Distributional anchor regression.

Area of Science:

• Causal inference
• Statistical modeling
• Machine learning

Background:

• Prediction models often fail with out-of-distribution (OOD) data due to differing data distributions.
• Achieving OOD generalization typically requires strong assumptions about the data generating process (DGP).
• Anchor regression offers protection against distributional shifts using causal regularization but is limited to squared-error loss.

Purpose of the Study:

• To generalize anchor regression for OOD generalization to censored and ordinal response variables.
• To develop a distributional version of anchor regression applicable to a wider range of data types.
• To assess the capabilities of the proposed method for OOD generalization.

Main Methods:

• Proposed a distributional anchor regression framework.
• Combined parametric transformation models for distributional regression with causal regularization.
• Utilized a generalized notion of residuals for censored and ordered response spaces.

Main Results:

• Demonstrated the applicability of the distributional anchor regression method.
• Showcased improved OOD generalization capabilities in exemplary applications and simulations.
• Validated the method's effectiveness for handling censored and ordinal data.

Conclusions:

• Distributional anchor regression successfully extends causal regularization to censored and ordinal data.
• The proposed method enhances OOD generalization beyond the limitations of previous anchor regression techniques.
• This work broadens the scope of causal methods for robust prediction models.