ElasticNetVerfahren

The Elastic Net method is a regularized regression technique that combines the penalties of both Lasso (L1 regularization) and Ridge (L2 regularization) regression. It was developed by Trevor Hastie, Robert Tibshirani, and Jerome Friedman. The primary goal of Elastic Net is to address some of the limitations of Lasso and Ridge regression, particularly in situations where predictors are highly correlated or when the number of predictors is large relative to the number of observations.

In Lasso regression, the penalty term is the sum of the absolute values of the coefficients. This can lead to feature selection by shrinking some coefficients exactly to zero. Ridge regression, on the other hand, uses the sum of the squared values of the coefficients, which shrinks coefficients towards zero but rarely sets them exactly to zero. Elastic Net introduces a penalty that is a linear combination of both the L1 and L2 penalties. This means it can perform feature selection like Lasso while also handling correlated predictors more robustly than Lasso, similar to Ridge.

The Elastic Net objective function aims to minimize the sum of squared errors plus a penalty term. This penalty term is controlled by two parameters: alpha (α) and lambda (λ). Alpha determines the balance between the L1 and L2 penalties, and lambda controls the overall strength of the regularization. When alpha is 1, Elastic Net is equivalent to Lasso. When alpha is 0, it is equivalent to Ridge regression. By tuning these parameters, Elastic Net can select relevant features and produce more stable models compared to Lasso when dealing with multicollinearity. It is widely used in machine learning and statistical modeling for its ability to handle complex datasets.