{"ID":2832354,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2512.05337","arxiv_id":"2512.05337","title":"Symmetric Linear Dynamical Systems are Learnable from Few Observations","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.","short_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...","url_abs":"https://arxiv.org/abs/2512.05337","url_pdf":"https://arxiv.org/pdf/2512.05337v1","authors":"[\"Minh Vu\",\"Andrey Y. Lokhov\",\"Marc Vuffray\"]","published":"2025-12-05T00:33:31Z","proceeding":"stat.ML","tasks":"[\"stat.ML\",\"cs.LG\",\"eess.SY\",\"math.OC\"]","methods":"[]","has_code":false}