[
    {
        "id": "osp-16387",
        "type": "article-journal",
        "title": "Learning structured linear dynamical systems from missing observations",
        "author": [
            {
                "family": "Ruwanpathirana",
                "given": "Aravinda Kanchana"
            },
            {
                "family": "Tyagi",
                "given": "Hemant"
            },
            {
                "family": "Wang",
                "given": "Sunny G. W."
            }
        ],
        "URL": "https://omanscience.com/ar/articles/learning-structured-linear-dynamical-systems-from-missing-observations",
        "language": "en",
        "issued": {
            "date-parts": [
                [
                    2026
                ]
            ]
        },
        "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 $p = o(1)$."
    }
]