Identifying Cause and Effect on Discrete Data using Additive Noise Models

Jonas Peters, Dominik Janzing, Bernhard Schölkopf
Proceedings of the Thirteenth International Conference on Artificial Intelligence and Statistics, PMLR 9:597-604, 2010.

Abstract

Inferring the causal structure of a set of random variables from a finite sample of the joint distribution is an important problem in science. Recently, methods using additive noise models have been suggested to approach the case of continuous variables. In many situations, however, the variables of interest are discrete or even have only finitely many states. In this work we extend the notion of additive noise models to these cases. Whenever the joint distribution $\mathbf{P}^{(X,Y)}$ admits such a model in one direction, e.g. $Y = f(X)+N$, $N \perp \!\!\! \perp X$, it does not admit the reversed model $X=g(Y)+\tilde{N}$, $\tilde{N} \perp \!\!\! \perp Y$ as long as the model is chosen in a generic way. Based on these deliberations we propose an efficient new algorithm that is able to distinguish between cause and effect for a finite sample of discrete variables. We show that this algorithm works both on synthetic and real data sets.

Cite this Paper

BibTeX
@InProceedings{pmlr-v9-peters10a, title = {Identifying Cause and Effect on Discrete Data using Additive Noise Models}, author = {Peters, Jonas and Janzing, Dominik and Schölkopf, Bernhard}, booktitle = {Proceedings of the Thirteenth International Conference on Artificial Intelligence and Statistics}, pages = {597--604}, year = {2010}, editor = {Teh, Yee Whye and Titterington, Mike}, volume = {9}, series = {Proceedings of Machine Learning Research}, address = {Chia Laguna Resort, Sardinia, Italy}, month = {13--15 May}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v9/peters10a/peters10a.pdf}, url = {https://proceedings.mlr.press/v9/peters10a.html}, abstract = {Inferring the causal structure of a set of random variables from a finite sample of the joint distribution is an important problem in science. Recently, methods using additive noise models have been suggested to approach the case of continuous variables. In many situations, however, the variables of interest are discrete or even have only finitely many states. In this work we extend the notion of additive noise models to these cases. Whenever the joint distribution $\mathbf{P}^{(X,Y)}$ admits such a model in one direction, e.g. $Y = f(X)+N$, $N \perp \!\!\! \perp X$, it does not admit the reversed model $X=g(Y)+\tilde{N}$, $\tilde{N} \perp \!\!\! \perp Y$ as long as the model is chosen in a generic way. Based on these deliberations we propose an efficient new algorithm that is able to distinguish between cause and effect for a finite sample of discrete variables. We show that this algorithm works both on synthetic and real data sets.} }
Endnote
%0 Conference Paper %T Identifying Cause and Effect on Discrete Data using Additive Noise Models %A Jonas Peters %A Dominik Janzing %A Bernhard Schölkopf %B Proceedings of the Thirteenth International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2010 %E Yee Whye Teh %E Mike Titterington %F pmlr-v9-peters10a %I PMLR %P 597--604 %U https://proceedings.mlr.press/v9/peters10a.html %V 9 %X Inferring the causal structure of a set of random variables from a finite sample of the joint distribution is an important problem in science. Recently, methods using additive noise models have been suggested to approach the case of continuous variables. In many situations, however, the variables of interest are discrete or even have only finitely many states. In this work we extend the notion of additive noise models to these cases. Whenever the joint distribution $\mathbf{P}^{(X,Y)}$ admits such a model in one direction, e.g. $Y = f(X)+N$, $N \perp \!\!\! \perp X$, it does not admit the reversed model $X=g(Y)+\tilde{N}$, $\tilde{N} \perp \!\!\! \perp Y$ as long as the model is chosen in a generic way. Based on these deliberations we propose an efficient new algorithm that is able to distinguish between cause and effect for a finite sample of discrete variables. We show that this algorithm works both on synthetic and real data sets.
RIS
TY - CPAPER TI - Identifying Cause and Effect on Discrete Data using Additive Noise Models AU - Jonas Peters AU - Dominik Janzing AU - Bernhard Schölkopf BT - Proceedings of the Thirteenth International Conference on Artificial Intelligence and Statistics DA - 2010/03/31 ED - Yee Whye Teh ED - Mike Titterington ID - pmlr-v9-peters10a PB - PMLR DP - Proceedings of Machine Learning Research VL - 9 SP - 597 EP - 604 L1 - http://proceedings.mlr.press/v9/peters10a/peters10a.pdf UR - https://proceedings.mlr.press/v9/peters10a.html AB - Inferring the causal structure of a set of random variables from a finite sample of the joint distribution is an important problem in science. Recently, methods using additive noise models have been suggested to approach the case of continuous variables. In many situations, however, the variables of interest are discrete or even have only finitely many states. In this work we extend the notion of additive noise models to these cases. Whenever the joint distribution $\mathbf{P}^{(X,Y)}$ admits such a model in one direction, e.g. $Y = f(X)+N$, $N \perp \!\!\! \perp X$, it does not admit the reversed model $X=g(Y)+\tilde{N}$, $\tilde{N} \perp \!\!\! \perp Y$ as long as the model is chosen in a generic way. Based on these deliberations we propose an efficient new algorithm that is able to distinguish between cause and effect for a finite sample of discrete variables. We show that this algorithm works both on synthetic and real data sets. ER -
APA
Peters, J., Janzing, D. & Schölkopf, B.. (2010). Identifying Cause and Effect on Discrete Data using Additive Noise Models. Proceedings of the Thirteenth International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 9:597-604 Available from https://proceedings.mlr.press/v9/peters10a.html.

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