Ordering-Based Causal Discovery for Linear and Nonlinear Relations

TL;DR

CaPS is a new ordering-based causal discovery algorithm capable of effectively identifying causal relations in datasets containing both linear and nonlinear relations, outperforming existing methods on synthetic and real data.

Contribution

Introduces CaPS, a novel causal discovery method that handles mixed linear and nonlinear relations using a new topological ordering criterion and parent scores.

Findings

Outperforms state-of-the-art baselines on synthetic data with mixed relations.

Demonstrates effectiveness on real-world datasets.

Accelerates pruning and improves accuracy in causal inference.

Abstract

Identifying causal relations from purely observational data typically requires additional assumptions on relations and/or noise. Most current methods restrict their analysis to datasets that are assumed to have pure linear or nonlinear relations, which is often not reflective of real-world datasets that contain a combination of both. This paper presents CaPS, an ordering-based causal discovery algorithm that effectively handles linear and nonlinear relations. CaPS introduces a novel identification criterion for topological ordering and incorporates the concept of "parent score" during the post-processing optimization stage. These scores quantify the strength of the average causal effect, helping to accelerate the pruning process and correct inaccurate predictions in the pruning step. Experimental results demonstrate that our proposed solutions outperform state-of-the-art baselines on synthetic data with varying ratios of linear and nonlinear relations. The results obtained from real-world data also support the competitiveness of CaPS. Code and datasets are available at https://github.com/E2real/CaPS.