Inferring deterministic causal relations

Povilas Daniusis, Dominik Janzing, Joris Mooij, Jakob Zscheischler, Bastian Steudel, Kun Zhang, Bernhard Schölkopf
Proceedings of the 26th Conference on Uncertainty in Artificial Intelligence, PMLR R8:159-166, 2010.

Abstract

We consider two variables that are related to each other by an invertible function. While it has previously been shown that the dependence structure of the noise can provide hints to determine which of the two variables is the cause, we presently show that even in the deterministic (noise-free) case, there are asymmetries that can be exploited for causal inference. Our method is based on the idea that if the function and the probability density of the cause are chosen independently, then the distribution of the effect will, in a certain sense, depend on the function. We provide a theoretical analysis of this method, showing that it also works in the low noise regime, and link it to information geometry. We report strong empirical results on various real-world data sets from different domains.

Cite this Paper

BibTeX
@InProceedings{pmlr-vR8-daniusis10a, title = {Inferring deterministic causal relations}, author = {Daniusis, Povilas and Janzing, Dominik and Mooij, Joris and Zscheischler, Jakob and Steudel, Bastian and Zhang, Kun and Sch{\"o}lkopf, Bernhard}, booktitle = {Proceedings of the 26th Conference on Uncertainty in Artificial Intelligence}, pages = {159--166}, year = {2010}, editor = {Grünwald, Peter and Spirtes, Peter}, volume = {R8}, series = {Proceedings of Machine Learning Research}, month = {08--11 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/r8/main/assets/daniusis10a/daniusis10a.pdf}, url = {https://proceedings.mlr.press/r8/daniusis10a.html}, abstract = {We consider two variables that are related to each other by an invertible function. While it has previously been shown that the dependence structure of the noise can provide hints to determine which of the two variables is the cause, we presently show that even in the deterministic (noise-free) case, there are asymmetries that can be exploited for causal inference. Our method is based on the idea that if the function and the probability density of the cause are chosen independently, then the distribution of the effect will, in a certain sense, depend on the function. We provide a theoretical analysis of this method, showing that it also works in the low noise regime, and link it to information geometry. We report strong empirical results on various real-world data sets from different domains.}, note = {Reissued by PMLR on 04 October 2026.} }
Endnote
%0 Conference Paper %T Inferring deterministic causal relations %A Povilas Daniusis %A Dominik Janzing %A Joris Mooij %A Jakob Zscheischler %A Bastian Steudel %A Kun Zhang %A Bernhard Schölkopf %B Proceedings of the 26th Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2010 %E Peter Grünwald %E Peter Spirtes %F pmlr-vR8-daniusis10a %I PMLR %P 159--166 %U https://proceedings.mlr.press/r8/daniusis10a.html %V R8 %X We consider two variables that are related to each other by an invertible function. While it has previously been shown that the dependence structure of the noise can provide hints to determine which of the two variables is the cause, we presently show that even in the deterministic (noise-free) case, there are asymmetries that can be exploited for causal inference. Our method is based on the idea that if the function and the probability density of the cause are chosen independently, then the distribution of the effect will, in a certain sense, depend on the function. We provide a theoretical analysis of this method, showing that it also works in the low noise regime, and link it to information geometry. We report strong empirical results on various real-world data sets from different domains. %Z Reissued by PMLR on 04 October 2026.
APA
Daniusis, P., Janzing, D., Mooij, J., Zscheischler, J., Steudel, B., Zhang, K. & Schölkopf, B.. (2010). Inferring deterministic causal relations. Proceedings of the 26th Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research R8:159-166 Available from https://proceedings.mlr.press/r8/daniusis10a.html. Reissued by PMLR on 04 October 2026.

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