Year: 2026
Type: preprint
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.
Source: arXiv (Cornell University)
Authors: Chen, Jacob M., Shpitser, Ilya
Institution: Johns Hopkins University
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: Office of Naval Research
Award: G1557819072
OpenAlex ID: W7220934690