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# Distinguishing Causes from Effects using Nonlinear Acyclic Causal Models

*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.