An Interventional Perspective on Identifiability in Gaussian LTI Systems with Independent Component Analysis

Goutham Rajendran, Patrik Reizinger, Wieland Brendel, Pradeep Kumar Ravikumar
Proceedings of the Third Conference on Causal Learning and Reasoning, PMLR 236:41-70, 2024.

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).

Cite this Paper

BibTeX
@InProceedings{pmlr-v236-rajendran24a, title = {An Interventional Perspective on Identifiability in Gaussian LTI Systems with Independent Component Analysis}, author = {Rajendran, Goutham and Reizinger, Patrik and Brendel, Wieland and Ravikumar, Pradeep Kumar}, booktitle = {Proceedings of the Third Conference on Causal Learning and Reasoning}, pages = {41--70}, year = {2024}, editor = {Locatello, Francesco and Didelez, Vanessa}, volume = {236}, series = {Proceedings of Machine Learning Research}, month = {01--03 Apr}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v236/rajendran24a/rajendran24a.pdf}, url = {https://proceedings.mlr.press/v236/rajendran24a.html}, 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).} }
Endnote
%0 Conference Paper %T An Interventional Perspective on Identifiability in Gaussian LTI Systems with Independent Component Analysis %A Goutham Rajendran %A Patrik Reizinger %A Wieland Brendel %A Pradeep Kumar Ravikumar %B Proceedings of the Third Conference on Causal Learning and Reasoning %C Proceedings of Machine Learning Research %D 2024 %E Francesco Locatello %E Vanessa Didelez %F pmlr-v236-rajendran24a %I PMLR %P 41--70 %U https://proceedings.mlr.press/v236/rajendran24a.html %V 236 %X 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).
APA
Rajendran, G., Reizinger, P., Brendel, W. & Ravikumar, P.K.. (2024). An Interventional Perspective on Identifiability in Gaussian LTI Systems with Independent Component Analysis. Proceedings of the Third Conference on Causal Learning and Reasoning, in Proceedings of Machine Learning Research 236:41-70 Available from https://proceedings.mlr.press/v236/rajendran24a.html.

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