Nonlinear Causal Discovery through a Sequential Edge Orientation Approach

TL;DR

This paper introduces a new efficient and robust method for nonlinear causal discovery that leverages pairwise additive noise models and a sequential edge orientation approach, outperforming existing methods.

Contribution

It develops a novel constraint-based algorithm for learning causal DAGs under nonlinear ANMs, with proven consistency and a ranking procedure for edge orientation.

Findings

Method outperforms existing nonlinear DAG learning algorithms in experiments.

Algorithm is computationally efficient and robust to model misspecification.

Proven structural learning consistency in the large-sample limit.

Abstract

Recent advances have established the identifiability of a directed acyclic graph (DAG) under additive noise models (ANMs), spurring the development of various causal discovery methods. However, most existing methods make restrictive model assumptions, rely heavily on general independence tests, or require substantial computational time. To address these limitations, we propose a sequential procedure to orient undirected edges in a completed partial DAG (CPDAG), representing an equivalence class of DAGs, by leveraging the pairwise additive noise model (PANM) to identify their causal directions. We prove that this procedure can recover the true causal DAG assuming a restricted ANM. Building on this result, we develop a novel constraint-based algorithm for learning causal DAGs under nonlinear ANMs. Given an estimated CPDAG, we develop a ranking procedure that sorts undirected edges by their adherence to the PANM, which defines an evaluation order of the edges. To determine the edge direction, we devise a statistical test that compares the log-likelihood values, evaluated with respect to the competing directions, of a sub-graph comprising just the candidate nodes and their identified parents in the partial DAG. We further establish the structural learning consistency of our algorithm in the large-sample limit. Extensive experiments on synthetic and real-world datasets demonstrate that our method is computationally efficient, robust to model misspecification, and consistently outperforms many existing nonlinear DAG learning methods.