Empirical Bayes Conformal Prediction for Vision and Language Models
Authors: Jiapeng Zeng, Yogesh Prabhu, Zhanpeng Zeng, Michael A. Newton, Vikas Singh
Organizations: University of Wisconsin–Madison · University of California San Diego · Xiamen University
Abstract
Conformal prediction (CP) gives distribution-free coverage for modern vision and language models, but it is often forced to make a ranking decision from a single unstable nonconformity score. Standard CP uses one realization, while average-then-calibrate variants smooth multiple realizations into a point estimate. Both options discard the inconsistency that can help identify whether a candidate is indeed stable. A weak answer can enter the conformal set even if the evidence is not strong, simply because one posterior sample or prompt phrasing made it look strong. But variability can help distinguish a stable signal from noise-driven fluctuations. We describe an empirical Bayes conformal prediction framework that uses r-values to convert score variability into an uncertainty informed nonconformity score. The resulting r-value estimates how likely a candidate's latent score belongs to the top-ranked group after accounting for both its mean score and its uncertainty. It admits both a closed-form Normal-Normal empirical Bayes estimator and a nonparametric posterior-sampling estimator. Using the r-value as the nonconformity score preserves the target conformal coverage while provably reducing the inclusion of high variance false candidates under mild regularity conditions. Across image classification, CLIP-based VLM benchmarks, and LLMs, we show that r-value conformal prediction preserves target coverage while improving ranking stability and reducing set size when variability is informative, and reverting to CP-like behavior when variability vanishes.
Conformal predictions have attracted significant attention in the field of uncertainty quantification, mainly because of their strong marginal coverage guarantees. Full conditional guarantee is not an attainable goal, a well known fact in conformal predictions literature. As a result, several approaches have tried to approximate this behavior by adapting the conformal sets of test-time samples according to their similarity to calibration examples. Although the latter has gained traction and shown impressive performances for regression problems, its application to image classification remains under-explored. We conduct an extensive benchmarking on natural image classification tasks with vision-language models (VLMs), using our open source implementation of a recent localized conformal prediction algorithm. We show that straightforward usage of the cosine similarity between test-time and calibration visual features, an intuitive choice for VLMs, is not sufficient to improve over the non-local baselines. In response, we propose a simple non-linear transformation of the cosine similarities, which conserves marginal coverage guarantees and achieves statistically significant mean set sizes reduction. Code is available at https://github.com/cfuchs2023/lcp-vlm/.
Bayes-assisted conformal prediction combines the strengths of Bayesian modelling with exact, distribution-free frequentist coverage guarantees. Although conformal validity is preserved even when the Bayesian working model (BWM) is misspecified, the size of the resulting prediction sets can degrade substantially when the prior is poorly aligned with the observed data. We address this limitation by introducing RoBAS (Robust Bayes-Assisted Shrinkage): a Bayes-assisted framework for constructing robust nonconformity scores, with two instantiations: one induced by a heavy-tailed BWM, and a closed-form empirical Bayes shrinkage score. The resulting scores adapt to the quality of the working information encoded in the prior: when this information is reliable, they exploit it to produce efficient prediction sets; when it is weak or inaccurate, they revert to the Distance-To-Average (DTA) score, a robust non-informative baseline. We evaluate the proposed scores on tabular and image regression tasks where the training distribution may differ from the calibration and test distributions, while the calibration and test data themselves remain exchangeable. We find that they are competitive with widely used scores in the absence of such shift, while substantially reducing interval widths in shifted settings.
Kianoosh Ashouritaklimi, Stefano Cortinovis, François Caron
Vision-language models (VLMs) are increasingly used as automated judges for multimodal systems, yet their scores provide no indication of reliability. We study this problem through conformal prediction, a distribution-free framework that converts a judge's point score into a calibrated prediction interval using only score-token log-probabilities, with no retraining. We present the first systematic analysis of conformal prediction for VLM-as-a-Judge across 3 judges and 14 visual task categories. Our results show that evaluation uncertainty is strongly task-dependent: intervals cover ~40% of the score range for aesthetics and natural images but expand to ~70% for chart and mathematical reasoning, yielding a quantitative reliability map for multimodal evaluation. We further identify a failure mode not captured by standard evaluation metrics, ranking-scoring decoupling, where judges achieve high ranking correlation while producing wide, uninformative intervals, correctly ordering responses but failing to assign reliable absolute scores. Finally, we show that interval width is driven primarily by task difficulty and annotation quality, i.e., the same judge and method yield 4.5x narrower intervals on a clean, multi-annotator captioning benchmark. Code: https://github.com/divake/VLM-Judge-Uncertainty