Regularization techniques like L1 (Lasso) and L2 (Ridge) regularization are used in machine learning and deep learning to prevent overfitting and improve the generalization performance of models. They work by adding a regularization term to the loss function during training, penalizing the model for having large weights. Here's an explanation of L1 and L2 regularization:
L1 (Lasso) Regularization:
L1 regularization, also known as Lasso regularization, adds a penalty term to the loss function that is proportional to the absolute values of the model's weights. The L1 regularization term is defined as the L1 norm (sum of absolute values) of the weight vector:
Regularization Term = λ * ||w||₁
- λ (lambda) is the regularization strength hyperparameter, controlling the amount of regularization applied.
- ||w||₁ represents the L1 norm of the weight vector w.
The overall loss function with L1 regularization is a combination of the original loss (e.g., mean squared error for regression or cross-entropy for classification) and the L1 regularization term:
Regularized Loss = Original Loss + Regularization Term
Effect of L1 Regularization:
L1 regularization encourages sparse weight vectors, meaning it pushes some of the weights to become exactly zero. This sparsity property makes L1 regularization useful for feature selection, as it effectively shrinks some model parameters to zero, effectively removing irrelevant features. It can also simplify the model and make it more interpretable.
L2 (Ridge) Regularization:
L2 regularization, also known as Ridge regularization, adds a penalty term to the loss function that is proportional to the square of the model's weights. The L2 regularization term is defined as the L2 norm (Euclidean norm or sum of squared values) of the weight vector:
Regularization Term = λ * ||w||₂²
- λ (lambda) is the regularization strength hyperparameter.
- ||w||₂ represents the L2 norm of the weight vector w.
The overall loss function with L2 regularization is a combination of the original loss and the L2 regularization term:
Regularized Loss = Original Loss + Regularization Term
Effect of L2 Regularization:
L2 regularization encourages smaller weight values but doesn't typically force weights to become exactly zero. Instead, it distributes the penalty across all weights, pushing them towards smaller values. This results in smoother weight vectors and helps prevent the model from becoming too sensitive to individual data points.
Choosing Between L1 and L2:
- Use L1 regularization when feature selection or sparsity is desirable.
- Use L2 regularization as a default choice to prevent overfitting and stabilize training, especially when you don't have a specific reason to prefer sparsity.
Often, a combination of L1 and L2 regularization called Elastic Net regularization is used, which provides a trade-off between feature selection and smoothness of weights. The choice between regularization techniques and the appropriate regularization strength (λ) should be determined through cross-validation and experimentation to find the best configuration for your specific problem.