Pairwise Measures of Causal Direction in Linear Non-Gaussian Acyclic Models

Aapo Hyvarinen
Proceedings of 2nd Asian Conference on Machine Learning, PMLR 13:1-16, 2010.

Abstract

We present new measures of the causal direction between two nongaussian random variables. They are based on the likelihood ratio under the linear non-gaussian acyclic model (LiNGAM). We also develop simple first-order approximations and analyze them based on related cumulant-based measures. The cumulant-based measures can be shown to give the right causal directions, and they are statistically consistent even in the presence of measurement noise. We further show how to apply these measures to estimate LiNGAM for more than two variables, and even in the case of more variables than observations. The proposed framework is statistically at least as good as existing ones in the cases of few data points or noisy data, and it is computationally and conceptually very simple.

Cite this Paper

BibTeX
@InProceedings{pmlr-v13-hyvarinen10a, title = {Pairwise Measures of Causal Direction in Linear Non-Gaussian Acyclic Models}, author = {Hyvarinen, Aapo}, booktitle = {Proceedings of 2nd Asian Conference on Machine Learning}, pages = {1--16}, year = {2010}, editor = {Sugiyama, Masashi and Yang, Qiang}, volume = {13}, series = {Proceedings of Machine Learning Research}, address = {Tokyo, Japan}, month = {08--10 Nov}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v13/hyvarinen10a/hyvarinen10a.pdf}, url = {https://proceedings.mlr.press/v13/hyvarinen10a.html}, abstract = {We present new measures of the causal direction between two nongaussian random variables. They are based on the likelihood ratio under the linear non-gaussian acyclic model (LiNGAM). We also develop simple first-order approximations and analyze them based on related cumulant-based measures. The cumulant-based measures can be shown to give the right causal directions, and they are statistically consistent even in the presence of measurement noise. We further show how to apply these measures to estimate LiNGAM for more than two variables, and even in the case of more variables than observations. The proposed framework is statistically at least as good as existing ones in the cases of few data points or noisy data, and it is computationally and conceptually very simple.} }
Endnote
%0 Conference Paper %T Pairwise Measures of Causal Direction in Linear Non-Gaussian Acyclic Models %A Aapo Hyvarinen %B Proceedings of 2nd Asian Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2010 %E Masashi Sugiyama %E Qiang Yang %F pmlr-v13-hyvarinen10a %I PMLR %P 1--16 %U https://proceedings.mlr.press/v13/hyvarinen10a.html %V 13 %X We present new measures of the causal direction between two nongaussian random variables. They are based on the likelihood ratio under the linear non-gaussian acyclic model (LiNGAM). We also develop simple first-order approximations and analyze them based on related cumulant-based measures. The cumulant-based measures can be shown to give the right causal directions, and they are statistically consistent even in the presence of measurement noise. We further show how to apply these measures to estimate LiNGAM for more than two variables, and even in the case of more variables than observations. The proposed framework is statistically at least as good as existing ones in the cases of few data points or noisy data, and it is computationally and conceptually very simple.
RIS
TY - CPAPER TI - Pairwise Measures of Causal Direction in Linear Non-Gaussian Acyclic Models AU - Aapo Hyvarinen BT - Proceedings of 2nd Asian Conference on Machine Learning DA - 2010/10/31 ED - Masashi Sugiyama ED - Qiang Yang ID - pmlr-v13-hyvarinen10a PB - PMLR DP - Proceedings of Machine Learning Research VL - 13 SP - 1 EP - 16 L1 - http://proceedings.mlr.press/v13/hyvarinen10a/hyvarinen10a.pdf UR - https://proceedings.mlr.press/v13/hyvarinen10a.html AB - We present new measures of the causal direction between two nongaussian random variables. They are based on the likelihood ratio under the linear non-gaussian acyclic model (LiNGAM). We also develop simple first-order approximations and analyze them based on related cumulant-based measures. The cumulant-based measures can be shown to give the right causal directions, and they are statistically consistent even in the presence of measurement noise. We further show how to apply these measures to estimate LiNGAM for more than two variables, and even in the case of more variables than observations. The proposed framework is statistically at least as good as existing ones in the cases of few data points or noisy data, and it is computationally and conceptually very simple. ER -
APA
Hyvarinen, A.. (2010). Pairwise Measures of Causal Direction in Linear Non-Gaussian Acyclic Models. Proceedings of 2nd Asian Conference on Machine Learning, in Proceedings of Machine Learning Research 13:1-16 Available from https://proceedings.mlr.press/v13/hyvarinen10a.html.

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