Let aT denote the transpose of the vector a. For the ith sample (i = 1, . . ., n), we let Xi = [Xi1 . . . Xip]T denote the p × 1 gene expression profile vector (ie, Xij is the gene expression measurement of the jth gene, j = 1, . . ., p). We suppose that the data have already been preprocessed and normalized. In addition, it is assumed that the gene expression data are standardized so that for each gene, the mean is zero and standard deviation one. Let gi denote the tumor class for the ith sample (i = 1, . . ., n); we assume that there are two classes so that gi takes values g ∈ {0, 1}. Here and in the sequel, we will refer to g = 1 as the diseased class and g = 0 as the healthy class; however, the methods proposed here are applicable to any two-class setting. In “LASSO estimation,” we assume the existence of a continuous response variable Yi for the ith sample (i = 1, . . ., n).
