On the Identifiability of the Post-Nonlinear Causal Model

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By taking into account the nonlinear effect of the cause, the inner noise effect, and the measurement distortion effect in the observed variables, the post-nonlinear (PNL) causal model has demonstrated its excellent performance in distinguishing the cause from effect. However, its identifiability has not been properly addressed, and how to apply it in the case of more than two variables is also a problem. In this paper, we conduct a systematic investigation on its identifiability in the two-variable case. We show that this model is identifiable in most cases; by enumerating all possible situations in which the model is not identifiable, we provide sufficient conditions for its identifiability. Simulations are given to support the theoretical results. Moreover, in the case of more than two variables, we show that the whole causal structure can be found by applying the PNL causal model to each structure in the Markov equivalent class and testing if the disturbance is independent of the direct causes for each variable. In this way the exhaustive search over all possible causal structures is avoided.

Kun Zhang, Aapo Hyvarinen · 2012

Related benchmarks

Task	Dataset	Result
Bivariate Causal Discovery	LS	Accuracy33	33
Bivariate Causal Discovery	PER	Accuracy42	33
Bivariate Causal Discovery	SIM-c	Accuracy54	33
Bivariate Causal Discovery	SIM	Accuracy46	33
Bivariate Causal Discovery	Qd-V	Accuracy46	33
Bivariate Causal Discovery	Net	Accuracy51	33
Bivariate Causal Discovery	AN	Accuracy30	33
Bivariate Causal Discovery	D4 s1	Accuracy33	33
Bivariate Causal Discovery	NN-V	Accuracy41	33
Bivariate Causal Discovery	Tue	Accuracy51	33