Learning structured linear dynamical systems from missing observations

Key points

• An estimator which minimizes a bias-corrected, potentially non-convex objective function is proposed.1
• 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 $p$.1
• 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.1
• 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 $p = o(1)$.1

Sources (1)

• [1]Learning structured linear dynamical systems from missing observations
  arXiv (AI, ML, NLP, CV, robotics, multi-agent) · Oct 8, 12:44 PM

  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.

Extractive summary: sentences quoted from the sources.