Primary Submission Category: Causal Discovery
Nonlinear Causal Learning through Sequential Orientation of Edges in an Equivalence Class
Authors: Stella Huang, Qing Zhou,
Presenting Author: Stella Huang*
While recent advances have established the identifiability of a directed acyclic graph (DAG) under assumptions on the structural causal model (SCM), many existing causal discovery methods rely heavily on strong structural and distributional assumptions, perform only bivariate comparisons for random variables, or require substantial computational time. In this work, we introduce a novel constraint-based algorithm for learning the causal DAG under the non-linear setting. Building upon the equivalence class of a DAG, our approach incorporates a novel procedure to sequentially determine the true causal direction of undirected edges. We propose a ranking procedure to determine the evaluation order of edges by formulating the pairwise Additive Noise Model (PANM) to establish the necessary conditions for edge orientation. The edges are then ordered by an associated independence measure, in which the first rank is guaranteed to fulfill the conditions for orientation. To determine the true edge direction, we employ a statistical test that compares the log-likelihoods, evaluated with respect to the competing directions, of the sub-graph consisting of the two nodes and their parents. We further establish its theoretical guarantees at the population level and consistency in the large-sample limit. Experimental results demonstrate that our method is robust and computationally efficient, both when model assumptions hold and when they are violated.