RaSE: A Variable Screening Framework via Random Subspace Ensembles

With the rapid advancement of computing power and technology, high-dimensional data become ubiquitous in many disciplines such as genomics, image analysis, and tomography. With high-dimensional data, the number of variables p could be much larger than the sample size n. What makes statistical inference possible is the sparsity assumption, which assumes only a few variables have contributions to the response. Under this sparsity assumption, there has been a rich literature on the topic of variable selection, including LASSO (Tibshirani, 1996), SCAD (Fan and Li, 2001), elastic net (Zou and Hastie, 2005), and MCP (Zhang, 2010). Despite of the success of these methods in many applications, for the ultra-high dimensional scenario where the dimension p grows exponentially with n, they may not work well due to the "curse of dimensionality" in terms of simultaneous challenges to computational expediency, statistical accuracy, and algorithmic stability (Fan and Lv, 2008).