Inferring Cause and Effect in the Presence of Heteroscedastic Noise

Sascha Xu, Osman A Mian, Alexander Marx, Jilles Vreeken
Proceedings of the 39th International Conference on Machine Learning, PMLR 162:24615-24630, 2022.

Abstract

We study the problem of identifying cause and effect over two univariate continuous variables $X$ and $Y$ from a sample of their joint distribution. Our focus lies on the setting when the variance of the noise may be dependent on the cause. We propose to partition the domain of the cause into multiple segments where the noise indeed is dependent. To this end, we minimize a scale-invariant, penalized regression score, finding the optimal partitioning using dynamic programming. We show under which conditions this allows us to identify the causal direction for the linear setting with heteroscedastic noise, for the non-linear setting with homoscedastic noise, as well as empirically confirm that these results generalize to the non-linear and heteroscedastic case. Altogether, the ability to model heteroscedasticity translates into an improved performance in telling cause from effect on a wide range of synthetic and real-world datasets.

Cite this Paper

BibTeX
@InProceedings{pmlr-v162-xu22f, title = {Inferring Cause and Effect in the Presence of Heteroscedastic Noise}, author = {Xu, Sascha and Mian, Osman A and Marx, Alexander and Vreeken, Jilles}, booktitle = {Proceedings of the 39th International Conference on Machine Learning}, pages = {24615--24630}, year = {2022}, editor = {Chaudhuri, Kamalika and Jegelka, Stefanie and Song, Le and Szepesvari, Csaba and Niu, Gang and Sabato, Sivan}, volume = {162}, series = {Proceedings of Machine Learning Research}, month = {17--23 Jul}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v162/xu22f/xu22f.pdf}, url = {https://proceedings.mlr.press/v162/xu22f.html}, abstract = {We study the problem of identifying cause and effect over two univariate continuous variables $X$ and $Y$ from a sample of their joint distribution. Our focus lies on the setting when the variance of the noise may be dependent on the cause. We propose to partition the domain of the cause into multiple segments where the noise indeed is dependent. To this end, we minimize a scale-invariant, penalized regression score, finding the optimal partitioning using dynamic programming. We show under which conditions this allows us to identify the causal direction for the linear setting with heteroscedastic noise, for the non-linear setting with homoscedastic noise, as well as empirically confirm that these results generalize to the non-linear and heteroscedastic case. Altogether, the ability to model heteroscedasticity translates into an improved performance in telling cause from effect on a wide range of synthetic and real-world datasets.} }
Endnote
%0 Conference Paper %T Inferring Cause and Effect in the Presence of Heteroscedastic Noise %A Sascha Xu %A Osman A Mian %A Alexander Marx %A Jilles Vreeken %B Proceedings of the 39th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2022 %E Kamalika Chaudhuri %E Stefanie Jegelka %E Le Song %E Csaba Szepesvari %E Gang Niu %E Sivan Sabato %F pmlr-v162-xu22f %I PMLR %P 24615--24630 %U https://proceedings.mlr.press/v162/xu22f.html %V 162 %X We study the problem of identifying cause and effect over two univariate continuous variables $X$ and $Y$ from a sample of their joint distribution. Our focus lies on the setting when the variance of the noise may be dependent on the cause. We propose to partition the domain of the cause into multiple segments where the noise indeed is dependent. To this end, we minimize a scale-invariant, penalized regression score, finding the optimal partitioning using dynamic programming. We show under which conditions this allows us to identify the causal direction for the linear setting with heteroscedastic noise, for the non-linear setting with homoscedastic noise, as well as empirically confirm that these results generalize to the non-linear and heteroscedastic case. Altogether, the ability to model heteroscedasticity translates into an improved performance in telling cause from effect on a wide range of synthetic and real-world datasets.
APA
Xu, S., Mian, O.A., Marx, A. & Vreeken, J.. (2022). Inferring Cause and Effect in the Presence of Heteroscedastic Noise. Proceedings of the 39th International Conference on Machine Learning, in Proceedings of Machine Learning Research 162:24615-24630 Available from https://proceedings.mlr.press/v162/xu22f.html.

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