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

Uncertainty estimation is crucial for the reliability of safety-critical human and artificial intelligence (AI) interaction systems, particularly in the domain of healthcare engineering. However, a robust and general uncertainty measure for free-form answers has not been well-established in open-ended medical question-answering (QA) tasks, where generative inequality introduces a large number of irrelevant words and sequences within the generated set for uncertainty quantification (UQ), which can lead to biases. This paper introduces Word-Sequence Entropy (WSE), a method that calibrates uncertainty at both the word and sequence levels, considering semantic relevance. WSE quantifies uncertainty in a way that is more closely aligned with the reliability of LLMs during uncertainty quantification (UQ). We compare WSE with six baseline methods on five free-form medical QA datasets, utilizing seven popular large language models (LLMs). Experimental results demonstrate that WSE exhibits superior performance in UQ under two standard criteria for correctness evaluation. Additionally, in terms of real-world medical QA applications, the performance of LLMs is significantly enhanced (e.g., a 6.36% improvement in model accuracy on the COVID-QA dataset) by employing responses with lower uncertainty that are identified by WSE as final answers, without any additional task-specific fine-tuning or architectural modifications.