{"ID":2837310,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2511.18737","arxiv_id":"2511.18737","title":"Joint learning of a network of linear dynamical systems via total variation penalization","abstract":"We consider the problem of joint estimation of the parameters of $m$ linear dynamical systems, given access to single realizations of their respective trajectories, each of length $T$. The linear systems are assumed to reside on the nodes of an undirected and connected graph $G = ([m], \\mathcal{E})$, and the system matrices are assumed to either vary smoothly or exhibit small number of ``jumps'' across the edges. We consider a total variation penalized least-squares estimator and derive non-asymptotic bounds on the mean squared error (MSE) which hold with high probability. In particular, the bounds imply for certain choices of well connected $G$ that the MSE goes to zero as $m$ increases, even when $T$ is constant. The theoretical results are supported by extensive experiments on synthetic and real data.","short_abstract":"We consider the problem of joint estimation of the parameters of $m$ linear dynamical systems, given access to single realizations of their respective trajectories, each of length $T$. The linear systems are assumed to reside on the nodes of an undirected and connected graph $G = ([m], \\mathcal{E})$, and the system mat...","url_abs":"https://arxiv.org/abs/2511.18737","url_pdf":"https://arxiv.org/pdf/2511.18737v2","authors":"[\"Claire Donnat\",\"Olga Klopp\",\"Hemant Tyagi\"]","published":"2025-11-24T04:07:46Z","proceeding":"math.ST","tasks":"[\"math.ST\",\"math.OC\",\"stat.ML\"]","methods":"[]","has_code":false}