L1regulaatio

L1-regulaatio, also known as Lasso (Least Absolute Shrinkage and Selection Operator) regularization, is a technique used in machine learning and statistics to improve the performance of models, particularly in situations with a large number of features. It achieves this by adding a penalty term to the objective function during the model training process. This penalty is proportional to the absolute value of the regression coefficients.

The core idea behind L1-regulaatio is to shrink some of the coefficients towards zero. Unlike L2-regulaatio (Ridge regression), which shrinks coefficients proportionally, L1-regulaatio has a tendency to force many coefficients to become exactly zero. This property makes L1-regulaatio a powerful tool for feature selection. By setting less important feature coefficients to zero, the model effectively discards those features, leading to a simpler and potentially more interpretable model.

The mathematical form of the L1-regularized objective function typically involves minimizing the sum of squared errors (or another loss function) plus a term representing the sum of the absolute values of the coefficients, multiplied by a regularization parameter (lambda). The value of lambda controls the strength of the regularization. A larger lambda results in more coefficients being shrunk to zero, leading to a sparser model.

L1-regulaatio is particularly useful when dealing with high-dimensional datasets where the number of features is much larger than the number of observations. It can help prevent overfitting by regularizing the model's complexity and can identify the most relevant features for prediction. However, if there are highly correlated features, L1-regulaatio might arbitrarily select one of them and set the others to zero, which may not always be the desired behavior.