Causal Discovery with General Non-Linear Relationships using Non-Linear ICA

Ricardo Pio Monti, Kun Zhang, Aapo Hyvärinen
Proceedings of The 35th Uncertainty in Artificial Intelligence Conference, PMLR 115:186-195, 2020.

Abstract

We consider the problem of inferring causal relationships between two or more passively observed variables. While the problem of such causal discovery has been extensively studied especially in the bivariate setting, the majority of current methods assume a linear causal relationship, and the few methods which consider non-linear dependencies usually make the assumption of additive noise. Here, we propose a framework through which we can perform causal discovery in the presence of general non-linear relationships. The proposed method is based on recent progress in non-linear independent component analysis and exploits the non-stationarity of observations in order to recover the underlying sources or latent disturbances. We show rigorously that in the case of bivariate causal discovery, such non-linear ICA can be used to infer the causal direction via a series of independence tests. We further propose an alternative measure of causal direction based on asymptotic approximations to the likelihood ratio, as well as an extension to multivariate causal discovery. We demonstrate the capabilities of the proposed method via a series of simulation studies and conclude with an application to neuroimaging data.

Cite this Paper

BibTeX
@InProceedings{pmlr-v115-monti20a, title = {Causal Discovery with General Non-Linear Relationships using Non-Linear ICA}, author = {Monti, Ricardo Pio and Zhang, Kun and Hyv{\"{a}}rinen, Aapo}, booktitle = {Proceedings of The 35th Uncertainty in Artificial Intelligence Conference}, pages = {186--195}, year = {2020}, editor = {Adams, Ryan P. and Gogate, Vibhav}, volume = {115}, series = {Proceedings of Machine Learning Research}, month = {22--25 Jul}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v115/monti20a/monti20a.pdf}, url = {https://proceedings.mlr.press/v115/monti20a.html}, abstract = {We consider the problem of inferring causal relationships between two or more passively observed variables. While the problem of such causal discovery has been extensively studied especially in the bivariate setting, the majority of current methods assume a linear causal relationship, and the few methods which consider non-linear dependencies usually make the assumption of additive noise. Here, we propose a framework through which we can perform causal discovery in the presence of general non-linear relationships. The proposed method is based on recent progress in non-linear independent component analysis and exploits the non-stationarity of observations in order to recover the underlying sources or latent disturbances. We show rigorously that in the case of bivariate causal discovery, such non-linear ICA can be used to infer the causal direction via a series of independence tests. We further propose an alternative measure of causal direction based on asymptotic approximations to the likelihood ratio, as well as an extension to multivariate causal discovery. We demonstrate the capabilities of the proposed method via a series of simulation studies and conclude with an application to neuroimaging data. } }
Endnote
%0 Conference Paper %T Causal Discovery with General Non-Linear Relationships using Non-Linear ICA %A Ricardo Pio Monti %A Kun Zhang %A Aapo Hyvärinen %B Proceedings of The 35th Uncertainty in Artificial Intelligence Conference %C Proceedings of Machine Learning Research %D 2020 %E Ryan P. Adams %E Vibhav Gogate %F pmlr-v115-monti20a %I PMLR %P 186--195 %U https://proceedings.mlr.press/v115/monti20a.html %V 115 %X We consider the problem of inferring causal relationships between two or more passively observed variables. While the problem of such causal discovery has been extensively studied especially in the bivariate setting, the majority of current methods assume a linear causal relationship, and the few methods which consider non-linear dependencies usually make the assumption of additive noise. Here, we propose a framework through which we can perform causal discovery in the presence of general non-linear relationships. The proposed method is based on recent progress in non-linear independent component analysis and exploits the non-stationarity of observations in order to recover the underlying sources or latent disturbances. We show rigorously that in the case of bivariate causal discovery, such non-linear ICA can be used to infer the causal direction via a series of independence tests. We further propose an alternative measure of causal direction based on asymptotic approximations to the likelihood ratio, as well as an extension to multivariate causal discovery. We demonstrate the capabilities of the proposed method via a series of simulation studies and conclude with an application to neuroimaging data.
APA
Monti, R.P., Zhang, K. & Hyvärinen, A.. (2020). Causal Discovery with General Non-Linear Relationships using Non-Linear ICA. Proceedings of The 35th Uncertainty in Artificial Intelligence Conference, in Proceedings of Machine Learning Research 115:186-195 Available from https://proceedings.mlr.press/v115/monti20a.html.

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