  We consider the problem of sparse variable selection on high dimension
heterogeneous data sets, which has been taking on renewed interest recently due
to the growth of biological and medical data sets with complex, non-i.i.d.
structures and huge quantities of response variables. The heterogeneity is
likely to confound the association between explanatory variables and responses,
resulting in enormous false discoveries when Lasso or its variants are
na\"ively applied. Therefore, developing effective confounder correction
methods is a growing heat point among researchers. However, ordinarily
employing recent confounder correction methods will result in undesirable
performance due to the ignorance of the convoluted interdependency among
response variables. To fully improve current variable selection methods, we
introduce a model, the tree-guided sparse linear mixed model, that can utilize
the dependency information from multiple responses to explore how specifically
clusters are and select the active variables from heterogeneous data. Through
extensive experiments on synthetic and real data sets, we show that our
proposed model outperforms the existing methods and achieves the highest ROC
area.
