Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
169 tokens/sec
GPT-4o
7 tokens/sec
Gemini 2.5 Pro Pro
45 tokens/sec
o3 Pro
4 tokens/sec
GPT-4.1 Pro
38 tokens/sec
DeepSeek R1 via Azure Pro
28 tokens/sec
2000 character limit reached

Learning the Causal Structure of Networked Dynamical Systems under Latent Nodes and Structured Noise (2312.05974v3)

Published 10 Dec 2023 in cs.LG and stat.ME

Abstract: This paper considers learning the hidden causal network of a linear networked dynamical system (NDS) from the time series data at some of its nodes -- partial observability. The dynamics of the NDS are driven by colored noise that generates spurious associations across pairs of nodes, rendering the problem much harder. To address the challenge of noise correlation and partial observability, we assign to each pair of nodes a feature vector computed from the time series data of observed nodes. The feature embedding is engineered to yield structural consistency: there exists an affine hyperplane that consistently partitions the set of features, separating the feature vectors corresponding to connected pairs of nodes from those corresponding to disconnected pairs. The causal inference problem is thus addressed via clustering the designed features. We demonstrate with simple baseline supervised methods the competitive performance of the proposed causal inference mechanism under broad connectivity regimes and noise correlation levels, including a real world network. Further, we devise novel technical guarantees of structural consistency for linear NDS under the considered regime.

