Distinguishing Causes from Effects using Nonlinear Acyclic Causal Models

Kun Zhang, Aapo Hyvärinen
Proceedings of Workshop on Causality: Objectives and Assessment at NIPS 2008, PMLR 6:157-164, 2010.

Abstract

Distinguishing causes from effects is an important problem in many areas. In this paper, we propose a very general but well defined nonlinear acyclic causal model, namely, post-nonlinear acyclic causal model with inner additive noise, to tackle this problem. In this model, each observed variable is generated by a nonlinear function of its parents, with additive noise, followed by a nonlinear distortion. The nonlinearity in the second stage takes into account the effect of sensor distortions, which are usually encountered in practice. In the two-variable case, if all the nonlinearities involved in the model are invertible, by relating the proposed model to the post-nonlinear independent component analysis (ICA) problem, we give the conditions under which the causal relation can be uniquely found. We present a two-step method, which is constrained nonlinear ICA followed by statistical independence tests, to distinguish the cause from the effect in the two-variable case. We apply this method to solve the problem “CauseEffectPairs” in the Pot-luck challenge, and successfully identify causes from effects.

Cite this Paper

BibTeX
@InProceedings{pmlr-v6-zhang10a, title = {Distinguishing Causes from Effects using Nonlinear Acyclic Causal Models}, author = {Zhang, Kun and Hyvärinen, Aapo}, booktitle = {Proceedings of Workshop on Causality: Objectives and Assessment at NIPS 2008}, pages = {157--164}, year = {2010}, editor = {Guyon, Isabelle and Janzing, Dominik and Schölkopf, Bernhard}, volume = {6}, series = {Proceedings of Machine Learning Research}, address = {Whistler, Canada}, month = {12 Dec}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v6/zhang10a/zhang10a.pdf}, url = {https://proceedings.mlr.press/v6/zhang10a.html}, abstract = {Distinguishing causes from effects is an important problem in many areas. In this paper, we propose a very general but well defined nonlinear acyclic causal model, namely, post-nonlinear acyclic causal model with inner additive noise, to tackle this problem. In this model, each observed variable is generated by a nonlinear function of its parents, with additive noise, followed by a nonlinear distortion. The nonlinearity in the second stage takes into account the effect of sensor distortions, which are usually encountered in practice. In the two-variable case, if all the nonlinearities involved in the model are invertible, by relating the proposed model to the post-nonlinear independent component analysis (ICA) problem, we give the conditions under which the causal relation can be uniquely found. We present a two-step method, which is constrained nonlinear ICA followed by statistical independence tests, to distinguish the cause from the effect in the two-variable case. We apply this method to solve the problem “CauseEffectPairs” in the Pot-luck challenge, and successfully identify causes from effects.} }
Endnote
%0 Conference Paper %T Distinguishing Causes from Effects using Nonlinear Acyclic Causal Models %A Kun Zhang %A Aapo Hyvärinen %B Proceedings of Workshop on Causality: Objectives and Assessment at NIPS 2008 %C Proceedings of Machine Learning Research %D 2010 %E Isabelle Guyon %E Dominik Janzing %E Bernhard Schölkopf %F pmlr-v6-zhang10a %I PMLR %P 157--164 %U https://proceedings.mlr.press/v6/zhang10a.html %V 6 %X Distinguishing causes from effects is an important problem in many areas. In this paper, we propose a very general but well defined nonlinear acyclic causal model, namely, post-nonlinear acyclic causal model with inner additive noise, to tackle this problem. In this model, each observed variable is generated by a nonlinear function of its parents, with additive noise, followed by a nonlinear distortion. The nonlinearity in the second stage takes into account the effect of sensor distortions, which are usually encountered in practice. In the two-variable case, if all the nonlinearities involved in the model are invertible, by relating the proposed model to the post-nonlinear independent component analysis (ICA) problem, we give the conditions under which the causal relation can be uniquely found. We present a two-step method, which is constrained nonlinear ICA followed by statistical independence tests, to distinguish the cause from the effect in the two-variable case. We apply this method to solve the problem “CauseEffectPairs” in the Pot-luck challenge, and successfully identify causes from effects.
RIS
TY - CPAPER TI - Distinguishing Causes from Effects using Nonlinear Acyclic Causal Models AU - Kun Zhang AU - Aapo Hyvärinen BT - Proceedings of Workshop on Causality: Objectives and Assessment at NIPS 2008 DA - 2010/02/18 ED - Isabelle Guyon ED - Dominik Janzing ED - Bernhard Schölkopf ID - pmlr-v6-zhang10a PB - PMLR DP - Proceedings of Machine Learning Research VL - 6 SP - 157 EP - 164 L1 - http://proceedings.mlr.press/v6/zhang10a/zhang10a.pdf UR - https://proceedings.mlr.press/v6/zhang10a.html AB - Distinguishing causes from effects is an important problem in many areas. In this paper, we propose a very general but well defined nonlinear acyclic causal model, namely, post-nonlinear acyclic causal model with inner additive noise, to tackle this problem. In this model, each observed variable is generated by a nonlinear function of its parents, with additive noise, followed by a nonlinear distortion. The nonlinearity in the second stage takes into account the effect of sensor distortions, which are usually encountered in practice. In the two-variable case, if all the nonlinearities involved in the model are invertible, by relating the proposed model to the post-nonlinear independent component analysis (ICA) problem, we give the conditions under which the causal relation can be uniquely found. We present a two-step method, which is constrained nonlinear ICA followed by statistical independence tests, to distinguish the cause from the effect in the two-variable case. We apply this method to solve the problem “CauseEffectPairs” in the Pot-luck challenge, and successfully identify causes from effects. ER -
APA
Zhang, K. & Hyvärinen, A.. (2010). Distinguishing Causes from Effects using Nonlinear Acyclic Causal Models. Proceedings of Workshop on Causality: Objectives and Assessment at NIPS 2008, in Proceedings of Machine Learning Research 6:157-164 Available from https://proceedings.mlr.press/v6/zhang10a.html.

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