An interventional perspective on identifiability in gaussian lti systems with independent component analysis

Abstract

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. The project’s repository is at [github. com/rpatrik96/lti-ica](https://github. com/rpatrik96/lti-ica).

Patrik Reizinger

PhD candidate

I am a final-year Ph.D. student supervised by Wieland Brendel, Ferenc Huszár, Matthias Bethge, and Bernhard Schölkopf. I am part of the ELLIS and IMPRS-IS programs. I have also spent time at the Vector Institute and at the University of Cambridge.

Wieland Brendel

Principal Investigator (PI)

Wieland Brendel received his Diploma in physics from the University of Regensburg (2010) and his Ph.D. in computational neuroscience from the École normale supérieure in Paris (2014). He joined the University of Tübingen as a postdoctoral researcher in the group of Matthias Bethge, became a Principal Investigator and Team Lead in the Tübingen AI Center (2018) and an Emmy Noether Group Leader for Robust Machine Learning (2020). In May 2022, Wieland joined the Max-Planck Institute for Intelligent Systems as an independent Group Leader and is now a Hector-endowed Fellow at the ELLIS Institute Tübingen (since September 2023). He received the 2023 German Pattern Recognition Award for his substantial contributions on robust, generalisable and interpretable machine vision. Aside of his research, Wieland co-founded a nationwide school competition (bw-ki.de) and a machine learning startup focused on visual quality control.