Learning a directed acyclic graph with additive heteroscedastic errors

2026-05-25

AI Summary

This study addresses the problem of recovering the directed acyclic graph (DAG) structure of structural equation models from observational data contaminated with additive heteroscedastic noise. The work proposes a novel heteroscedasticity-based causal discovery method, establishing for the first time that heteroscedasticity serves as a critical signal for identifying causal directions. It develops a multivariate causal discovery framework that extends beyond traditional mean-based modeling by leveraging the invariance of conditional scale coefficients across quantiles to recursively identify sink nodes and infer the causal topological order. The proposed RESQUE algorithm, which integrates residual construction with composite quantile regression, demonstrates superior performance over existing methods on both synthetic and benchmark datasets, particularly excelling when causal information is partially encoded in the variance component.

Abstract

This paper studies causal discovery for a directed acyclic graph under a structural equation model with additive heteroscedastic errors. We first establish new identifiability results for location-scale noise models, showing that heteroscedasticity can be leveraged to recover causal directions. Based on these insights, we propose a novel iterative procedure, Residual Simultaneous Quantile Estimation (RESQUE), where each iteration consists of a residual-construction stage and a composite quantile regression stage, enabling recursive identification of sink nodes via the invariance of conditional scale coefficients across quantiles. We then establish its theoretical guarantees for recovering topological order and graph structure, even when the number of variables diverges with the sample size. Simulation studies and application to benchmark datasets show that RESQUE performs favorably compared with existing methods, especially when causal information is partly encoded in the variance component. These results highlight exploiting structured variance signals for causal discovery and provide a principled framework for multivariate causal discovery beyond mean-based modeling.

Problem

• causal discovery
• directed acyclic graph
• heteroscedastic errors
• structural equation model
• additive noise model

Innovation

• heteroscedasticity
• causal discovery
• quantile regression
• directed acyclic graph
• RESQUE