Anatole von Lilienfeld Argonne National Laboratory Many of the most relevant chemical properties of matter depend explicitly on atomistic details, rendering a first principles approach mandatory. Alas, even when using high-performance computing, brute force high-throughput screening of compounds is beyond any capacity for all but the simplest systems and properties due to the combinatorial nature of chemical space, i.e. all the compositional, constitutional, and conformational isomers. Consequently, efficient exploration algorithms should exploit all implicit redundancies present in high-throughput approaches. In this talk, I will describe recently developed statistical approaches for inferring quantum mechanical observables in chemical space.