Distributional Anchor Regression

TL;DR

This paper extends anchor regression to distributional settings, enabling robust out-of-distribution predictions for censored and ordinal data by integrating causal regularization with distributional regression models.

Contribution

It introduces a distributional version of anchor regression that handles censored and ordinal responses, broadening its applicability beyond squared-error loss.

Findings

Demonstrates improved OOD generalization in simulations

Shows effectiveness on an exemplary real-world application

Extends anchor regression to distributional and censored data

Abstract

Prediction models often fail if train and test data do not stem from the same distribution. Out-of-distribution (OOD) generalization to unseen, perturbed test data is a desirable but difficult-to-achieve property for prediction models and in general requires strong assumptions on the data generating process (DGP). In a causally inspired perspective on OOD generalization, the test data arise from a specific class of interventions on exogenous random variables of the DGP, called anchors. Anchor regression models, introduced by Rothenhaeusler et al. (2021), protect against distributional shifts in the test data by employing causal regularization. However, so far anchor regression has only been used with a squared-error loss which is inapplicable to common responses such as censored continuous or ordinal data. Here, we propose a distributional version of anchor regression which generalizes the method to potentially censored responses with at least an ordered sample space. To this end, we combine a flexible class of parametric transformation models for distributional regression with an appropriate causal regularizer under a more general notion of residuals. In an exemplary application and several simulation scenarios we demonstrate the extent to which OOD generalization is possible.