A Penalized Regression Method for Genomic Prediction Reduces Mismatch between Training and Testing Sets

Abstract

Genomic selection (GS) is changing plant breeding by significantly reducing the resources needed for phenotyping. However, its accuracy can be compromised by mismatches between training and testing sets, which impact efficiency when the predictive model does not adequately reflect the genetic and environmental conditions of the target population. To address this challenge, this study introduces a straightforward method using binary-Lasso regression to estimate β coefficients. In this approach, the response variable assigns 1 to testing set inputs and 0 to training set inputs. Subsequently, Lasso, Ridge, and Elastic Net regression models use the inverse of these β coefficients (in absolute values) as weights during training (WLasso, WRidge, and WElastic Net). This weighting method gives less importance to features that discriminate more between training and testing sets. The effectiveness of this method is evaluated across six datasets, demonstrating consistent improvements in terms of the normalized root mean square error. Importantly, the model's implementation is facilitated using the glmnet library, which supports straightforward integration for weighting β coefficients.

Keywords: Elastic Net regression; Lasso regression; Ridge regression; genomic selection; mismatch; weighted regression.

Figure 1

Normalized root mean square error (NRMSE) for the “Maize_1” dataset. A comparison is presented for the 6 evaluated models (Enet, Lasso, Ridge, WEnet, WLasso, and WRidge) and the 2 traits (GDD_ASI and GDD_DTT).

Figure 2

Normalized root mean square error (NRMSE) for the “Maize 3” dataset. A comparison is presented for the 6 evaluated models (Enet, Lasso, Ridge, WEnet, WLasso, and WRidge) and the 2 traits (GDD_ASI and GDD_DTT).

Figure 3

Normalized root mean square error (NRMSE) for the “Soybean 1” dataset. A comparison is presented for the 6 evaluated models (Enet, Lasso, Ridge, WEnet, WLasso, and WRidge) and the 2 traits (Height and R8).

Figure 4

Normalized root mean square error (NRMSE) for the “Soybean 2” dataset. A comparison is presented for the 6 evaluated models (Enet, Lasso, Ridge, WEnet, WLasso, and WRidge) and the 2 traits (Height and R8).

Figure 5

Normalized root mean square error (NRMSE) for all datasets. A comparison is presented for the 6 evaluated models (Enet, Lasso, Ridge, WEnet, WLasso, and WRidge).

Figure A1

Dataset Maize 2. Normalized root mean square error (NRMSE) for the Maize_2 dataset. A comparison is presented for the 6 evaluated models (Enet, Lasso, Ridge, WEnet, WLasso, and WRidge) and the 2 traits (GDD_ASI and GDD_DTT).

Figure A2

Dataset Maize 4. Normalized root mean square error (NRMSE) for the Maize_4 dataset. A comparison is presented for the 6 evaluated models (Enet, Lasso, Ridge, WEnet, WLasso, and WRidge) and the 2 traits (GDD_ASI and GDD_DTT).

Figure A3

Dataset Soybean 3. Normalized root mean square error (NRMSE) for the Soybean_3 dataset. A comparison is presented for the 6 evaluated models (Enet, Lasso, Ridge, WEnet, WLasso, and WRidge) and the 2 traits (Height and R8).

Figure A4

Dataset Soybean 4. Normalized root mean square error (NRMSE) for the Soybean_4 dataset. A comparison is presented for the 6 evaluated models (Enet, Lasso, Ridge, WEnet, WLasso, and WRidge) and the 2 traits (Height and R8).