# Learning structured linear dynamical systems from missing observations

arXiv: https://arxiv.org/abs/2610.11869 · HTML: https://mlsanity.com/paper/2610.11869/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 6 of its 53 references that are in the map.
- First posted on arXiv 8 Oct 2026.

## Builds on (most cited first, 6 of 6)

- [High Dimensional M-Estimation with Missing Outcomes: A Semi-Parametric Framework](https://mlsanity.com/paper/1911.11345/) (2019)
- [Learning linear dynamical systems under convex constraints](https://mlsanity.com/paper/2303.15121/) (2023)
- [Online Joint Topology Identification and Signal Estimation from Streams with Missing Data](https://mlsanity.com/paper/2012.05957/) (2020)
- [Semi-supervised linear regression with missing covariates](https://mlsanity.com/paper/2602.13729/) (2026)
- [Finite Sample Analysis of System Poles for Ho-Kalman Algorithm](https://mlsanity.com/paper/2503.16331/) (2025)
- [Provably Efficient Sensor Allocation for Unknown High-dimensional Systems with Limited Sensing](https://mlsanity.com/paper/2605.16584/) (2026)

## Abstract (arXiv)

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).