Joint learning of a network of linear dynamical systems via total variation penalization
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866908783069888512 |
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| author | Donnat, Claire Klopp, Olga Tyagi, Hemant |
| author_facet | Donnat, Claire Klopp, Olga Tyagi, Hemant |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_18737 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Joint learning of a network of linear dynamical systems via total variation penalization Donnat, Claire Klopp, Olga Tyagi, Hemant Statistics Theory Optimization and Control Machine Learning 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. |
| title | Joint learning of a network of linear dynamical systems via total variation penalization |
| topic | Statistics Theory Optimization and Control Machine Learning |
| url | https://arxiv.org/abs/2511.18737 |