Learning structured linear dynamical systems from missing observations

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 $p = o(1)$.

Machine Learning (stat.ML); Machine Learning (cs.LG); Systems and Control (eess.SY); Optimization and Control (math.OC); Statistics Theory (math.ST)

arXiv:2610.11869 [stat.ML]

(or arXiv:2610.11869v1 [stat.ML] for this version)

https://doi.org/10.48550/arXiv.2610.11869 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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