Abstract
We consider the problem of learning structured linear dynamical systems over convex sets $\mathcal{K}$, 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 $\mathcal{K}$, 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) $\mathcal{K}$ is a subspace, (ii) $\mathcal{K}$ is the set of bi-isotonic matrices, and (iii) $\mathcal{K}$ 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 $p = o(1)$.
Keywords
Publication details
- Journal
- Not available
- Open access
- Green open access
Cite this article
APA 7
Ruwanpathirana, A. K., Tyagi, H., & Wang, S. G. W. (2026). Learning structured linear dynamical systems from missing observations. https://omanscience.com/en/articles/learning-structured-linear-dynamical-systems-from-missing-observations
MLA 9
Ruwanpathirana, Aravinda Kanchana, et al. "Learning structured linear dynamical systems from missing observations." https://omanscience.com/en/articles/learning-structured-linear-dynamical-systems-from-missing-observations.
Chicago (author–date)
Ruwanpathirana, Aravinda Kanchana, Hemant Tyagi, and Sunny G. W. Wang. 2026. "Learning structured linear dynamical systems from missing observations." https://omanscience.com/en/articles/learning-structured-linear-dynamical-systems-from-missing-observations.
Harvard
Ruwanpathirana, A. K., Tyagi, H. and Wang, S. G. W. (2026) 'Learning structured linear dynamical systems from missing observations', Available at: https://omanscience.com/en/articles/learning-structured-linear-dynamical-systems-from-missing-observations.
Vancouver
Ruwanpathirana AK, Tyagi H, Wang SGW. Learning structured linear dynamical systems from missing observations. https://omanscience.com/en/articles/learning-structured-linear-dynamical-systems-from-missing-observations
IEEE
A. K. Ruwanpathirana, H. Tyagi, and S. G. W. Wang, "Learning structured linear dynamical systems from missing observations," https://omanscience.com/en/articles/learning-structured-linear-dynamical-systems-from-missing-observations.