Epistasis Detection via the Joint Cumulant

Selecting influential non-linear 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 billions of interactive pairs are screened 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. Finite sample simulation studies designed for both continuous and categorical predictors are performed to demonstrate the versatility and practicability of the 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 for 4098 subjects collected from polycystic ovary syndrome patients and healthy controls.