Language Model Augmented Semi-Supervised Statistical Inference

Semi‑supervised statistical inference plays a key role in biomedical research, where labeled data often have higher quality but are limited due to costly clinical annotation. Yet, existing semi‑supervised statistical inference methods rely heavily on structured variables and strictly matched covariates between labeled and unlabeled datasets -- limitations ill‑suited for the heterogeneity and unstructured nature of real-world biomedical data. Modern biomedical studies increasingly collect unstructured data (clinical notes, patient audio and video recordings), with inconsistent protocols across datasets causing covariate misalignment (for instance, detailed medication histories may be recorded in one study but not another). Recent advances in pre‑trained multimodal large language models (LLMs), which excel at handling unstructured data, present an attractive potential solution. To transform this potential into rigorous semi-supervised statistical inference methods for biomedical research, two key challenges must be addressed: (1) How can we reliably integrate LLMs to enhance semi-supervised inference efficiency without compromising statistical validity? (2) How can those efficiency gains persist despite mismatched covariates between labeled and unlabeled datasets? In this paper, we tackle these challenges by systematically calibrating pseudo-labels provided LLMs with a novel prediction-invariance identification strategy. Our resulting semi‑supervised inference framework improves parameter estimation efficiency while maintaining full statistical validity, as demonstrated through our theoretical results and illustrated in a case study for identifying key biomarkers in Alzheimer’s disease detection with speech data.

Many medical studies have lots of patient records but only a small number of expert-confirmed diagnoses, making it hard to find reliable links between patient features and disease. This paper introduces a method that uses AI language models to make helpful guesses from notes, speech, or other rich records, then checks and adjusts those guesses using the expert-confirmed cases. It also handles situations where different studies collect different kinds of information, so the method only borrows extra information when it appears safe to do so. In tests, including an Alzheimer’s disease speech study, the method gave more precise and still reliable estimates of which patient and speech features are linked to disease.