A Causal Framework for Distribution Generalization

Area of Science:

• Causal inference
• Machine learning
• Statistical modeling

Background:

• Predicting outcomes Y from covariates X is difficult when test and training distributions diverge.
• Distribution shifts can stem from interventions in structural causal models, necessitating robust prediction strategies.
• Causal regression models are invariant to interventions but not always optimal for worst-case risk minimization.

Purpose of the Study:

• To introduce a formal framework, distribution generalization, for analyzing prediction under interventions in partially observed nonlinear models.
• To analyze direct and indirect interventions via exogenous variables.
• To identify conditions under which causal functions are minimax optimal and to propose practical methods.

Main Methods:

• Developed the distribution generalization framework for analyzing prediction under interventions.
• Characterized interventions for which causal functions are minimax optimal.
• Proposed the Nonlinear IV Extrapolation (NILE) method for practical distribution generalization.

Main Results:

• Proved sufficient conditions for distribution generalization and presented impossibility results.
• Demonstrated that NILE achieves distribution generalization in a nonlinear instrumental variable (IV) setting with linear extrapolation.
• Established the consistency of the NILE method.

Conclusions:

• The distribution generalization framework provides a theoretical basis for robust prediction under interventions.
• The NILE method offers a practical solution for achieving distribution generalization in complex nonlinear settings.
• Empirical results validate the effectiveness of the proposed approach.