mlsanityData to 14 Oct 2026

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

arXiv 2311.18048 ↗First posted 29 Nov 2023cs.LG cs.CE cs.SYcited by 9

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Abstract (arXiv)

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.

Key facts. Cited by 9 papers in the map (data through 14 Oct 2026). Builds on 44 of its 84 references that are in the map. First posted on arXiv 29 Nov 2023.

Builds on

44 of 84 references.

References · 44

  1. 2015Causal inference using invariant prediction: identification and confidence intervalscited by 536
  2. 2019Variational Autoencoders and Nonlinear ICA: A Unifying Frameworkcited by 503
  3. 2020Underspecification Presents Challenges for Credibility in Modern Machine Learningcited by 496
  4. 2021Self-Supervised Learning with Data Augmentations Provably Isolates Content from Stylecited by 312
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32 more
  1. 2020Towards Nonlinear Disentanglement in Natural Data with Temporal Sparse Codingcited by 122
  2. 2023Nonparametric Identifiability of Causal Representations from Unknown Interventionscited by 106
  3. 2020ICE-BeeM: Identifiable Conditional Energy-Based Deep Models Based on Nonlinear ICAcited by 102
  4. 2021Learning Temporally Causal Latent Processes from General Temporal Datacited by 98
  5. 2021Independent mechanism analysis, a new concept?cited by 97
  6. 2023Learning Linear Causal Representations from Interventions under General Nonlinear Mixingcited by 92
  7. 2018Near optimal finite time identification of arbitrary linear dynamical systemscited by 89
  8. 2019The Incomplete Rosetta Stone Problem: Identifiability Results for Multi-View Nonlinear ICAcited by 86
  9. 2023Identifiability Guarantees for Causal Disentanglement from Soft Interventionscited by 84
  10. 2016Gradient Descent Learns Linear Dynamical Systemscited by 79
  11. 2018Non-asymptotic Identification of LTI Systems from a Single Trajectorycited by 78
  12. 2020Hidden Markov Nonlinear ICA: Unsupervised Learning from Nonstationary Time Seriescited by 77
  13. 2022Weakly Supervised Representation Learning with Sparse Perturbationscited by 65
  14. 2021Disentangling Identifiable Features from Noisy Data with Structured Nonlinear ICAcited by 64
  15. 2022Temporally Disentangled Representation Learningcited by 61
  16. 2019Learning Linear Dynamical Systems with Semi-Parametric Least Squarescited by 58
  17. 2019Causal Discovery with General Non-Linear Relationships Using Non-Linear ICAcited by 58
  18. 2023Identifiability of latent-variable and structural-equation models: from linear to nonlinearcited by 58
  19. 2023Posterior Collapse and Latent Variable Non-identifiabilitycited by 57
  20. 2023Causal Component Analysiscited by 56
  21. 2021Learning latent causal graphs via mixture oraclescited by 55
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  23. 2022Causal Structure Learning: a Combinatorial Perspectivecited by 46
  24. 2022Causal de Finetti: On the Identification of Invariant Causal Structure in Exchangeable Datacited by 42
  25. 2023Learning nonparametric latent causal graphs with unknown interventionscited by 34
  26. 2017Learning Causal Structures Using Regression Invariancecited by 32
  27. 2023A New Approach to Learning Linear Dynamical Systemscited by 23
  28. 2020Independent Innovation Analysis for Nonlinear Vector Autoregressive Processcited by 19
  29. 2022Learning Mixtures of Linear Dynamical Systemscited by 15
  30. 2018Direct Estimation of Differences in Causal Graphscited by 14
  31. 2021Structure learning in polynomial time: Greedy algorithms, Bregman information, and exponential familiescited by 11
  32. 2023Tensor Decompositions Meet Control Theory: Learning General Mixtures of Linear Dynamical Systemscited by 10

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2024: 5; 2025: 3; 2026: 1.

9 papers.

  1. 2024On the Origins of Linear Representations in Large Language Modelscited by 79
  2. 2024InfoNCE: Identifying the Gap Between Theory and Practicecited by 40
  3. 2024Learning Interpretable Concepts: Unifying Causal Representation Learning and Foundation Modelscited by 29
  4. 2024Marrying Causal Representation Learning with Dynamical Systems for Sciencecited by 23
  5. 2024Identifiable Exchangeable Mechanisms for Causal Structure and Representation Learningcited by 16
  6. 2025Position: An Empirically Grounded Identifiability Theory Will Accelerate Self-Supervised Learning Researchcited by 9
  7. 2025Towards Identifiability of Interventional Stochastic Differential Equationscited by 1
  8. 2025Estimating Treatment Effects with Independent Component Analysiscited by 0
  9. 2026Limits of Learning Linear Dynamics from Experimentscited by 0