Sparse Variable Selection on High Dimensional Heterogeneous Data with Tree Structured Responses

TL;DR

This paper introduces a tree-guided sparse linear mixed model for variable selection in high-dimensional, heterogeneous data with complex response dependencies, improving accuracy over existing methods.

Contribution

The proposed model leverages response variable dependencies via a tree structure to enhance variable selection in heterogeneous data, addressing confounder effects.

Findings

Outperforms existing methods in synthetic data tests.

Achieves highest ROC area in real data experiments.

Effectively utilizes response dependencies for better variable selection.

Abstract

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.