CSGFlow: Causal-structure-guided flow for missing value imputation

doi:10.1016/j.knosys.2026.116006

Return

CSGFlow: Causal-structure-guided flow for missing value imputation

2026-04-15

PRE

Buliao Huang

Yunhui Zhu *

DOI：10.1016/j.knosys.2026.116006

Original

Original request for help

Save

Abstract

En 中文

Missing data are ubiquitous in real-world applications, yet imputing incomplete observations remains challenging due to complex, nonlinear dependencies among variables. While deep generative models, such as normalizing flows, have achieved impressive results in modeling high-dimensional distributions, most existing approaches are correlation-based and fail to account for the underlying causal mechanisms. This limitation can lead to biased or less interpretable imputations, especially when dependencies among observed variables are complex or when the data distribution varies across environments. To address this challenge, we propose a Causal-Structure-Guided Flow (CSGFlow) framework that unifies causal discovery and generative imputation within a single probabilistic model. CSGFlow embeds the causal graph into a RealNVP-based flow architecture, ensuring that each variable’s transformation is conditioned on its causal parents, thereby producing imputations that respect the underlying causal structure and maintain statistical fidelity. A causality-constrained loss further enforces consistency between the imputations and causal graph, enhancing the reliability and interpretability. By iteratively refining both the causal graph and the generative model, CSGFlow produces imputations that are simultaneously causally coherent and statistically faithful. Extensive experiments on synthetic and real-world datasets demonstrate that CSGFlow achieves state-of-the-art performance.

Keywords:

Causal discovery

Missing data imputation

Normalizing flows

Generative models

Causal structure