# Learning clusters of partially observed linear dynamical systems

arXiv: https://arxiv.org/abs/2507.17638 · HTML: https://mlsanity.com/paper/2507.17638/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Jul 2025.

## Built on by (most cited first, 1 of 1)

- [Harnessing Data from Clustered LQR Systems: Personalized and Collaborative Policy Optimization](https://mlsanity.com/paper/2511.17489/) (2025)

## Abstract (arXiv)

We study the problem of learning clusters of partially observed linear dynamical systems from multiple input-output trajectories. This setting is particularly relevant when there are limited observations (e.g., short trajectories) from individual data sources, making direct estimation challenging. In such cases, incorporating data from multiple related sources can improve learning. We propose an estimation algorithm that leverages different data requirements for the tasks of clustering and system identification. First, short impulse responses are estimated from individual trajectories and clustered. Then, refined models for each cluster are jointly estimated using multiple trajectories. We establish end-to-end finite sample guarantees for estimating Markov parameters and state space realizations and highlight trade-offs among the number of observed systems, the trajectory lengths, and the complexity of the underlying models.