A direct method for estimating a causal ordering in a linear non-Gaussian acyclic model

Shohei Shimizu, Aapo Hyvärinen, Yoshinobu Kawahara, Takashi Washio
Proceedings of the 25th Conference on Uncertainty in Artificial Intelligence, PMLR R7:514-521, 2009.

Abstract

Structural equation models and Bayesian networks have been widely used to analyze causal relations between continuous variables. In such frameworks, linear acyclic models are typically used to model the datagenerating process of variables. Recently, it was shown that use of non-Gaussianity identifies a causal ordering of variables in a linear acyclic model without using any prior knowledge on the network structure, which is not the case with conventional methods. However, existing estimation methods are based on iterative search algorithms and may not converge to a correct solution in a finite number of steps. In this paper, we propose a new direct method to estimate a causal ordering based on non-Gaussianity. In contrast to the previous methods, our algorithm requires no algorithmic parameters and is guaranteed to converge to the right solution within a small fixed number of steps if the data strictly follows the model.

Cite this Paper

BibTeX
@InProceedings{pmlr-vR7-shimizu09a, title = {A direct method for estimating a causal ordering in a linear non-{G}aussian acyclic model}, author = {Shimizu, Shohei and Hyv{\"a}rinen, Aapo and Kawahara, Yoshinobu and Washio, Takashi}, booktitle = {Proceedings of the 25th Conference on Uncertainty in Artificial Intelligence}, pages = {514--521}, year = {2009}, editor = {Bilmes, Jeff and Ng, Andrew Y.}, volume = {R7}, series = {Proceedings of Machine Learning Research}, month = {18--21 Jun}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/r7/main/assets/shimizu09a/shimizu09a.pdf}, url = {https://proceedings.mlr.press/r7/shimizu09a.html}, abstract = {Structural equation models and Bayesian networks have been widely used to analyze causal relations between continuous variables. In such frameworks, linear acyclic models are typically used to model the datagenerating process of variables. Recently, it was shown that use of non-Gaussianity identifies a causal ordering of variables in a linear acyclic model without using any prior knowledge on the network structure, which is not the case with conventional methods. However, existing estimation methods are based on iterative search algorithms and may not converge to a correct solution in a finite number of steps. In this paper, we propose a new direct method to estimate a causal ordering based on non-Gaussianity. In contrast to the previous methods, our algorithm requires no algorithmic parameters and is guaranteed to converge to the right solution within a small fixed number of steps if the data strictly follows the model.}, note = {Reissued by PMLR on 04 October 2026.} }
Endnote
%0 Conference Paper %T A direct method for estimating a causal ordering in a linear non-Gaussian acyclic model %A Shohei Shimizu %A Aapo Hyvärinen %A Yoshinobu Kawahara %A Takashi Washio %B Proceedings of the 25th Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2009 %E Jeff Bilmes %E Andrew Y. Ng %F pmlr-vR7-shimizu09a %I PMLR %P 514--521 %U https://proceedings.mlr.press/r7/shimizu09a.html %V R7 %X Structural equation models and Bayesian networks have been widely used to analyze causal relations between continuous variables. In such frameworks, linear acyclic models are typically used to model the datagenerating process of variables. Recently, it was shown that use of non-Gaussianity identifies a causal ordering of variables in a linear acyclic model without using any prior knowledge on the network structure, which is not the case with conventional methods. However, existing estimation methods are based on iterative search algorithms and may not converge to a correct solution in a finite number of steps. In this paper, we propose a new direct method to estimate a causal ordering based on non-Gaussianity. In contrast to the previous methods, our algorithm requires no algorithmic parameters and is guaranteed to converge to the right solution within a small fixed number of steps if the data strictly follows the model. %Z Reissued by PMLR on 04 October 2026.
APA
Shimizu, S., Hyvärinen, A., Kawahara, Y. & Washio, T.. (2009). A direct method for estimating a causal ordering in a linear non-Gaussian acyclic model. Proceedings of the 25th Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research R7:514-521 Available from https://proceedings.mlr.press/r7/shimizu09a.html. Reissued by PMLR on 04 October 2026.

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