INTRODUCTION
MATERIALS AND METHODS
Data
Methods
LASSO (Tibshirani, 1996)
Fused LASSO (Tibshirani et al., 2005)
Elastic net (Zou and Hastie, 2005)
Comparing methods
Partition the data into the firstdeep training and validation sets; then partition the firstdeep training set into the seconddeep training and test set (twodeep CV).
At the seconddeep, construct the model using the subtraining set and calculate CV; then choose the optimal tuning parameter that minimizes CV.
At the firstdeep, fit the model and estimate the coefficients in the firstdeep training set with the estimated regularization parameter from the seconddeep set.
RESULT AND DISCUSSION
Table 1
Table 2
Fold  Regularized regression  



LASSO  Fused LASSO  Elastic net  
1  0.3627  0.4150  0.3972 
2  0.6802  0.6978  0.6966 
3  0.6136  0.6410  0.6239 
4  0.5600  0.5848  0.5694 
5  0.7295  0.7510  0.7338 
6  0.5973  0.6265  0.6011 
7  0.4849  0.5126  0.4925 
8  0.5931  0.6070  0.5962 
9  0.5200  0.5422  0.5291 
10  0.5708  0.5891  0.5777 
Ave corr1  0.5712  0.5967  0.5818 
Table 3
Table 4
Name of SNP  Coef2 

M1GA0023299  0.0099 
MARC0015851  0.0094 
H3GA0002658  0.0084 
ASGA0001125  0.0074 
ALGA0106999  0.0069 
MARC0016306  0.0068 
ASGA0080059  0.0064 
ASGA0054467  −0.0063 
MARC0027886  −0.0064 
MARC0023564  −0.0064 