Estimation of Post-Nonlinear Causal Models Using Autoencoding Structure

Discovering causal relations in complex systems is an important problem in many research fields. To describe such systems involving nonlinear causal relations, the post-nonlinear (PNL) causal model has been proposed. However, despite its identifiability, estimation methods of PNL model have not been developed as well as linear models. In this paper, we proposed a new estimation method of PNL model using an autoencoding structure. Our method estimates the model by minimizing two losses corresponding to two assumptions of PNL model: independence between the cause and the noise and invertibility of a nonlinear distortion. Experimental results on artificial data show that our method estimates underlying model satisfying both assumptions. In addition, the proposed method finds correct causal directions 1.5 times as many real-world problems as the existing method assuming linear causal relations.