Papers
Topics
Authors
Recent
Search
2000 character limit reached

Identifiable Representation and Model Learning for Latent Dynamic Systems

Published 23 Oct 2024 in cs.LG, cs.SY, eess.SY, and stat.ML | (2410.17882v2)

Abstract: Learning identifiable representations and models from low-level observations is helpful for an intelligent spacecraft to complete downstream tasks reliably. For temporal observations, to ensure that the data generating process is provably inverted, most existing works either assume the noise variables in the dynamic mechanisms are (conditionally) independent or require that the interventions can directly affect each latent variable. However, in practice, the relationship between the exogenous inputs/interventions and the latent variables may follow some complex deterministic mechanisms. In this work, we study the problem of identifiable representation and model learning for latent dynamic systems. The key idea is to use an inductive bias inspired by controllable canonical forms, which are sparse and input-dependent by definition. We prove that, for linear and affine nonlinear latent dynamic systems with sparse input matrices, it is possible to identify the latent variables up to scaling and determine the dynamic models up to some simple transformations. The results have the potential to provide some theoretical guarantees for developing more trustworthy decision-making and control methods for intelligent spacecrafts.

Definition Search Book Streamline Icon: https://streamlinehq.com
References (49)
  1. L. Yuan and H. Huang, “Current trends of spacecraft intelligent autonomous control(in chinese),” in Aerospace Contrd and Application, 2019, pp. 45(4): 7–18.
  2. A. Chen, Y. Xie, Y. Wang, and L. Li, “Knowledge graph-based image recognition transfer learning method for on-orbit service manipulation,” Space: Science & Technology, 2021.
  3. L. Li and Y. Xie, “Space robotic manipulation: a multi-task learning perspective(in chinese),” in Chinese Space Science and Technology, 2022, pp. 42(03): 10–24.
  4. Y. Bengio, A. Courville, and P. Vincent, “Representation learning: A review and new perspectives,” IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 35, no. 8, pp. 1798–1828, 2013.
  5. B. Schölkopf, F. Locatello, S. Bauer, N. R. Ke, N. Kalchbrenner, A. Goyal, and Y. Bengio, “Toward causal representation learning,” Proceedings of the IEEE, vol. 109, no. 5, pp. 612–634, 2021.
  6. M. Watter, J. Springenberg, J. Boedecker, and M. Riedmiller, “Embed to control: A locally linear latent dynamics model for control from raw images,” Advances in neural information processing systems, vol. 28, 2015.
  7. C. Gelada, S. Kumar, J. Buckman, O. Nachum, and M. G. Bellemare, “DeepMDP: Learning continuous latent space models for representation learning,” in International Conference on Machine Learning.   PMLR, 2019, pp. 2170–2179.
  8. D. Hafner, T. Lillicrap, I. Fischer, R. Villegas, D. Ha, H. Lee, and J. Davidson, “Learning latent dynamics for planning from pixels,” in International Conference on Machine Learning.   PMLR, 2019, pp. 2555–2565.
  9. D. Hafner, T. Lillicrap, J. Ba, and M. Norouzi, “Dream to control: Learning behaviors by latent imagination,” arXiv preprint arXiv:1912.01603, 2019.
  10. M. Tomar, U. A. Mishra, A. Zhang, and M. E. Taylor, “Learning representations for pixel-based control: What matters and why?” Transactions on Machine Learning Research, 2023. [Online]. Available: https://openreview.net/forum?id=wIXHG8LZ2w
  11. F. Locatello, S. Bauer, M. Lucic, G. Raetsch, S. Gelly, B. Schölkopf, and O. Bachem, “Challenging common assumptions in the unsupervised learning of disentangled representations,” in International Conference on Machine Learning.   PMLR, 2019, pp. 4114–4124.
  12. I. Khemakhem, D. Kingma, R. Monti, and A. Hyvarinen, “Variational autoencoders and nonlinear ICA: A unifying framework,” in International Conference on Artificial Intelligence and Statistics.   PMLR, 2020, pp. 2207–2217.
  13. B. Kivva, G. Rajendran, P. Ravikumar, and B. Aragam, “Identifiability of deep generative models without auxiliary information,” Advances in Neural Information Processing Systems, vol. 35, pp. 15 687–15 701, 2022.
