CFSM: A Novel Causal Feature Selection Module for Two-Dimensional Out-of-Distribution Generalization

In real-world scenarios, training and test data are often collected in diverse settings, leading to domain shifts arising from evolving environments and selection bias. While causality-inspired methods have shown promising results in tackling the out-of-distribution (OOD) generalization issue, prior methods treat the discovered differences across domains as confounding variables. While effective in handling domain differences (i.e., unseen environmental features in test data), they may fail when confronted with intricate spurious correlations in real-world datasets. In this study, we first analyze this limitation to inadequate modeling of causal intervention and derive the OOD generalization bound to explain the challenges it introduces. To address this problem, we propose a modified causal intervention approach to mitigate various types of confounders. Motivated by the mathematical formulation of our modified causal intervention, we introduce the Causal Feature Selection Module (CFSM) to suppress model weights on both domain-differences features and spurious correlation features. Integrated within the Base Feature Extraction Module, In-Sample Module, and Cross-Sample Module (B-I-C architecture), CFSM collectively neutralizes the confounding effects arising from both domain discrepancies and correlation distinctions, thereby achieving causal feature selection. Under mild assumptions, we prove that the proposed CFSM method can achieve strictly lower OOD errors. Further experiments conducted on various benchmark datasets demonstrate the effectiveness of the proposed method. Compared to previous deconfounding methods, our method not only mitigates the effect of domain-differences features but also the hard-to-identify spurious correlation features, achieving significant improvements in two-dimensional OOD generalization.