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Table 2 Average number and percentage of biologically relevant variables in the model with S N R=0.5 and (β j =0.1,j=1,2,…20)

From: Tilting the lasso by knowledge-based post-processing

Over 100 runs Adaptive lasso B1 B2 B3
Average number of selected variables 41 41 41 41
q=10 and ρ=0.1     
Average number of Biologically relevant variables 12 20 15 14
Average percentage of Biologically relevant variables 29.3 % 48.8 % 36.6 % 34.1 %
Standard deviation 9.1 0.86 1.24 3.11
q=20and ρ=0.25     
Average number of Biologically relevant variables 12 38 34 29
Average percentage of Biologically relevant variables 29.3 % 92.7 % 82.9 % 70.7 %
Standard deviation 9.1 0.85 1.22 3.08
q=30and ρ=0.3     
Average number of Biologically relevant variables 12 39 35 30
Average percentage of Biologically relevant variables 29.3 % 95.1 % 85.4 % 73.2 %
Standard deviation 9.1 0.85 1.23 3.09
q=40and ρ=0.4     
Average number of Biologically relevant variables 12 39 36 31
Average percentage of Biologically relevant variables 29.3 % 95.1 % 87.8 % 75.6 %
Standard deviation 9.1 0.84 1.22 3.07
Over 100 runs Lasso B1 B2 B3
Average number of selected variables 53 53 53 53
q=10 and ρ=0.1     
Average number of Biologically relevant variables 12 24 18 16
Average percentage of Biologically relevant variables 22.6 % 45.3 % 34.0 % 30.2 %
Standard deviation 10.2 0.99 1.55 3.94
q=20and ρ=0.25     
Average number of Biologically relevant variables 12 46 39 34
Average percentage of Biologically relevant variables (%) 22.6 % 86.8 % 72.1 % 64.2 %
Standard deviation 10.2 0.97 1.53 3.89
q=30and ρ=0.3     
Average number of Biologically relevant variables 12 47 39 36
Average percentage of Biologically relevant variables (%) 22.6 % 88.7 % 73.6 % 67.9 %
Standard deviation 10.2 0.97 1.53 3.89
q=40and ρ=0.4     
Average number of Biologically relevant variables 12 48 40 37
Average percentage of Biologically relevant variables (%) 22.6 % 90.6 % 75.5 % 69.8 %
Standard deviation 10.2 0.96 1.51 3.86
  1. Percentage and standard deviations are over 100 runs from data \(\mathcal {D}_{2}\) using correlation structure for simulation study 1 with different bag sizes q and correlation thresholds ρ from Adaptive lasso and Bag types B1, B2 and B3 based on Adaptive lasso selection and also from Lasso and Bag types B1, B2 and B3 based on lasso selection
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