Quantile Based Variable Mining : Detection, FDR based Extraction and Interpretation

Abstract: This paper outlines a unified framework for high dimensional variable selection for classification problems. Traditional approaches to finding interesting variables mostly utilize only partial information through moments (like mean difference). On the contrary, in this paper we address the question of variable selection in full generality from a distributional point of view. If a variable is not important for classification, then it will have similar distributional aspect under different classes. This simple and straightforward observation motivates us to quantify `How and Why' the distribution of a variable changes over classes through CR-statistic. The second contribution of our paper is to develop and investigate the FDR based thresholding technology from a completely new point of view for adaptive thresholding, which leads to a elegant algorithm called CDfdr. This paper attempts to show how all of these problems of detection, extraction and interpretation for interesting variables can be treated in a unified way under one broad general theme - comparison analysis. It is proposed that a key to accomplishing this unification is to think in terms of the quantile function and the comparison density. We illustrate and demonstrate the power of our methodology using three real data sets.