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Table 4 Average number and percentage of biologically relevant variables in the model with S N R=2 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 44 44 44 44
Average number of Biologically relevant variables 16 42 41 37
Average percentage of Biologically relevant variables (%) 36.4 % 95.5 % 93.2 % 84.1 %
Standard deviation 9.01 0.92 1.11 3.91
PMSE (absolute) 1.895 1.878 1.880 1.901
PRPMSE % 100 % 99.1 % 99.2 % 100.3 %
(St.dev)   (1.01) (2.14) (6.16)
Favorable substitution %   92 % 78 % 70 %
(St.dev)   (0.99) (1.37) (8.92)
MISE 1.986 2.003 2.052 2.097
Over 100 runs Lasso B1 B2 B3
Average number of selected variables 55 55 55 55
Average number of Biologically relevant variables 16 48 45 40
Average percentage of Biologically relevant variables (%) 22.8 % 87.3 % 81.8 % 72.7 %
Standard deviation 10.2 0.99 1.53 4.12
PMSE (absolute) 2.132 2.104 2.117 2.158
PRPMSE % 100 % 98.7 % 99.3 % 101.2 %
(St.dev)   (1.11) (2.31) (6.89)
Favorable substitution %   89 % 70 % 68 %
(St.dev)   (1.01) (1.69) (9.53)
MISE 2.234 2.298 2.306 2.342
  1. Percentage and standard deviations are over 100 runs from data \(\mathcal {D}_{2}\). The average of the PMSE and PRPMSE over 100 runs and the percentage of such runs for which the bootstrap 95 % CI includes 1 or less than 1 and mean integrated squared error (MISE), with S N R=2 and (β j =0.1,j=1,2,…,20) from data \(\mathcal {D}_{3}\) using correlation structure for simulation study 1
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