Representative Random Sampling of Chemical Space

An overwhelming majority of molecules remain unexplored. This is mostly due to the sheer number of them, which prohibits any enumeration of chemical space, the set of all such molecules. In practice, only subsets of chemical space are considered, but those subsets exhibit substantial bias, prohibiting the data-driven characterization of chemical space itself. In this work, we provide a method to produce unbiased representative random samples of the chemical space without enumeration of constituent molecules and to estimate the number of molecules in any custom chemical space. The approach is applicable to molecules that can be represented as graphs and runs efficiently even for molecules of 30 atoms. We use it to estimate the representativeness of current databases with respect to their underlying chemical space and establish a necessary criterion for a lower bound of database sizes to be representative of an underlying chemical space.