Genomics has revolutionized biology, enabling the interrogation of whole transcriptomes, genome-wide binding sites for proteins, and many other molecular processes. However, individual genomic assays measure elements that interact in vivo as components of larger molecular machines. Understanding how these high-order interactions drive gene expression presents a substantial statistical challenge. Building on random forests (RFs) and random intersection trees (RITs) and through extensive, biologically inspired simulations, we developed the iterative random forest algorithm (iRF) to seek predictable and stable high-order Boolean interactions.  We demonstrate the utility of iRF for high-order Boolean interaction discovery in two prediction problems: enhancer activity in the early Drosophila embryo and red hair phenotype using UK BioBank data. The latter is a proof-of-concept step towards suggesting gene variantsbehind cardiovasuclar phenotypes for single cell experiments as part of a Chan-Zuckerberg Biohub Intercampus Award to UC Berkeley, UCSF and Stanford. Finally, a connection is made between iRF and our PCS framework where PCS stands for predictability, computability and Stability.