Nonlinear Functional Causal Models for Distinguishing Cause from Effect
Kun Zhang, Aapo Hyvärinen · Wiley series in probability and statistics · 2016
Finding causal directions is a fundamental problem in scientific data analysis and other fields. This chapter defines the basic nonlinear model, shows how it can be estimated, and then addresses a more general theory with more complex nonlinear relationships. It discusses several functional causal models, namely, the linear model, nonlinear additive noise model, and post-nonlinear (PNL) causal model. The chapter talks about the possibility of doing causal discovery with the general form of functional causal models. It discusses the identifiability conditions of the causal direction for the PNL causal model, which naturally contain those for the linear model and nonlinear additive noise model as special cases. Finally, developing efficient methods for causal discovery of more than two variables based on functional causal models is an important step toward solving large-scale real-world causal analysis problems in various domains including neuroscience and biology.