Extracting Probabilistic Knowledge from Large Language Models for Bayesian Network Parameterization

Abstract: LLMs have demonstrated potential as factual knowledge bases; however, their capability to generate probabilistic knowledge about real-world events remains understudied. This paper investigates using probabilistic knowledge inherent in LLMs to derive probability estimates for statements concerning events and their interrelationships captured via a Bayesian Network (BN). Using LLMs in this context allows for the parameterization of BNs, enabling probabilistic modeling within specific domains. Experiments on eighty publicly available Bayesian Networks, from healthcare to finance, demonstrate that querying LLMs about the conditional probabilities of events provides meaningful results when compared to baselines, including random and uniform distributions, as well as approaches based on next-token generation probabilities. We explore how these LLM-derived distributions can serve as expert priors to refine distributions extracted from minimal data, significantly reducing systematic biases. Overall, this work introduces a promising strategy for automatically constructing Bayesian Networks by combining probabilistic knowledge extracted from LLMs with small amounts of real-world data. Additionally, we evaluate several prompting strategies for eliciting probabilistic knowledge from LLMs and establish the first comprehensive baseline for assessing LLM performance in extracting probabilistic knowledge.