[2510.06091] Learning Mixtures of Linear Dynamical Systems via Hybrid Tensor-EM Method

Computer Science > Machine Learning arXiv:2510.06091 (cs) [Submitted on 7 Oct 2025 (v1), last revised 27 Feb 2026 (this version, v2)] Title:Learning Mixtures of Linear Dynamical Systems via Hybrid Tensor-EM Method Authors:Lulu Gong, Shreya Saxena View a PDF of the paper titled Learning Mixtures of Linear Dynamical Systems via Hybrid Tensor-EM Method, by Lulu Gong and Shreya Saxena View PDF HTML (experimental) Abstract:Mixtures of linear dynamical systems (MoLDS) provide a path to model time-series data that exhibit diverse temporal dynamics across trajectories. However, its application remains challenging in complex and noisy settings, limiting its effectiveness for neural data analysis. Tensor-based moment methods can provide global identifiability guarantees for MoLDS, but their performance degrades under noise and complexity. Commonly used expectation-maximization (EM) methods offer flexibility in fitting latent models but are highly sensitive to initialization and prone to poor local minima. Here, we propose a tensor-based method that provides identifiability guarantees for learning MoLDS, which is followed by EM updates to combine the strengths of both approaches. The novelty in our approach lies in the construction of moment tensors using the input-output data to recover globally consistent estimates of mixture weights and system parameters. These estimates can then be refined through a Kalman EM algorithm, with closed-form updates for all LDS parameters. We validate...