Non-Parametric Path Analysis in Structural Causal Models

Abstract

One of the fundamental tasks in causal inference is to decompose the observed association between a decision X and an outcome Y into its most basic structural mechanisms. In this paper, we introduce counterfactual measures for effects along with a specific mechanism, represented as a path from X to Y in an arbitrary structural causal model. We derive a novel non-parametric decomposition formula that expresses the covariance of X and Y as a sum over unblocked paths from X to Y contained in an arbitrary causal model. This formula allows a fine-grained path analysis without requiring a commitment to any particular parametric form, and can be seen as a generalization of Wright's decomposition method in linear systems (1923,1932) and Pearl's non-parametric mediation formula (2001).