Two-stage identification for nonlinear causal relationships

The discovery of causal relationships between observed variables has received much attention in the past. For continuous-valued data, linear acyclic causal models are commonly used to model the data-generating process, and structural equation models, Bayesian networks are widely applied to analyze the structures. In reality, many causal relationships are more or less nonlinear, raising some doubts as to the applicability and usefulness of purely linear methods. In this paper, we generalize the basic linear model to nonlinear model, and propose a two-step method, which first make use of the feature-selection based approach to obtain the d-separation equivalence class, undetermined causal directions are then found by nonlinear regression and pairwise independence tests. In addition to theoretical algorithm we empirically demonstrate the power of the proposed method through experiments.