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

TL;DR

This paper explores how intervention strategies can improve the identifiability of system parameters in Gaussian LTI systems, linking experiment design with causal representation learning.

Contribution

It introduces a method to identify system parameters through diverse interventions in multi-environment settings, connecting ICA-based identifiability with experiment design in dynamical systems.

Findings

Interventions enable parameter identification in Gaussian LTI systems.

Diverse intervention signals improve causal representation learning.

Connections established between experiment design and ICA-based identifiability.

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.