmetric Linear Dynamical Systems are Learnable from Few Observations |
| topic | Machine Learning Systems and Control Optimization and Control |
| url | https://arxiv.org/abs/2512.05337 |