Definition Search Book Streamline Icon: https://streamlinehq.com
References (50)
  1. Gene regulatory network inference from sparsely sampled noisy data. Nature Communications, 11(3493).
  2. Learning Linear Bayesian Networks with Latent Variables. In Proceedings of the 30th International Conference on Machine Learning, volume 28 of Proceedings of Machine Learning Research, 249–257. Atlanta, Georgia, USA: PMLR.
  3. Learning loopy graphical models with latent variables: Efficient methods and guarantees. Ann. Statist., 41(2): 401–435.
  4. Fundamental limits in structured principal component analysis and how to reach them. Proceedings of the National Academy of Sciences of the United States of America, 120: e2302028120.
  5. Optimal errors and phase transitions in high-dimensional generalized linear models. Proceedings of the National Academy of Sciences, 116: 201802705.
  6. Dynamical Processes on Complex Networks. Cambridge University Press.
  7. Ordinary Differential Equations: Qualitative Theory. Graduate studies in mathematics. American Mathematical Society. ISBN 9780821887493.
  8. Estimating Treatment Effects from Irregular Time Series Observations with Hidden Confounders. In Proceedings of the Thirty-Seventh AAAI Conference on Artificial Intelligence and Thirty-Fifth Conference on Innovative Applications of Artificial Intelligence and Thirteenth Symposium on Educational Advances in Artificial Intelligence, AAAI’23/IAAI’23/EAAI’23. AAAI Press. ISBN 978-1-57735-880-0.
  9. Model-free inference of direct network interactions from nonlinear collective dynamics. Nature Communications, 8(2192).
  10. An Unbiased Symmetric Matrix Estimator for Topology Inference under Partial Observability. IEEE Signal Processing Letters, 29(02): 1257–1261.
  11. CUTS: Neural Causal Discovery from Irregular Time-Series Data. In The Eleventh International Conference on Learning Representations (ICLR).
  12. Reconstructing links in directed networks from noisy dynamics. Phys. Rev. E, 95: 010301.
  13. Approximating discrete probability distributions with dependence trees. IEEE Transactions on Information Theory, 14(3): 462–467.
  14. Chung, F. 1994. Spectral Graph Theory. Number 92 in CBMS Regional Conference Series. Conference Board of the Mathematical Sciences. ISBN 9780821889367.
  15. ‘Functional Connectivity’ is a Sensitive Predictor of Epilepsy Diagnosis after the First Seizure. PloS one, 5.
  16. Revealing Dynamics, Communities, and Criticality from Data. Phys. Rev. X, 10: 021047.
  17. Sparse inverse covariance estimation with the graphical lasso. Biostatistics, 9(3): 432–441.
  18. The effect of network topology on the spread of epidemics. In Proceedings IEEE 24th Annual Joint Conference of the IEEE Computer and Communications Societies., volume 2, 1455–1466.
  19. Causal Inference by Identification of Vector Autoregressive Processes with Hidden Components. In Proc. International Conference on Machine Learning, volume 37, 1917–1925.
  20. Fundamentals of Convex Analysis. Grundlehren Text Editions. Springer-Verlag Berlin Heidelberg. ISBN 978-3-540-42205-1.
  21. Data-Driven Linear Koopman Embedding for Networked Systems: Model-Predictive Grid Control. IEEE Systems Journal, 17(3): 4809–4820.
  22. Linking Functional Connectivity and Structural Connectivity Quantitatively: A Comparison of Methods. Brain Connectivity, 6(2): 99–108.
  23. A Deterministic Model for Gonorrhea in a Nonhomogeneous Population. Mathematical Biosciences, 28: 221–236.
  24. Revisiting correlation-based functional connectivity and its relationship with structural connectivity. Network Neuroscience, 4(4): 1235–1251.
  25. Structure estimation for discrete graphical models: Generalized covariance matrices and their inverses. The Annals of Statistics, 41(6): 3022 – 3049.
  26. Deep learning for universal linear embeddings of nonlinear dynamics. Nature Communications, 9.
  27. Recovering the Graph Underlying Networked Dynamical Systems under Partial-observability: a Deep Learning Approach. In Proceedings of the 37th AAAI Coference on Artificial Intelligence. AAAI.
  28. Interpretable Models for Granger Causality Using Self-explaining Neural Networks. In International Conference on Learning Representations.
  29. Network reconstruction of dynamical polytrees with unobserved nodes. In Proc. IEEE Conference on Decision and Control (CDC), 4629–4634. Maui, Hawaii.
  30. Identification of network components in presence of unobserved nodes. In Proc. IEEE Conference on Decision and Control (CDC), 1563–1568. Osaka, Japan.
  31. Graph Learning under Partial Observability. Proceedings of the IEEE, 108: 2049 – 2066.
  32. Graph Learning over Partially Observed Diffusion Networks: Role of Degree Concentration. IEEE Open Journal of Signal Processing, 335–371.
  33. Linear identification of nonlinear systems: A lifting technique based on the Koopman operator. In 2016 IEEE 55th Conference on Decision and Control (CDC), 6500–6505. Las Vegas, USA.
  34. SILVar: Single Index Latent Variable Models. IEEE Transactions on Signal Processing, 66(11): 2790–2803.
  35. Causal Transformer for Estimating Counterfactual Outcomes. In ICML, 15293–15329.
  36. Which graphical models are difficult to learn? In Advances in Neural Information Processing Systems, volume 22. Vancouver, Canada.
  37. Fast and accurate inference of gene regulatory networks through robust precision matrix estimation. Bioinformatics, 38(10): 2802–2809.
  38. Pearl, J. 2009. Causality. Cambridge University Press, 2 edition.
  39. Scikit-learn: Machine Learning in Python. Journal of Machine Learning Research, 12: 2825–2830.
  40. Learning Networks of Stochastic Differential Equations. In Advances in Neural Information Processing Systems, volume 23. Curran Associates, Inc.
  41. Elements of Causal Inference: Foundations and Learning Algorithms. The MIT Press. ISBN 0262037319.
  42. Noise Bridges Dynamical Correlation and Topology in Coupled Oscillator Networks. Phys. Rev. Lett., 104: 058701.
  43. Generalized network dismantling. Proceedings of the National Academy of Sciences, 116(14): 6554–6559.
  44. Inferring causation from time series in Earth system sciences. Nature Communications, 10.
  45. Local Tomography of Large Networks under the Low-Observability Regime. IEEE Transactions on Information Theory, 66: 587 – 613.
  46. Topology identification under spatially correlated noise. Automatica, 156: 111182.
  47. Spirtes, P. 2001. An Anytime Algorithm for Causal Inference. In Richardson, T. S.; and Jaakkola, T. S., eds., Proceedings of the Eighth International Workshop on Artificial Intelligence and Statistics, volume R3 of Proceedings of Machine Learning Research, 278–285. PMLR. Reissued by PMLR on 31 March 2021.
  48. Causation, Prediction, and Search. MIT press, 2nd edition.
  49. Inferring Epidemic Network Topology from Surveillance Data. PloS one, 9: e100661.
  50. Human brain structural connectivity matrices–ready for modelling. Scientific Data, 9: 486.
Citations (2)
View on Semantic Scholar

Summary

We haven't generated a summary for this paper yet.

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