Nonlinear Causal Discovery via Dynamic Latent Variables
Distinguishing causality from mere correlation is a cornerstone in empirical research, as conflating the two can result in significant errors in decision-making, affecting policy formulation and the validity of scientific inferences. Traditional experimental designs, such as randomized trials, often...
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| Published in: | IEEE transactions on automation science and engineering Vol. 22; pp. 10381 - 10391 |
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| Main Authors: | , , , |
| Format: | Journal Article |
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2025
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| Abstract | Distinguishing causality from mere correlation is a cornerstone in empirical research, as conflating the two can result in significant errors in decision-making, affecting policy formulation and the validity of scientific inferences. Traditional experimental designs, such as randomized trials, often fall short in complex systems where variables interact in a high-dimensional space with limited data. This paper aims to address these challenges by introducing an innovative causal discovery approach, extending beyond conventional methodologies by incorporating algorithmic advances in computational efficiency and design. We present a novel double Gaussian process state space causal model (GPSSCM) that contends with the multifaceted nature of causal inference, accounting for noisy observations and latent variables, which are commonly encountered in dynamic systems. Our methodological contribution includes the application of a Markov chain Monte Carlo technique for unraveling latent state dynamics and an expectation-maximization (EM) algorithm for robust parameter estimation. The acyclic nature of the causal graph is ensured through an integrated acyclic constraint within the EM framework, maintaining the integrity of the causal model. The efficacy of our proposed GPSSCM is evaluated through a series of tests on both synthetic data and empirical case studies from the industrial domain. The results highlight the model's capacity to accurately infer complex nonlinear causal relationships, demonstrating its superiority over traditional structural equation modeling, especially when dealing with time series data and latent variables. This paper not only contributes a sophisticated tool for researchers and practitioners but also enriches the literature on causal discovery by offering a new perspective on the analysis of intricate systems, thereby facilitating more informed and ethical decision-making across various scientific fields. Note to Practitioners-Understanding the intricate web of causality is crucial for making informed decisions in various scientific and professional fields. Our study presents a Gaussian process state space causal model, which enhances the analysis of dynamic causal relationships in complex systems, particularly when dealing with noisy observations and latent variables. Leveraging a combination of Markov chain Monte Carlo and expectation maximization algorithms, the model ensures accurate estimation of parameters and causal structures. This paper is particularly relevant for those in fields such as economics, transportation, and biology, offering a sophisticated tool to support ethical decision-making and safeguard against errors in high-stakes environments. The practical implications of this research are underscored by its ability to inform targeted interventions and predict outcomes under new conditions, advancing the comprehension and application of causality in real-world scenarios. |
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| AbstractList | Distinguishing causality from mere correlation is a cornerstone in empirical research, as conflating the two can result in significant errors in decision-making, affecting policy formulation and the validity of scientific inferences. Traditional experimental designs, such as randomized trials, often fall short in complex systems where variables interact in a high-dimensional space with limited data. This paper aims to address these challenges by introducing an innovative causal discovery approach, extending beyond conventional methodologies by incorporating algorithmic advances in computational efficiency and design. We present a novel double Gaussian process state space causal model (GPSSCM) that contends with the multifaceted nature of causal inference, accounting for noisy observations and latent variables, which are commonly encountered in dynamic systems. Our methodological contribution includes the application of a Markov chain Monte Carlo technique for unraveling latent state dynamics and an expectation-maximization (EM) algorithm for robust parameter estimation. The acyclic nature of the causal graph is ensured through an integrated acyclic constraint within the EM framework, maintaining the integrity of the causal model. The efficacy of our proposed GPSSCM is evaluated through a series of tests on both synthetic data and empirical case studies from the industrial domain. The results highlight the model's capacity to accurately infer complex nonlinear causal relationships, demonstrating its superiority over traditional structural equation modeling, especially when dealing with time series data and latent variables. This paper not only contributes a sophisticated tool for researchers and practitioners but also