Strong Sure Screening of Ultra-high Dimensional Data with Interaction Effects
arXiv:1801.07785
Abstract
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.
References in corpus (5)
- The composite absolute penalties family for grouped and hierarchical variable selection
- High-dimensional classification using features annealed independence rules
- Statistical Challenges with High Dimensionality: Feature Selection in Knowledge Discovery
- Structured variable selection and estimation
- A fast algorithm for detecting gene-gene interactions in genome-wide association studies