Distinguishing Causes from Effects using Nonlinear Acyclic Causal Models
Kun Zhang and Aapo Hyvärinen (University of Helsinki, Finland)
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.