L1regularisoinnissa

L1 regularisoinnissa, often referred to as Lasso regression, is a type of linear regression that incorporates an L1 penalty term into the cost function. This penalty term is proportional to the absolute value of the magnitude of the coefficients. The objective is to minimize the sum of squared errors plus this L1 penalty. The L1 penalty has the effect of shrinking the coefficients of less important features towards zero. A key characteristic of L1 regularisoinnissa is its ability to perform automatic feature selection by driving the coefficients of irrelevant features to exactly zero, effectively removing them from the model. This can lead to sparser and more interpretable models, especially when dealing with high-dimensional datasets where many features might be redundant or irrelevant. The mathematical formulation involves minimizing ||y - Xw||^2 + lambda * ||w||_1, where y is the target variable, X is the feature matrix, w is the vector of coefficients, ||.||^2 denotes the squared L2 norm, ||.||_1 denotes the L1 norm, and lambda is the regularization parameter that controls the strength of the penalty. A larger lambda results in more coefficients being shrunk to zero. Unlike L2 regularization (Ridge regression), which shrinks coefficients towards zero but rarely to exactly zero, L1 regularisoinnissa's inherent sparsity makes it a powerful tool for feature selection and building more parsimonious models.