Score-Based Methods for Selecting Direct Causes in Reweighted Distributions

2026-10-06

AI Summary

This study addresses the limitation that the conventional Bayesian Information Criterion (BIC) cannot be directly applied to model selection under reweighted distributions in causal inference. To overcome this, we propose a generalized BIC extended to reweighted distribution settings, enabling the accurate identification of direct causes within marginal structural models. We theoretically establish the asymptotic consistency of the proposed method in the presence of unmeasured confounders and weight estimation errors. Simulation experiments demonstrate that the proposed reweighted BIC exhibits favorable asymptotic properties and significantly outperforms existing alternative methods, achieving precise selection of direct causes.

Abstract

Scoring methods based on the Bayesian information criterion (BIC) are commonly used for model selection tasks such as choosing features in a regression model or learning directed acyclic graphs from data. In certain model classes, model selection based on the BIC is consistent. However, since the BIC is based on the observed likelihood function, it does not apply directly to reweighted distributions arising in causal inference, missing data, and domain shift applications. Here, we propose a generalized version of the BIC that allows for model selection in reweighted distributions. We prove its corresponding consistency property and demonstrate how it can be used for selecting direct causes of an outcome variable in a marginal structural model. Our proposed method accounts for scenarios with unmeasured confounders and where the weights must be estimated from data. Through simulation studies, we demonstrate the asymptotic properties of the reweighted BIC and compare it with alternative methods for model selection.

Problem

• Bayesian information criterion
• reweighted distributions
• model selection
• causal inference
• direct causes

Innovation

• Generalized BIC
• Reweighted Distributions
• Causal Inference
• Marginal Structural Model
• Unmeasured Confounders