Figure 1 illustrates a multivariate response regression model. Reduced rank estimation of the coefficient matrix (Figure 2) extends PCA analysis to multivariate responses. As the number of predictors exceeds the sample size, sparse estimation becomes popular (Figure 3, the blank areas inside the boxes are all zeros.). Then when both the number of responses and the number of predictors are larger than the sample size, one may consider two levels of sparsity (Figure 4): predictor selection and response selection. Recently we proposed a multivariate response model where the coefficient matrix took a form similar to the one in Figure 4 and used the model to study the regulation of global gene expression by multiple regulatory programs. For more details, please refer to my to-appear-in-PNAS paper Learning regulatory programs by threshold SVD regression.