Ridle for sparse regression with mandatory covariates with application to the genetic assessment of histologic grades of breast cancer

Table 1 Simulation example 1: effect of signal strengths

	Method	rpe	g-measure	Sensitivity	Specificity
β ₀=0.5	Ridge	1.008 (0.009)
	Lasso	1.004 (0.018)	0.582 (0.009)	0.350 (0.018)	0.957 (0.006)
	Elastic net	0.923 (0.020)	0.676 (0.007)	0.600 (0.041)	0.848 (0.023)
	\(\mathcal {M}\)-unpenalized lasso	0.675 (0.028)	1.000 (0.000)	1.000 (0.000)	1.000 (0.000)
	\(\mathcal {M}\)-unpenalized elastic net	0.697 (0.026)	1.000 (0.001)	1.000 (0.000)	1.000 (0.002)
	Ridle	0.281 (0.016)	0.998 (0.001)	1.000 (0.000)	0.996 (0.002)
β ₀=1.5	Ridge	6.549 (0.056)
	Lasso	3.300 (0.083)	0.839 (0.005)	0.750 (0.017)	0.926 (0.003)
	elastic net	3.230 (0.118)	0.853 (0.004)	0.900 (0.008)	0.850 (0.005)
	\(\mathcal {M}\)-unpenalized lasso	0.691 (0.023)	1.000 (0.000)	1.000 (0.000)	1.000 (0.000)
	\(\mathcal {M}\)-unpenalized elastic net	0.701(0.028)	1.000 (0.001)	1.000 (0.000)	1.000 (0.001)
	Ridle	0.473 (0.014)	0.998 (0.001)	1.000 (0.000)	0.996 (0.002)
β ₀=3	Ridge	24.559 (0.317)
	Lasso	8.074 (0.433)	0.908 (0.005)	0.900 (0.013)	0.935 (0.002)
	Elastic net	6.735 (0.339)	0.903 (0.002)	0.950 (0.013)	0.852 (0.003)
	\(\mathcal {M}\)-unpenalized lasso	0.676 (0.032)	1.000 (0.000)	1.000 (0.000)	1.000 (0.000)
	\(\mathcal {M}\)-unpenalized elastic net	0.725 (0.030)	1.000 (0.000)	1.000 (0.000)	1.000 (0.001)
	Ridle	0.605 (0.025)	0.998 (0.001)	1.000 (0.000)	0.996 (0.002)

The \(\mathcal {M}\)-unpenalized lasso and \(\mathcal {M}\)-unpenalized elastic net were performed without penalization on the mandatory covariates
n=50, p=250, \(|\mathcal {M}|=20\). The smallest rpe and largest two g-measures are boldfaced

ISSN: 1471-2288