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Table 5 Gene expression analysis on histologic grades of breast cancer

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

  No. selected \(\mathcal {M}\) No. selected \(\mathcal {O}\) MSE
Ridge 4 430 0.487
Lasso 2 19 0.260
Elastic net 2 14 0.286
\(\mathcal {M}\)-unpenalized lasso 4 21 0.257
\(\mathcal {M}\)-unpenalized elastic net 4 7 0.296
Ridle 4 24 0.239
  1. The \(\mathcal {M}\)-unpenalized lasso and \(\mathcal {M}\)-unpenalized elastic net were performed without penalization on the mandatory covariates. The elastic net and \(\mathcal {M}\)-unpenalized elastic net are built with alpha=0.2575 and alpha=0.8462, respectively, selected by cross-validation. Numbers of selected mandatory covariates \(\mathcal {M}\) and optional variables \(\mathcal {O}\), and mean-squared error (MSE) are shown. Smallest MSE is boldfaced