Joint learning of a network of linear dynamical systems via total variation penalization

• URL: http://arxiv.org/abs/2511.18737v1
• Date: Mon, 24 Nov 2025 04:07:46 GMT
• Title: Joint learning of a network of linear dynamical systems via total variation penalization
• Authors: Claire Donnat, Olga Klopp, Hemant Tyagi,
• Abstract summary: We consider the problem of joint estimation of the parameters of $m$ linear dynamical systems.<n>We derive non-asymptotic bounds on the mean squared error which hold with high probability.
• Score: 4.6390064640459
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

Related papers

• Explicit Discovery of Nonlinear Symmetries from Dynamic Data [50.20526548924647]
  LieNLSD is the first method capable of determining the number of infinitesimal generators with nonlinear terms and their explicit expressions.<n>LieNLSD shows qualitative advantages over existing methods and improves the long rollout accuracy of neural PDE solvers by over 20%.
  arXiv  Detail & Related papers  (2025-10-02T09:54:08Z)
• The Sample Complexity of Online Reinforcement Learning: A Multi-model Perspective [55.15192437680943]
  We study the sample complexity of online reinforcement learning in the general setting of nonlinear dynamical systems with continuous state and action spaces.<n>Our algorithm achieves a policy regret of $mathcalO(N epsilon2 + mathrmln(m(epsilon)/epsilon2)$, where $epsilon$ is the time horizon.<n>In the special case where the dynamics are parametrized by a compact and real-valued set of parameters, we prove a policy regret of $mathcalO(sqrt
  arXiv  Detail & Related papers  (2025-01-27T10:01:28Z)
• Joint Learning of Linear Dynamical Systems under Smoothness Constraints [5.2395896768723045]
  We consider the problem of joint learning of multiple linear dynamical systems.<n>In particular, we show conditions under which the mean-squared error bounds on the mean-squared error (MSE) converges to zero as $m$ increases.
  arXiv  Detail & Related papers  (2024-06-03T08:29:42Z)
• Learning with Norm Constrained, Over-parameterized, Two-layer Neural Networks [54.177130905659155]
  Recent studies show that a reproducing kernel Hilbert space (RKHS) is not a suitable space to model functions by neural networks. In this paper, we study a suitable function space for over- parameterized two-layer neural networks with bounded norms.
  arXiv  Detail & Related papers  (2024-04-29T15:04:07Z)
• From Spectral Theorem to Statistical Independence with Application to System Identification [11.98319841778396]
  We provide first quantitative handle on decay rate of finite powers of state transition matrix $|Ak|$. It is shown that when a stable dynamical system has only one distinct eigenvalue and discrepancy of $n-1$: $|A|$ has a dependence on $n$, resulting dynamics are inseparable. We show that element-wise error is essentially a variant of well-know Littlewood-Offord problem.
  arXiv  Detail & Related papers  (2023-10-16T15:40:43Z)
• Sparse random matrices and Gaussian ensembles with varying randomness [0.0]
  We study a system of $N$ qubits with a random Hamiltonian obtained by drawing coupling constants from Gaussian distributions in various ways. We find some evidence that the behaviour changes in an abrupt manner when the number of non-zero independent terms in the Hamiltonian is exponentially large in $N$.
  arXiv  Detail & Related papers  (2023-05-12T14:19:27Z)
• Adaptive Stochastic Variance Reduction for Non-convex Finite-Sum Minimization [52.25843977506935]
  We propose an adaptive variance method, called AdaSpider, for $L$-smooth, non-reduction functions with a finitesum structure. In doing so, we are able to compute an $epsilon-stationary point with $tildeOleft + st/epsilon calls.
  arXiv  Detail & Related papers  (2022-11-03T14:41:46Z)
• On the Effective Number of Linear Regions in Shallow Univariate ReLU Networks: Convergence Guarantees and Implicit Bias [50.84569563188485]
  We show that gradient flow converges in direction when labels are determined by the sign of a target network with $r$ neurons. Our result may already hold for mild over- parameterization, where the width is $tildemathcalO(r)$ and independent of the sample size.
  arXiv  Detail & Related papers  (2022-05-18T16:57:10Z)
• Single Trajectory Nonparametric Learning of Nonlinear Dynamics [8.438421942654292]
  Given a single trajectory of a dynamical system, we analyze the performance of the nonparametric least squares estimator (LSE) We leverage recently developed information-theoretic methods to establish the optimality of the LSE for non hypotheses classes. We specialize our results to a number of scenarios of practical interest, such as Lipschitz dynamics, generalized linear models, and dynamics described by functions in certain classes of Reproducing Kernel Hilbert Spaces (RKHS)
  arXiv  Detail & Related papers  (2022-02-16T19:38:54Z)
• Optimal and instance-dependent guarantees for Markovian linear stochastic approximation [47.912511426974376]
  We show a non-asymptotic bound of the order $t_mathrmmix tfracdn$ on the squared error of the last iterate of a standard scheme. We derive corollaries of these results for policy evaluation with Markov noise.
  arXiv  Detail & Related papers  (2021-12-23T18:47:50Z)
• Improved rates for prediction and identification of partially observed linear dynamical systems [4.68299658663016]
  Identification of a linear time-in dynamical system from partial observations is a fundamental problem in control theory. We propose an algorithm that learns such systems with non-asymptotic statistical rates depending on the inherentity $d$ of the system. Our algorithm is based on multi-scale low-rank approximation SVD applied to Hankel matrices of increasing sizes.
  arXiv  Detail & Related papers  (2020-11-19T18:04:18Z)
• On Linear Stochastic Approximation: Fine-grained Polyak-Ruppert and Non-Asymptotic Concentration [115.1954841020189]
  We study the inequality and non-asymptotic properties of approximation procedures with Polyak-Ruppert averaging. We prove a central limit theorem (CLT) for the averaged iterates with fixed step size and number of iterations going to infinity.
  arXiv  Detail & Related papers  (2020-04-09T17:54:18Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.