Omitted Variable Bias in Language Models Under Distribution Shift

Victoria Lin; Louis-Philippe Morency; Eli Ben-Michael

cs.LGFeb 18, 2026

Omitted Variable Bias in Language Models Under Distribution Shift

Authors: Victoria Lin, Louis-Philippe Morency, Eli Ben-Michael

Organizations: Carnegie Mellon University, Pittsburgh, PA, USA

Abstract

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.

Figures & tables

	$\eta$	$b(\eta)$	Label	Mean parameter
Regression	$f(x)\in\mathbb{R}$	$\frac{1}{2}\eta^{2}$	$Y\in\mathbb{R}$	$\mu=\eta$
Binary classification	$f(x)\in\mathbb{R}$ (logit)	$\log(1+\exp(\eta))$	$Y\in\{0,1\}$	$p=\sigma(\eta)$
Multiclass classification	$f(x)\in\mathbb{R}^{K}$ (logits)	$\log\sum_{j=1}^{K}\exp(\eta_{j})$	$Y\in\{0,1\}^{K}$	$p_{j}=\frac{\exp(\eta_{j})}{\sum_{k\in K}\exp(\eta_{k})}$
Text generation	$f^{(t)}(x)\in\mathbb{R}^{K}$ (logits at step $t$ )	$\sum_{t=1}^{T}\log\sum_{j=1}^{K}\exp(\eta_{j}^{(t)})$	$Y^{(t)}\in\{0,1\}^{K}$	$p_{j}^{(t)}=\frac{\exp(\eta_{j}^{(t)})}{\sum_{k\in K}\exp(\eta_{k}^{(t)})}$

Table 1: NLP tasks with GLM log-likelihood losses and their correspondence to language model outputs

f(x)

Panel of Figure 1 — Figure 1: Evaluations of true and distribution shift-adjusted performance on MATH-Perturb.

Figure 2: Strength of omitted variables under distribution shift in the Math Reasoning dataset.

Figure 3: Amazon dataset. On the left, we plot the test performance difference (higher is better) between our approach and a model trained with a standard DR objective against the true strength of omitted variables. On the right, we plot the test performance of our approach and both baselines.

Panel of Figure 4 — Figure 4: Test performance difference (higher is better) between our approach and a model trained with a standard DR objective against assumed strength of omitted variables.

Appendix figures & tables3 assets

Supplementary material from the paper’s appendix.

Appendix

	Language	Library	Model
LIWC	Python	liwc	-
Empath	Python	empath	-
SenteCon	Python	sentecon	-
BERT	Python	transformers	bert-base-uncased
RoBERTa	Python	transformers	roberta-base
MiniLM	Python	sentence-transformers	all-MiniLM-L6-v2

Appendix

Table 2: Technical details for language model implementations.

Figure 5: OVB metrics under distribution shift in the Math Reasoning dataset.

Panel of Figure 6 — Figure 6: Test performances of our approach, the DR baseline, and the unadjusted baseline plotted against strength of omitted variables.

OOD Generalization

Out-of-distribution generalization studies how machine-learning models perform when test data, domains, tasks, or environments differ from training.

See all 395 papers

Auditing Conformal Prediction for Language Models Under Inference-Time Model Shift
Oct 20, 2026Achref Doula, Max MühlhäuserConformal Prediction for Language Models Language Model Calibration
Tongji University, Shanghai, China · Technical University of Darmstadt, Darmstadt, Germany
INCONVENIENT: A Benchmark to Assess LLM Generalization Capabilities from Convenience Samples
Oct 15, 2026Sara Rezaeimanesh, Chad Klochko, Kundan Thind +1Distribution Shift Robustness Tabular ML
Michigan State University, East Lansing, MI, USA · Henry Ford Health, Detroit, MI, USA
Perturbation is All You Need for Extrapolating Language Models
May 5, 2026Zetai Cen, Jin Zhu, Xinwei Shen +1OOD Generalization Autoregressive Language Modeling
School of Mathematics, University of Bristol · School of Mathematics, University of Birmingham · Department of Statistics, University of Washington +1

Oct 20, 2026J/K move · Enter open · S save

Auditing Conformal Prediction for Language Models Under Inference-Time Model Shift

Achref Doula, Max Mühlhäuser

Tongji University, Shanghai, China · Technical University of Darmstadt, Darmstadt, Germany

Conformal Prediction for Language Models Language Model Calibration LLM Auditing

Open paper AskPDF arXiv

Conformal prediction (CP) for language models is typically evaluated under a matched protocol, in which calibration and deployment use the same post-training inference configuration, such as quantization mode and inference temperature. In deployment, these choices often differ from those used at calibration to meet memory or throughput constraints or serving policies. We argue that this exposes a limitation in current CP evaluation protocols for language models. We formalize the underlying phenomenon as inference-time model shift: a change in the conformal score distribution induced by inference configuration rather than by the input--label distribution, and theoretically characterize how it breaks split-conformal exchangeability even when the task distribution and trained model are unchanged. We then evaluate its consequences across 8 language models, 4 finite-label benchmarks, and 12 inference configurations. We find that matched evaluation can substantially overstate deployment-time coverage, and that the effect is heterogeneous across models and datasets. We argue that inference configuration should be reported as a first-class experimental axis in CP evaluations for language-model systems.

Abstract

OOD Generalization

Explore similar work

Auditing Conformal Prediction for Language Models Under Inference-Time Model Shift

INCONVENIENT: A Benchmark to Assess LLM Generalization Capabilities from Convenience Samples

Perturbation is All You Need for Extrapolating Language Models