Tilting the lasso by knowledge-based post-processing

BMC Bioinformatics

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)

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

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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