  14. F. Träuble, E. Creager, N. Kilbertus, F. Locatello, A. Dittadi, A. Goyal, B. Schölkopf, and S. Bauer, “On disentangled representations learned from correlated data,” in International Conference on Machine Learning.   PMLR, 2021, pp. 10 401–10 412.
  15. M. Yang, F. Liu, Z. Chen, X. Shen, J. Hao, and J. Wang, “CausalVAE: Disentangled representation learning via neural structural causal models,” in Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, 2021, pp. 9593–9602.
  16. X. Shen, F. Liu, H. Dong, Q. Lian, Z. Chen, and T. Zhang, “Weakly supervised disentangled generative causal representation learning,” The Journal of Machine Learning Research, vol. 23, no. 1, pp. 10 994–11 048, 2022.
  17. J. Brehmer, P. De Haan, P. Lippe, and T. S. Cohen, “Weakly supervised causal representation learning,” Advances in Neural Information Processing Systems, vol. 35, pp. 38 319–38 331, 2022.
  18. K. Ahuja, J. S. Hartford, and Y. Bengio, “Weakly supervised representation learning with sparse perturbations,” Advances in Neural Information Processing Systems, vol. 35, pp. 15 516–15 528, 2022.
  19. W. Yao, Y. Sun, A. Ho, C. Sun, and K. Zhang, “Learning temporally causal latent processes from general temporal data,” in International Conference on Learning Representations, 2021.
  20. P. Lippe, S. Magliacane, S. Löwe, Y. M. Asano, T. Cohen, and S. Gavves, “CITRIS: Causal identifiability from temporal intervened sequences,” in International Conference on Machine Learning.   PMLR, 2022, pp. 13 557–13 603.
  21. S. Lachapelle, P. Rodriguez, Y. Sharma, K. E. Everett, R. Le Priol, A. Lacoste, and S. Lacoste-Julien, “Disentanglement via mechanism sparsity regularization: A new principle for nonlinear ICA,” in Conference on Causal Learning and Reasoning.   PMLR, 2022, pp. 428–484.
  22. W. Yao, G. Chen, and K. Zhang, “Temporally disentangled representation learning,” Advances in Neural Information Processing Systems, vol. 35, pp. 26 492–26 503, 2022.
  23. Y.-R. Liu, B. Huang, Z. Zhu, H. Tian, M. Gong, Y. Yu, and K. Zhang, “Learning world models with identifiable factorization,” arXiv preprint arXiv:2306.06561, 2023.
  24. W. Liang, A. Kekić, J. von Kügelgen, S. Buchholz, M. Besserve, L. Gresele, and B. Schölkopf, “Causal component analysis,” arXiv preprint arXiv:2305.17225, 2023.
  25. J. von Kügelgen, M. Besserve, W. Liang, L. Gresele, A. Kekić, E. Bareinboim, D. M. Blei, and B. Schölkopf, “Nonparametric identifiability of causal representations from unknown interventions,” arXiv preprint arXiv:2306.00542, 2023.
  26. K. Ahuja, J. Hartford, and Y. Bengio, “Properties from mechanisms: An equivariance perspective on identifiable representation learning,” in International Conference on Learning Representations, 2021.
  27. M. Jaderberg, V. Mnih, W. M. Czarnecki, T. Schaul, J. Z. Leibo, D. Silver, and K. Kavukcuoglu, “Reinforcement learning with unsupervised auxiliary tasks,” in International Conference on Learning Representations, 2016.
  28. A. Lei, B. Schölkopf, and I. Posner, “Causal discovery for modular world models,” in NeurIPS 2022 Workshop on Neuro Causal and Symbolic AI (nCSI), 2022.
  29. P. Wu, A. Escontrela, D. Hafner, P. Abbeel, and K. Goldberg, “DayDreamer: World models for physical robot learning,” in Conference on Robot Learning.   PMLR, 2023, pp. 2226–2240.
  30. M. Laskin, A. Srinivas, and P. Abbeel, “CURL: Contrastive unsupervised representations for reinforcement learning,” in International Conference on Machine Learning.   PMLR, 2020, pp. 5639–5650.
  31. M. Schwarzer, A. Anand, R. Goel, R. D. Hjelm, A. Courville, and P. Bachman, “Data-efficient reinforcement learning with self-predictive representations,” in International Conference on Learning Representations, 2020.
  32. A. Zhang, R. T. McAllister, R. Calandra, Y. Gal, and S. Levine, “Learning invariant representations for reinforcement learning without reconstruction,” in International Conference on Learning Representations, 2020.
  33. A. Hyvarinen and H. Morioka, “Unsupervised feature extraction by time-contrastive learning and nonlinear ICA,” Advances in neural information processing systems, vol. 29, 2016.
