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This research addresses a critical reliability challenge in transfer learning by proposing statistical methods to evaluate surrogate-derived models when gold-standard labels are unavailable in the target population. By leveraging cross-fitted estimators across three-sample settings, the study establishes rigorous inference frameworks for metrics like AUC and ROC curves under covariate shift. The work includes practical validation on real-world benchmarks such as Chatbot Arena, offering actionable insights for deploying robust AI systems where outcome data is scarce or biased.
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Inferential Evaluation of Surrogate-Derived Models under Covariate Shift

arXiv2 min read

arXiv:2608.15783v1 Announce Type: cross Abstract: In transfer-learning settings, a model derived from abundant surrogate labels may be deployed in a target population where gold-standard outcomes are unobserved. Evaluating its target performance is essential for determining whether decisions based on the model remain reliable, yet it is difficult when gold labels are scarce, and covariate distributions differ across data sources. We study a three-sample setting with a small gold-labeled source, a larger surrogate-labeled source, and an unlabeled target. Under conditional transportability, we evaluate the surrogate-derived model against the latent gold-standard outcome in the target population. We propose cross-fitted estimators that transport information from the two labeled sources through source-specific density ratios. We also combine outcome-regression augmentation with a kernel correction for estimating the model near a threshold, accounting for uncertainty from all three samples. We establish asymptotically linear inference for TPR and FPR, consistency and pointwise inference for the ROC curve, and asymptotically normal inference for AUC. Simulations assess bias, coverage, and sensitivity to bandwidth and relative sample sizes. A retrospective temporal validation on Chatbot Arena and a semi-synthetic ACS-Income study provide validation in real-world AI applications.

Abstract:In transfer-learning settings, a model derived from abundant surrogate labels may be deployed in a target population where gold-standard outcomes are unobserved. Evaluating its target performance is essential for determining whether decisions based on the model remain reliable, yet it is difficult when gold labels are scarce, and covariate distributions differ across data sources. We study a three-sample setting with a small gold-labeled source, a larger surrogate-labeled source, and an unlabeled target. Under conditional transportability, we evaluate the surrogate-derived model against the latent gold-standard outcome in the target population. We propose cross-fitted estimators that transport information from the two labeled sources through source-specific density ratios. We also combine outcome-regression augmentation with a kernel correction for estimating the model near a threshold, accounting for uncertainty from all three samples. We establish asymptotically linear inference for TPR and FPR, consistency and pointwise inference for the ROC curve, and asymptotically normal inference for AUC. Simulations assess bias, coverage, and sensitivity to bandwidth and relative sample sizes. A retrospective temporal validation on Chatbot Arena and a semi-synthetic ACS-Income study provide validation in real-world AI applications.

Machine Learning (stat.ML); Machine Learning (cs.LG); Applications (stat.AP); Methodology (stat.ME)

arXiv:2608.15783 [stat.ML]

(or arXiv:2608.15783v1 [stat.ML] for this version)

https://doi.org/10.48550/arXiv.2608.15783 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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Full text under the publisher's open licence · 282 words

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