L1normisäännöllisyys

L1normisäännöllisyys, also known as Lasso regularization, is a technique used in machine learning and statistics to prevent overfitting and perform feature selection. It achieves this by adding a penalty term to the cost function that is proportional to the absolute value of the regression coefficients. This penalty is calculated using the L1 norm of the coefficient vector.

The L1 norm of a vector is the sum of the absolute values of its elements. In the context of regression, the L1 penalty is expressed as lambda * sum(|beta_i|), where lambda is a tuning parameter that controls the strength of the regularization, and beta_i represents the individual regression coefficients.

A key characteristic of L1 normisäännöllisyys is its tendency to drive some of the regression coefficients exactly to zero. This is unlike L2 regularization (Ridge regression), which shrinks coefficients towards zero but rarely makes them exactly zero. When a coefficient becomes zero, the corresponding feature is effectively removed from the model, leading to feature selection. This inherent feature selection capability makes L1 normisäännöllisyys particularly useful when dealing with high-dimensional datasets where many features might be irrelevant or redundant.

The choice of the tuning parameter lambda is crucial. A small lambda results in a model with less regularization, closer to an unregularized model. As lambda increases, the penalty becomes stronger, leading to more coefficients being forced to zero and a simpler model. Cross-validation is a common method used to determine the optimal value of lambda.