L1metoden

L1metoden, also known as L1 regularization or Lasso (Least Absolute Shrinkage and Selection Operator), is a technique used in statistical modeling and machine learning for feature selection and regularization. It is particularly useful when dealing with high-dimensional datasets where the number of features might be significantly larger than the number of observations.

The core idea behind L1metoden is to add a penalty term to the standard loss function of a model. This penalty is proportional to the absolute value of the magnitude of the coefficients of the model's parameters. Mathematically, for a linear regression model, the objective function to be minimized becomes the sum of squared errors plus the L1 penalty: Sum of (y_i - f(x_i))^2 + lambda * sum(|beta_j|), where lambda is a tuning parameter that controls the strength of the regularization.

A key characteristic of L1metoden is its ability to drive some of the model's coefficients exactly to zero. This effectively removes the corresponding features from the model, performing automatic feature selection. This sparsity-inducing property makes L1metoden a powerful tool for building simpler, more interpretable models and for identifying the most relevant predictors in a dataset.

In contrast to L2 regularization (Ridge regression), which shrinks coefficients towards zero but rarely to exactly zero, L1metoden is preferred when a sparse solution is desired. The choice of the lambda parameter is crucial and is typically determined through cross-validation, balancing model fit with the degree of regularization. L1metoden has found applications in various fields, including bioinformatics, econometrics, and image processing.