We study the problem of learning mixtures of linear dynamical systems (MLDS) from input-output data. This mixture setting allows us to leverage observations from related dynamical systems to improve the estimation of individual models. Building on spectral methods for mixtures of linear regressions, we propose a moment-based estimator that uses tensor decomposition to estimate the impulse response of component models of the mixture. The estimator improves upon existing tensor decomposition approaches for MLDS by utilizing the entire length of the observed trajectories. We provide sample complexity bounds for estimating MLDS in the presence of noise, in terms of both $N$ (number of trajectories) and $T$ (trajectory length), and demonstrate the performance of our estimator through simulations.

翻译：本文研究从输入输出数据中学习线性动态系统混合模型（MLDS）的问题。该混合设置使我们能够利用来自相关动态系统的观测数据来改进对各独立模型的估计。基于线性回归混合的谱方法，我们提出了一种基于矩的估计器，该估计器使用张量分解来估计混合模型中各组成系统的脉冲响应。该估计器通过利用观测轨迹的完整长度，改进了现有用于MLDS的张量分解方法。我们针对噪声环境下MLDS的估计问题，以$N$（轨迹数量）和$T$（轨迹长度）为变量给出了样本复杂度界限，并通过仿真实验验证了所提估计器的性能。