LassoSchätzung

LassoSchätzung, also known as Least Absolute Shrinkage and Selection Operator, is a regularization technique used in statistics and machine learning. It is a type of linear regression that modifies the objective function by adding a penalty term. Specifically, the Lasso objective function minimizes the sum of squared errors plus a penalty proportional to the absolute value of the coefficients. This penalty is often referred to as the L1 norm of the coefficient vector.

The key feature of LassoSchätzung is its ability to perform variable selection. The L1 penalty has the effect of shrinking some of the regression coefficients exactly to zero. This means that the corresponding predictor variables are effectively removed from the model, resulting in a sparser model. This is particularly useful when dealing with datasets that have a large number of predictor variables, many of which may be irrelevant or redundant. By setting some coefficients to zero, LassoSchätzung can improve model interpretability and potentially reduce overfitting.

The strength of the shrinkage is controlled by a tuning parameter, often denoted by lambda (λ). A larger value of λ results in more shrinkage and a sparser model. The optimal value of λ is typically determined through cross-validation. While LassoSchätzung is effective for variable selection, it can sometimes select only one variable from a group of highly correlated variables. Other regularization methods, like Ridge Regression (which uses an L2 penalty), shrink coefficients towards zero but do not typically set them exactly to zero. Variations and extensions of Lasso exist, such as Elastic Net, which combines both L1 and L2 penalties to address some of Lasso's limitations.