Final answer:
Elastic Net Regression performs feature selection by combining the L1 penalty, which can reduce some coefficients to zero, and the L2 penalty, which shrinks coefficients towards zero. This method selects the most relevant features while maintaining model stability and preventing overfitting.
Step-by-step explanation:
How Elastic Net Regression Performs Feature Selection
Elastic Net Regression is a regularization technique that combines the properties of both Ridge Regression (L2 regularization) and Lasso Regression (L1 regularization). The primary goal of Elastic Net Regression is to prevent overfitting, improve model generalization, and perform feature selection. This method incorporates penalties from both L1 and L2 regularization to produce a more robust model.
The Elastic Net Regression adds both the L1 and L2 penalty terms to the loss function. The L1 penalty has the effect of forcing some coefficient estimates to be exactly zero when their contribution to the model is not significant. This accounts for the feature selection capability of Elastic Net. Meanwhile, The L2 penalty shrinks the coefficients towards zero but doesn't set them to zero, thus, it is not primarily for feature selection but is effective in handling multicollinearity. The combination allows for learning a sparse model where few features contribute to the outcome with a stable model where all coefficients are included with some shrinkage.
By choosing an appropriate ratio between the L1 and L2 penalties, Elastic Net can be adjusted to select the most relevant features, which helps in reducing the complexity of the model and improving prediction accuracy. The tuning of this ratio is usually done via cross-validation.
Ultimately, Elastic Net Regression offers a middle ground between Ridge and Lasso Regression, seeking both the regularization properties of Ridge and the sparse solutions of Lasso, making it particularly useful when dealing with datasets with numerous correlated features or when selecting important features in a model.