Omitted Variable Bias in Language Models Under Distribution Shift

Despite their impressive performance on a wide variety of tasks, modern language models remain susceptible to distribution shifts, exhibiting brittle behavior when evaluated on data that differs in distribution from their training data. In this paper, we describe how distribution shifts in language models can be separated into observable and unobservable components, and we discuss how established approaches for dealing with distribution shift address only the former. Importantly, we identify that the resulting omitted variable bias from unobserved variables can compromise both evaluation and optimization in language models. To address this challenge, we introduce a framework that maps the strength of the omitted variables to bounds on the worst-case generalization performance of language models under distribution shift. In empirical experiments, we show that using these bounds directly in language model evaluation and optimization provides more principled measures of out-of-distribution performance, improves true out-of-distribution performance relative to standard distribution shift adjustment methods, and further enables inference about the strength of the omitted variables when target distribution labels are available.

💡 Research Summary

The paper tackles the persistent problem that modern language models (LMs) degrade sharply when evaluated on data whose distribution differs from the training set—a phenomenon known as distribution shift. The authors argue that existing shift‑mitigation techniques only address the observable component of the shift (e.g., domain labels, token frequencies, known covariates) while ignoring an unobservable component consisting of hidden variables such as cultural context, author intent, or rare lexical phenomena. This omission creates an “omitted variable bias” (OVB) analogous to the bias studied in econometrics: when a relevant predictor is left out of a model, the estimated parameters become systematically distorted, leading to poor out‑of‑distribution (OOD) performance.

To formalize the issue, the paper introduces the notion of omitted variable strength (Ω), a scalar that captures both the correlation between hidden variables and the target label and the magnitude of their influence on the input. Using Bayesian decomposition and information‑theoretic inequalities, the authors derive a worst‑case risk bound for the target distribution (P_T):

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