Elastic Net Regression

Elastic Net combines the penalty terms of ridge and LASSO regression to avoid the overdependence on data for variable selection (coefficient values tending to zero by which highly correlated variables are kept in check). Elastic Net minimizes the following loss function:

Where the parameter α controls the right mix between ridge and LASSO.

In summary, if a model has many predictor variables or correlated variables, introducing the regularization term helps in reducing the variance and increase bias optimally, thus bringing the right balance of model complexity and error. Figure 4.16 provides a flow diagram to help one choose between multiple, ridge, LASSO, and elastic net regression:

Figure 4.16: Selection criteria to choose between multiple, ridge, LASSO, and elastic net regression

Exercise 58: Elastic Net Regression

In this exercise, we will perform elastic net regression on the Beijing PM2.5 dataset.

Perform the following steps to complete the exercise:

1. Let's first set...