Régression Lasso
Lasso Régression, which stands for Least Absolute Shrinkage and Selection Operator, is a type of régression linéaire that incorporates regularization to enhance prediction accuracy and interpretability in modèles statistiques. It is particularly useful when dealing with datasets that have many features or variables.
L'objectif principal de la régression Lasso est de minimiser le fonction de perte of the linear model while also imposing a penalty on the absolute size of the coefficients. This penalty term, known as L1 regularization, encourages the model to shrink some coefficients to zero, effectively performing variable selection. This means that Lasso Regression can help identify the most significant predictors in a dataset and discard irrelevant or less impactful features.
Mathématiquement, la régression Lasso résout le problème d’optimisation:
minimize ||y - Xβ||² + λ||β||₁
Here, y represents the target variable, X is the matrice de caractéristiques, β denotes the coefficient vector, ||y - Xβ||² is the residual sum of squares, and λ is the regularization parameter that controls the strength of the penalty. A larger value of λ results in more coefficients being shrunk towards zero, which can help reduce overfitting but may also lead to underfitting if set too high.
Lasso Regression is widely used in fields such as finance, biology, and machine learning for its ability to simplify models and améliorer la précision des prédictions. It is particularly effective in high-dimensional datasets where the number of predictors exceeds the number of observations.