Learning structured linear dynamical systems from missing observations
Abstract
We consider the problem of learning structured linear dynamical systems over convex sets 𝒦, where only a small subset of the observations are available at each time point. An estimator which minimizes a bias-corrected, potentially non-convex objective function is proposed. Non-asymptotic bounds are obtained for the statistical error, which depend on the local complexity of 𝒦, the trajectory length T, and the sub-sampling probability p. Convergence of the projected gradient descent algorithm is also established. The general theory is applied to settings where (i) 𝒦 is a subspace, (ii) 𝒦 is the set of bi-isotonic matrices, and (iii) 𝒦 is the set of matrices whose rows are formed by sampling Lipschitz functions. We show meaningful recovery of the transition matrix is possible for values of T much smaller than what is required in the unconstrained case, and for p = o(1).
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BibTeX
@misc{ruwanpathirana2026learning,
title = {{Learning structured linear dynamical systems from missing observations}},
author = {Aravinda Kanchana Ruwanpathirana and Hemant Tyagi and Sunny G. W. Wang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.11869},
eprint = {2610.11869},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.11869},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Learning structured linear dynamical systems from missing observations
AU - Aravinda Kanchana Ruwanpathirana
AU - Hemant Tyagi
AU - Sunny G. W. Wang
PY - 2026
DA - 2026/10/08
PB - arXiv
DO - 10.48550/arxiv.2610.11869
UR - https://arxiv.org/abs/2610.11869
AB - We consider the problem of learning structured linear dynamical systems over convex sets 𝒦, where only a small subset of the observations are available at each time point. An estimator which minimizes a bias-corrected, potentially non-convex objective function is proposed. Non-asymptotic bounds are obtained for the statistical error, which depend on the local complexity of 𝒦, the trajectory length T, and the sub-sampling probability p. Convergence of the projected gradient descent algorithm is also established. The general theory is applied to settings where (i) 𝒦 is a subspace, (ii) 𝒦 is the set of bi-isotonic matrices, and (iii) 𝒦 is the set of matrices whose rows are formed by sampling Lipschitz functions. We show meaningful recovery of the transition matrix is possible for values of T much smaller than what is required in the unconstrained case, and for p = o(1).
ER -