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 ana- lyze causal relations between continuous vari- ables. In such frameworks, linear acyclic models are typically used to model the data- generating process of variables. Recently, it was shown that use of non-Gaussianity iden- tifies a causal ordering of variables in a linear acyclic model without using any prior knowl- edge on the network structure, which is not the case with conventional methods. How- ever, existing estimation methods are based on iterative search algorithms and may not converge to a correct solution in a finite num- ber 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 fol- lows 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 ana- lyze causal relations between continuous vari- ables. In such frameworks, linear acyclic models are typically used to model the data- generating process of variables. Recently, it was shown that use of non-Gaussianity iden- tifies a causal ordering of variables in a linear acyclic model without using any prior knowl- edge on the network structure, which is not the case with conventional methods. How- ever, existing estimation methods are based on iterative search algorithms and may not converge to a correct solution in a finite num- ber 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 fol- lows 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 ana- lyze causal relations between continuous vari- ables. In such frameworks, linear acyclic models are typically used to model the data- generating process of variables. Recently, it was shown that use of non-Gaussianity iden- tifies a causal ordering of variables in a linear acyclic model without using any prior knowl- edge on the network structure, which is not the case with conventional methods. How- ever, existing estimation methods are based on iterative search algorithms and may not converge to a correct solution in a finite num- ber 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 fol- lows 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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