  Selecting influential nonlinear interactive features from ultrahigh
dimensional data has been an important task in various fields. However,
statistical accuracy and computational feasibility are the two biggest concerns
when more than half a million features are collected in practice. Many extant
feature screening approaches are either focused on only main effects or heavily
rely on heredity structure, hence rendering them ineffective in a scenario
presenting strong interactive but weak main effects. In this article, we
propose a new interaction screening procedure based on joint cumulant (named
JCI-SIS). We show that the proposed procedure has strong sure screening
consistency and is theoretically sound to support its performance. Simulation
studies designed for both continuous and categorical predictors are performed
to demonstrate the versatility and practicability of our JCI-SIS method. We
further illustrate the power of JCI-SIS by applying it to screen 27,554,602,881
interaction pairs involving 234,754 single nucleotide polymorphisms (SNPs) for
each of the 4,000 subjects collected from polycystic ovary syndrome (PCOS)
patients and healthy controls.
