Predictive Correlation Screening: Application to Two-stage Predictor Design in High Dimension
This addresses the challenge of designing predictors in high-dimensional data, such as gene expression analysis, with incremental improvements in variable selection methods.
The authors tackled the problem of variable selection for predictor design in high-dimensional settings with small sample sizes by introducing Predictive Correlation Screening (PCS), which controls false positives and scales efficiently, showing superiority over LASSO and correlation learning in performance and computational complexity.
We introduce a new approach to variable selection, called Predictive Correlation Screening, for predictor design. Predictive Correlation Screening (PCS) implements false positive control on the selected variables, is well suited to small sample sizes, and is scalable to high dimensions. We establish asymptotic bounds for Familywise Error Rate (FWER), and resultant mean square error of a linear predictor on the selected variables. We apply Predictive Correlation Screening to the following two-stage predictor design problem. An experimenter wants to learn a multivariate predictor of gene expressions based on successive biological samples assayed on mRNA arrays. She assays the whole genome on a few samples and from these assays she selects a small number of variables using Predictive Correlation Screening. To reduce assay cost, she subsequently assays only the selected variables on the remaining samples, to learn the predictor coefficients. We show superiority of Predictive Correlation Screening relative to LASSO and correlation learning (sometimes popularly referred to in the literature as marginal regression or simple thresholding) in terms of performance and computational complexity.