Quantifying and Auditing LLM Evaluation via Positive–Unlabeled Learning

Large Language Models (LLMs) are increasingly used as judges for scalable evaluation, yet such LLM-as-a-Judge systems exhibit systematic biases that are decoupled from semantic quality, most notably verbosity bias. Meanwhile, human supervision is costly and typically selective, yielding reliable positive judgments but leaving most outputs unlabelled and potentially mixed in quality. We formulate LLM evaluation under selective human supervision as a positive–unlabelled learning problem and propose a geometric auditing framework based on Partial Optimal Transport. By aligning a small set of human-verified positives with a reliable subset of unlabelled outputs in a fixed embedding space, our method identifies human-consistent preferences and corrects biased judges without retraining. Experiments on simulated data and Chatbot Arena show that the method can improve judge–human agreement with few verified comparisons. For each unlabelled comparison, it also returns a normalized transport-alignment score that measures relative alignment with the verified-positive set; this score is not a calibrated probability.