LLM knowledge for improved Out-of-Distribution Tabular Prediction - A Cross-Validated Regularisation Approach
Sølve Langseth, Kristoffer Herland Hellton, Hugo L. Hammer
Abstract
Prediction models degrade when the deployment population differs from the one used to train them, and training data cannot say which feature-response relationships will transfer. Expert elicitation is slow and unscalable. We ask whether coefficient priors elicited from large language models (LLMs) improve out-of-distribution (OOD) prediction as the shrinkage target of a regularised regression instead of zero, across five tabular datasets split on real covariates, selecting providers and prior structures by source-domain cross-validation alone. The priors help on four of five datasets, by up to 7.9% OOD mean squared error, and ten of twenty-four prior-informed results resolve the mean improvement at conventional confidence; single-deployment intervals are much wider. On classification the gain is in probabilistic accuracy, not ranking, and control tests with corrupted priors attribute the benefit to feature-specific content rather than scale. Two findings temper this. Variation across candidate priors exceeds the average benefit, yet cross-validation margins fall below their own noise, so selection avoids the worst prior rather than finding the best. On three datasets the prior improves in-domain accuracy as much as out-of-domain, making it better regularisation than shift correction. Only where the training data are large enough that the in-domain gain disappears does elicited knowledge demonstrably improve transfer. Code, priors and results: https://github.com/hugohammer/llm-priors-ood.