Inference of Cause and Effect with Unsupervised Inverse Regression

Eleni Sgouritsa, Dominik Janzing, Philipp Hennig, Bernhard Schölkopf
Proceedings of the Eighteenth International Conference on Artificial Intelligence and Statistics, PMLR 38:847-855, 2015.

Abstract

We address the problem of causal discovery in the two-variable case given a sample from their joint distribution. The proposed method is based on a known assumption that, if X -> Y (X causes Y), the marginal distribution of the cause, P(X), contains no information about the conditional distribution P(Y|X). Consequently, estimating P(Y|X) from P(X) should not be possible. However, estimating P(X|Y) based on P(Y) may be possible. This paper employs this asymmetry to propose CURE, a causal discovery method which decides upon the causal direction by comparing the accuracy of the estimations of P(Y|X) and P(X|Y). To this end, we propose a method for estimating a conditional from samples of the corresponding marginal, which we call unsupervised inverse GP regression. We evaluate CURE on synthetic and real data. On the latter, our method outperforms existing causal inference methods.

Cite this Paper

BibTeX
@InProceedings{pmlr-v38-sgouritsa15, title = {{Inference of Cause and Effect with Unsupervised Inverse Regression}}, author = {Sgouritsa, Eleni and Janzing, Dominik and Hennig, Philipp and Schölkopf, Bernhard}, booktitle = {Proceedings of the Eighteenth International Conference on Artificial Intelligence and Statistics}, pages = {847--855}, year = {2015}, editor = {Lebanon, Guy and Vishwanathan, S. V. N.}, volume = {38}, series = {Proceedings of Machine Learning Research}, address = {San Diego, California, USA}, month = {09--12 May}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v38/sgouritsa15.pdf}, url = {https://proceedings.mlr.press/v38/sgouritsa15.html}, abstract = {We address the problem of causal discovery in the two-variable case given a sample from their joint distribution. The proposed method is based on a known assumption that, if X -> Y (X causes Y), the marginal distribution of the cause, P(X), contains no information about the conditional distribution P(Y|X). Consequently, estimating P(Y|X) from P(X) should not be possible. However, estimating P(X|Y) based on P(Y) may be possible. This paper employs this asymmetry to propose CURE, a causal discovery method which decides upon the causal direction by comparing the accuracy of the estimations of P(Y|X) and P(X|Y). To this end, we propose a method for estimating a conditional from samples of the corresponding marginal, which we call unsupervised inverse GP regression. We evaluate CURE on synthetic and real data. On the latter, our method outperforms existing causal inference methods.} }
Endnote
%0 Conference Paper %T Inference of Cause and Effect with Unsupervised Inverse Regression %A Eleni Sgouritsa %A Dominik Janzing %A Philipp Hennig %A Bernhard Schölkopf %B Proceedings of the Eighteenth International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2015 %E Guy Lebanon %E S. V. N. Vishwanathan %F pmlr-v38-sgouritsa15 %I PMLR %P 847--855 %U https://proceedings.mlr.press/v38/sgouritsa15.html %V 38 %X We address the problem of causal discovery in the two-variable case given a sample from their joint distribution. The proposed method is based on a known assumption that, if X -> Y (X causes Y), the marginal distribution of the cause, P(X), contains no information about the conditional distribution P(Y|X). Consequently, estimating P(Y|X) from P(X) should not be possible. However, estimating P(X|Y) based on P(Y) may be possible. This paper employs this asymmetry to propose CURE, a causal discovery method which decides upon the causal direction by comparing the accuracy of the estimations of P(Y|X) and P(X|Y). To this end, we propose a method for estimating a conditional from samples of the corresponding marginal, which we call unsupervised inverse GP regression. We evaluate CURE on synthetic and real data. On the latter, our method outperforms existing causal inference methods.
RIS
TY - CPAPER TI - Inference of Cause and Effect with Unsupervised Inverse Regression AU - Eleni Sgouritsa AU - Dominik Janzing AU - Philipp Hennig AU - Bernhard Schölkopf BT - Proceedings of the Eighteenth International Conference on Artificial Intelligence and Statistics DA - 2015/02/21 ED - Guy Lebanon ED - S. V. N. Vishwanathan ID - pmlr-v38-sgouritsa15 PB - PMLR DP - Proceedings of Machine Learning Research VL - 38 SP - 847 EP - 855 L1 - http://proceedings.mlr.press/v38/sgouritsa15.pdf UR - https://proceedings.mlr.press/v38/sgouritsa15.html AB - We address the problem of causal discovery in the two-variable case given a sample from their joint distribution. The proposed method is based on a known assumption that, if X -> Y (X causes Y), the marginal distribution of the cause, P(X), contains no information about the conditional distribution P(Y|X). Consequently, estimating P(Y|X) from P(X) should not be possible. However, estimating P(X|Y) based on P(Y) may be possible. This paper employs this asymmetry to propose CURE, a causal discovery method which decides upon the causal direction by comparing the accuracy of the estimations of P(Y|X) and P(X|Y). To this end, we propose a method for estimating a conditional from samples of the corresponding marginal, which we call unsupervised inverse GP regression. We evaluate CURE on synthetic and real data. On the latter, our method outperforms existing causal inference methods. ER -
APA
Sgouritsa, E., Janzing, D., Hennig, P. & Schölkopf, B.. (2015). Inference of Cause and Effect with Unsupervised Inverse Regression. Proceedings of the Eighteenth International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 38:847-855 Available from https://proceedings.mlr.press/v38/sgouritsa15.html.

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