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.
From: Hemant Tyagi [view email]
[v1]
Mon, 24 Nov 2025 04:07:46 UTC (10,759 KB)
[v2]
Fri, 23 Jan 2026 10:46:51 UTC (10,704 KB)
[v3]
Sun, 5 Jul 2026 07:29:00 UTC (10,705 KB)
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