Elastic Net é uma regularization technique used in regressão linear que combina as propriedades de ambos Lasso (Regularização L1) e Ridge (Regularização L2) regression. It is particularly useful when dealing with datasets that have many features, especially when some features are correlated.
Lasso regression can select a subset of features by forcing some coefficients to be exactly zero, which makes it useful for seleção de variáveis. However, when features are highly correlated, Lasso may arbitrarily select one feature over others. On the other hand, Ridge regression tends to include all features by shrinking the coefficients but does not perform feature selection.
Elastic Net addresses these issues by balancing the two approaches. It penalizes the size of the coefficients while also allowing for some coefficients to be zero, thereby performing both regularization and feature selection. The method introduces two parameters: alpha, which controls the overall strength of the penalty, and the mixing parameter (often denoted as lambda), which determines the balance between Lasso and Ridge penalties.
Matematicamente, o Elastic Net função de perda pode ser expressa como:
Loss = ||y – Xβ||² + α * (λ * ||β||² + (1 – λ) * ||β||₁)
Onde ||y – Xβ||² is the residual sum of squares, ||β||² is the L2 norm (Ridge penalty), and ||β||₁ é a norma L1 (penalidade Lasso).
Elastic Net is widely used in various fields, including genomics and finance, where datasets often contain many correlated variables. By effectively managing multicollinearity and melhorar a interpretabilidade do modelo, Elastic Net helps in creating robust predictive models.