Skip to main content

Table 3 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
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
PMSE (absolute) 1.148 1.145 1.143 1.154
PRPMSE % 100 % 99.7 % 99.6 % 100.5 %
(St.dev)   (0.89) (1.53) (5.98)
Favorable substitution %   91 % 78 % 69 %
(St.dev)   (0.99) (1.07) (6.93)
MISE 1.572 1.598 1.605 1.643
Over 100 runs Lasso B1 B2 B3
Average number of selected variables 53 53 53 53
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
PMSE (absolute) 1.576 1.570 1.567 1.596
PRPMSE % 100 % 99.6 % 99.4 % 101.3 %
(St.dev)   (0.97) (1.81) (6.71)
Favorable substitution %   88 % 71 % 63 %
(St.dev)   (1.02) (1.52) (7.68)
MISE 1.876 1.914 1.927 1.941
  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=0.5 and (β j =0.1,j=1,2,…,20) from data \(\mathcal {D}_{3}\) using correlation structure for simulation study 1
\