  Ultrahigh dimensional data sets are becoming increasingly prevalent in areas
such as bioinformatics, medical imaging, and social network analysis. Sure
independent screening of such data is commonly used to analyze such data.
Nevertheless, few methods exist for screening for interactions among
predictors. Moreover, extant interaction screening methods prove to be highly
inaccurate when applied to data sets exhibiting strong interactive effects, but
weak marginal effects, on the response. We propose a new interaction screening
procedure based on joint cumulants which is not inhibited by such limitations.
Under a collection of sensible conditions, we demonstrate that our interaction
screening procedure has the strong sure screening property. Four simulations
are used to investigate the performance of our method relative to two other
interaction screening methods. We also apply a two-stage analysis to a real
data example by first employing our proposed method, and then further examining
a subset of selected covariates using multifactor dimensionality reduction.
