An Interventional Perspective on Identifiability in Gaussian LTI Systems with Independent Component Analysis
This work addresses the challenge of system identification in dynamical systems for researchers and practitioners, offering an incremental improvement by integrating intervention design with existing identifiable representation learning methods.
The paper tackles the problem of identifying system parameters in Gaussian Linear Time-Invariant (LTI) systems by introducing diverse intervention signals in multi-environment settings, connecting experiment design with representational identifiability, and validates the approach on synthetic and simulated physical data.
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.