enriches the literature on causal discovery by offering a new perspective on the analysis of intricate systems, thereby facilitating more informed and ethical decision-making across various scientific fields. Note to Practitioners-Understanding the intricate web of causality is crucial for making informed decisions in various scientific and professional fields. Our study presents a Gaussian process state space causal model, which enhances the analysis of dynamic causal relationships in complex systems, particularly when dealing with noisy observations and latent variables. Leveraging a combination of Markov chain Monte Carlo and expectation maximization algorithms, the model ensures accurate estimation of parameters and causal structures. This paper is particularly relevant for those in fields such as economics, transportation, and biology, offering a sophisticated tool to support ethical decision-making and safeguard against errors in high-stakes environments. The practical implications of this research are underscored by its ability to inform targeted interventions and predict outcomes under new conditions, advancing the comprehension and application of causality in real-world scenarios. |
| Author | Zhang, Chen Yang, Xing Qiu, Hao Lan, Tian |
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| References_xml | – ident: ref14 doi: 10.7551/mitpress/1754.001.0001 – volume: 97 start-page: 2901 volume-title: Proc. Int. Conf. Mach. Learn. ident: ref4 article-title: Causal discovery and forecasting in nonstationary environments with state-space models – ident: ref7 doi: 10.1016/j.ijar.2008.02.006 – ident: ref29 doi: 10.1080/00207170802382376 – start-page: 213 volume-title: Proc. 19th Int. Conf. Artif. Intell. Statist. ident: ref30 article-title: Computationally efficient Bayesian learning of Gaussian process state space models – volume: 33 start-page: 14891 volume-title: Proc. Adv. Neural Inf. Process. Syst. ident: ref17 article-title: Generalized independent noise condition for estimating latent variable causal graphs – year: 2012 ident: ref18 article-title: On the identifiability of the post-nonlinear causal model publication-title: arXiv:1205.2599 – start-page: 3414 volume-title: Proc. Int. Conf. Artif. Intell. Statist. (AISTATS) ident: ref24 article-title: Learning sparse nonparametric DAGs – start-page: 1762 volume-title: Proc. 22nd Int. Conf. Artif. Intell. Statist. ident: ref3 article-title: Causal discovery in the presence of missing data – ident: ref8 doi: 10.1080/01621459.2023.2179490 – year: 2012 ident: ref9 article-title: Invariant Gaussian process latent variable models and application in causal discovery publication-title: arXiv:1203.3534 – start-page: 39939 volume-title: Proc. Int. Conf. Mach. Learn. ident: ref28 article-title: From temporal to contemporaneous iterative causal discovery in the presence of latent confounders – start-page: 1595 volume-title: Proc. Int. Conf. Artif. Intell. Statist. ident: ref10 article-title: DYNOTEARS: Structure learning from time-series data – volume: 18 start-page: 1441 volume-title: Proc. Adv. Neural Inf. Process. Syst. ident: ref23 article-title: Gaussian process dynamical models – ident: ref1 doi: 10.1002/widm.1449 – ident: ref6 doi: 10.1214/aoms/1177732676 – ident: ref15 doi: 10.24963/ijcai.2019/223 – ident: ref19 doi: 10.1080/01621459.1999.10473840 – start-page: 1052 volume-title: Proc. 38th Conf. Uncertainty Artif. Intell. ident: ref27 article-title: Greedy relaxations of the sparsest permutation algorithm – ident: ref13 doi: 10.1109/TNNLS.2021.3106111 – start-page: 183 volume-title: Proc. 4th Middle East Symp. Simulation Modelling (MESM) ident: ref31 article-title: SUMO (Simulation of Urban MObility)—An open-source traffic simulation – ident: ref12 doi: 10.1109/ICDM.2013.103 – ident: ref22 doi: 10.3182/20140824-6-ZA-1003.01843 – year: 2022 ident: ref2 article-title: A review and roadmap of deep learning causal discovery in different variable paradigms publication-title: arXiv:2209.06367 – ident: ref16 doi: 10.1093/biomet/asz048 – volume: 33 start-page: 17943 volume-title: Proc. Adv. Neural Inf. Process. Syst. ident: ref26 article-title: On the role of sparsity and dag constraints for learning linear dags – year: 2019 ident: ref25 article-title: DAG-GNN: DAG structure learning with graph neural networks publication-title: arXiv:1904.10098 – volume: 21 start-page: 1 volume-title: Proc. Adv. Neural Inf. Process. Syst. ident: ref11 article-title: Nonlinear causal discovery with additive noise models – volume: 34 start-page: 27772 volume-title: Proc. Adv. Neural Inf. Process. Syst. ident: ref21 article-title: Beware of the simulated DAG! Causal discovery benchmarks may be easy to game – start-page: 53 volume-title: Proc. Int. Workshop Climate Inform. (CI) ident: ref5 article-title: Causal discovery in the presence of confounding latent variables for climate science – start-page: 162 volume-title: Proc. Conf. Causal Learn. Reasoning ident: ref20 article-title: Typing assumptions improve identification in causal discovery |
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| SubjectTerms | Causal discovery Cause effect analysis Economics Estimation expectation maximization Gaussian process Gaussian processes Heuristic algorithms Inference algorithms Kernel Markov chain Monte Carlo Mathematical models Monte Carlo methods Numerical analysis state space model |
| Title | Nonlinear Causal Discovery via Dynamic Latent Variables |
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