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 depen- dence structure of the noise can provide hints to determine which of the two variables is the cause, we presently show that even in the de- terministic (noise-free) case, there are asym- metries that can be exploited for causal in- ference. Our method is based on the idea that if the function and the probability den- sity 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 depen- dence structure of the noise can provide hints to determine which of the two variables is the cause, we presently show that even in the de- terministic (noise-free) case, there are asym- metries that can be exploited for causal in- ference. Our method is based on the idea that if the function and the probability den- sity 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 depen- dence structure of the noise can provide hints to determine which of the two variables is the cause, we presently show that even in the de- terministic (noise-free) case, there are asym- metries that can be exploited for causal in- ference. Our method is based on the idea that if the function and the probability den- sity 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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