  Forming a molecular candidate set that contains a wide range of potentially
effective compounds is crucial to the success of drug discovery. While most
databases and machine-learning-based generation models aim to optimize
particular chemical properties, there is limited literature on how to properly
measure the coverage of the chemical space by those candidates included or
generated. This problem is challenging due to the lack of formal criteria to
select good measures of the chemical space. In this paper, we propose a novel
evaluation framework for measures of the chemical space based on two analyses:
an axiomatic analysis with three intuitive axioms that a good measure should
obey, and an empirical analysis on the correlation between a measure and a
proxy gold standard. Using this framework, we are able to identify #Circles, a
new measure of chemical space coverage, which is superior to existing measures
both analytically and empirically. We further evaluate how well the existing
databases and generation models cover the chemical space in terms of #Circles.
The results suggest that many generation models fail to explore a larger space
over existing databases, which leads to new opportunities for improving
generation models by encouraging exploration.
