We investigate the relationship between system identification and intervention design in dynamical systems. While previous research demonstrated how identifiable representation learning methods, such as Independent Component Analysis (ICA), can reveal cause-effect relationships, it relied on a passive perspective without considering how to collect data. Our work shows that in Gaussian Linear Time-Invariant (LTI) systems, the system parameters can be identified by introducing diverse intervention signals in a multi-environment setting. By harnessing appropriate diversity assumptions motivated by the ICA literature, our findings connect experiment design and representational identifiability in dynamical systems. We corroborate our findings on synthetic and (simulated) physical data. Additionally, we show that Hidden Markov Models, in general, and (Gaussian) LTI systems, in particular, fulfil a generalization of the Causal de Finetti theorem with continuous parameters.

翻译：我们研究了动态系统中系统识别与干预设计之间的关系。现有研究虽已证明可识别表示学习方法（如独立成分分析，ICA）能揭示因果关系，但仅采用被动视角，未考虑数据收集方式。本文表明：在高斯线性时不变（LTI）系统中，通过在多环境设定下引入多样化干预信号，可实现系统参数的识别。借助ICA文献中提出的适当多样性假设，我们的发现将实验设计与动态系统的表示可识别性联系起来。我们在合成数据与（模拟）物理数据上验证了结论。此外，我们证明隐马尔可夫模型（尤其高斯LTI系统）满足具有连续参数的因果德菲内蒂定理的推广形式。