Causal Discovery for Cross-Sectional Data Based on Super-Structure and Divide-and-Conquer

TL;DR

This paper introduces a lightweight, scalable causal discovery framework that reduces computational costs by relaxing Super-Structure constraints, enabling effective analysis of large, domain-knowledge-scarce datasets.

Contribution

It proposes a novel divide-and-conquer causal discovery method that relaxes Super-Structure requirements, significantly lowering CI test costs while maintaining accuracy.

Findings

Matches or closely approximates PC and FCI accuracy

Reduces CI test numbers drastically

Validates on synthetic and real-world data

Abstract

This paper tackles a critical bottleneck in Super-Structure-based divide-and-conquer causal discovery: the high computational cost of constructing accurate Super-Structures--particularly when conditional independence (CI) tests are expensive and domain knowledge is unavailable. We propose a novel, lightweight framework that relaxes the strict requirements on Super-Structure construction while preserving the algorithmic benefits of divide-and-conquer. By integrating weakly constrained Super-Structures with efficient graph partitioning and merging strategies, our approach substantially lowers CI test overhead without sacrificing accuracy. We instantiate the framework in a concrete causal discovery algorithm and rigorously evaluate its components on synthetic data. Comprehensive experiments on Gaussian Bayesian networks, including magic-NIAB, ECOLI70, and magic-IRRI, demonstrate that our method matches or closely approximates the structural accuracy of PC and FCI while drastically reducing the number of CI tests. Further validation on the real-world China Health and Retirement Longitudinal Study (CHARLS) dataset confirms its practical applicability. Our results establish that accurate, scalable causal discovery is achievable even under minimal assumptions about the initial Super-Structure, opening new avenues for applying divide-and-conquer methods to large-scale, knowledge-scarce domains such as biomedical and social science research.