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Table 1 Simulation example 1: effect of signal strengths

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

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