Word-Sequence Entropy: Towards Uncertainty Estimation in Free-Form Medical Question Answering Applications and Beyond

Uncertainty estimation plays a pivotal role in ensuring the reliability of safety-critical human-AI interaction systems, particularly in the medical domain. However, a general method for quantifying the uncertainty of free-form answers has yet to be established in open-ended medical question-answering (QA) tasks, where irrelevant words and sequences with limited semantic information can be the primary source of uncertainty due to the presence of generative inequality. In this paper, we propose the Word-Sequence Entropy (WSE), which calibrates the uncertainty proportion at both the word and sequence levels according to the semantic relevance, with greater emphasis placed on keywords and more relevant sequences when performing uncertainty quantification. We compare WSE with 6 baseline methods on 5 free-form medical QA datasets, utilizing 7 "off-the-shelf" large language models (LLMs), and show that WSE exhibits superior performance on accurate uncertainty measurement under two standard criteria for correctness evaluation (e.g., WSE outperforms existing state-of-the-art method by 3.23% AUROC on the MedQA dataset). Additionally, in terms of the potential for real-world medical QA applications, we achieve a significant enhancement in the performance of LLMs when employing sequences with lower uncertainty, identified by WSE, as final answers (e.g., +6.36% accuracy improvement on the COVID-QA dataset), without requiring any additional task-specific fine-tuning or architectural modifications.