  34. ——, “Nonlinear ICA of temporally dependent stationary sources,” in Artificial Intelligence and Statistics.   PMLR, 2017, pp. 460–469.
  35. H. Hälvä and A. Hyvarinen, “Hidden markov nonlinear ICA: Unsupervised learning from nonstationary time series,” in Conference on Uncertainty in Artificial Intelligence.   PMLR, 2020, pp. 939–948.
  36. A. Hyvärinen, I. Khemakhem, and H. Morioka, “Nonlinear independent component analysis for principled disentanglement in unsupervised deep learning,” Patterns, vol. 4, no. 10, 2023.
  37. D. Klindt, L. Schott, Y. Sharma, I. Ustyuzhaninov, W. Brendel, M. Bethge, and D. Paiton, “Towards nonlinear disentanglement in natural data with temporal sparse coding,” stat, vol. 1050, p. 21, 2020.
  38. P. Lippe, S. Magliacane, S. Löwe, Y. M. Asano, T. Cohen, and E. Gavves, “Causal representation learning for instantaneous and temporal effects in interactive systems,” in The Eleventh International Conference on Learning Representations, 2022.
  39. S. Lachapelle, P. R. López, Y. Sharma, K. Everett, R. L. Priol, A. Lacoste, and S. Lacoste-Julien, “Nonparametric partial disentanglement via mechanism sparsity: Sparse actions, interventions and sparse temporal dependencies,” arXiv preprint arXiv:2401.04890, 2024.
  40. F. Locatello, B. Poole, G. Rätsch, B. Schölkopf, O. Bachem, and M. Tschannen, “Weakly-supervised disentanglement without compromises,” in International Conference on Machine Learning.   PMLR, 2020, pp. 6348–6359.
  41. K. Ahuja, D. Mahajan, Y. Wang, and Y. Bengio, “Interventional causal representation learning,” in International Conference on Machine Learning.   PMLR, 2023, pp. 372–407.
  42. C. Squires, A. Seigal, S. S. Bhate, and C. Uhler, “Linear causal disentanglement via interventions,” in International Conference on Machine Learning.   PMLR, 2023, pp. 32 540–32 560.
  43. J. Zhang, C. Squires, K. Greenewald, A. Srivastava, K. Shanmugam, and C. Uhler, “Identifiability guarantees for causal disentanglement from soft interventions,” arXiv preprint arXiv:2307.06250, 2023.
  44. B. Varıcı, E. Acartürk, K. Shanmugam, and A. Tajer, “General identifiability and achievability for causal representation learning,” arXiv preprint arXiv:2310.15450, 2023.
  45. T. Wang, S. Du, A. Torralba, P. Isola, A. Zhang, and Y. Tian, “Denoised MDPs: Learning world models better than the world itself,” in International Conference on Machine Learning.   PMLR, 2022, pp. 22 591–22 612.
  46. B. Huang, C. Lu, L. Leqi, J. M. Hernández-Lobato, C. Glymour, B. Schölkopf, and K. Zhang, “Action-sufficient state representation learning for control with structural constraints,” in International Conference on Machine Learning.   PMLR, 2022, pp. 9260–9279.
  47. G. Rajendran, P. Reizinger, W. Brendel, and P. Ravikumar, “An interventional perspective on identifiability in gaussian LTI systems with independent component analysis,” arXiv preprint arXiv:2311.18048, 2023.
  48. D. G. Luenberger, “Canonical forms for linear multivariable systems,” IEEE Transactions on Automatic Control, vol. 12, no. 3, pp. 290–293, 1967.
  49. R. S. Zimmermann, Y. Sharma, S. Schneider, M. Bethge, and W. Brendel, “Contrastive learning inverts the data generating process,” in International Conference on Machine Learning.   PMLR, 2021, pp. 12 979–12 990.

Summary

No one has generated a summary of this paper yet.

Ai Sparkles Streamline Icon: https://streamlinehq.com Sign Up to Summarize

Paper to Video (Beta)

Whiteboard

No one has generated a whiteboard explanation for this paper yet.

Ai Sparkles Streamline Icon: https://streamlinehq.com Sign Up to Generate

Open Problems

We haven't generated a list of open problems mentioned in this paper yet.

Ai Sparkles Streamline Icon: https://streamlinehq.com Generate Now

Continue Learning

We haven't generated follow-up questions for this paper yet.

Ai Sparkles Streamline Icon: https://streamlinehq.com Generate Now

Authors (2)

  1. Congxi Zhang 
  2. Yongchun Xie 

Collections

Sign up for free to add this paper to one or more collections.

User Circle Single Streamline Icon: https://streamlinehq.com Sign Up

Tweets

Sign up for free to view the 1 tweet with 2 likes about this paper.

User Circle Single Streamline Icon: https://streamlinehq.com Sign Up for Free