Independent feature screening for ultrahigh-dimensional models with interactions

Feature selection is an important technique for ultrahigh-dimensional data analysis. Most feature selection methods such as SIS and its relevant versions heavily depend on the specified model structures. Furthermore, feature interactions are usually not taken into account in the existing literature. In this paper, we present a novel feature selection method for the model with variable interactions, without the use of structure assumption. Thus, the new ranking criterion is flexible and can deal with the models that contain interactions. Moreover, the new screening procedures are not complex, consequently, they are computationally efficient and the theoretical properties such as the ranking consistency and sure screening properties can be easily obtained. Several real and simulation examples are presented to illustrate the methodology.