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

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 naïvely 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.

References in corpus (9)

• Nearly unbiased variable selection under minimax concave penalty
• Population Structure and Cryptic Relatedness in Genetic Association Studies
• Smoothing proximal gradient method for general structured sparse regression
• Tree-guided group lasso for multi-response regression with structured sparsity, with an application to eQTL mapping
• Efficient computation with a linear mixed model on large-scale data sets with applications to genetic studies
• Variable selection in linear mixed effects models
• Graph-Structured Multi-task Regression and an Efficient Optimization Method for General Fused Lasso
• Discussion: One-step sparse estimates in nonconcave penalized likelihood models
• A Sparse Graph-Structured Lasso Mixed Model for Genetic Association with Confounding Correction