  Causal structure discovery from observations can be improved by integrating
background knowledge provided by an expert to reduce the hypothesis space.
Recently, Large Language Models (LLMs) have begun to be considered as sources
of prior information given the low cost of querying them relative to a human
expert. In this work, firstly, we propose a set of metrics for assessing LLM
judgments for causal graph discovery independently of the downstream algorithm.
Secondly, we systematically study a set of prompting designs that allows the
model to specify priors about the structure of the causal graph. Finally, we
present a general methodology for the integration of LLM priors in graph
discovery algorithms, finding that they help improve performance on
common-sense benchmarks and especially when used for assessing edge
directionality. Our work highlights the potential as well as the shortcomings
of the use of LLMs in this problem space.
