L2 Regularization

What is L2 Regularization? L2 Regularization Explained

L2 regularization, also known as Ridge regularization, is a technique used in machine learning and statistical modeling to add a penalty term to the objective function during training. It helps prevent overfitting by adding a penalty based on the squared magnitudes of the model coefficients.

In L2 regularization, a penalty term proportional to the square of the L2 norm of the model coefficients is added to the loss function. The modified objective function becomes a combination of the loss function and the L2 penalty term. The objective is to minimize this modified objective function.

The L2 regularization term can be represented as:

L2 = λ * Σ(w^2),

where λ is the regularization parameter and w is the vector of model coefficients.

Key points about L2 regularization:

Controls model complexity: This technique helps control model complexity by shrinking the magnitude of the model coefficients. It discourages large coefficient values, making the model more robust to noisy or irrelevant features.

Continuous shrinkage: It applies a continuous shrinkage to the coefficients, rather than pushing them exactly to zero like L1 regularization. As λ increases, the coefficients are shrunk more towards zero, but they generally remain non-zero.

Ridge effect: It is often referred to as Ridge regularization due to its effect on the model coefficients. It tends to push the coefficients towards smaller values without eliminating any of them completely, which can lead to a smoother and more stable model.

Equal impact on correlated features: The technique has the property of treating all correlated features equally. It distributes the penalty across correlated features, unlike L1 regularization, which tends to select one feature from a group of correlated features.

Scaling sensitivity: It is sensitive to feature scaling. If the features have significantly different scales, L2 regularization may excessively penalize the coefficients of the features with larger magnitudes. Therefore, it is important to scale the features appropriately before applying L2 regularization.

Trade-off between regularization and model fit: The strength of L2 regularization is controlled by the value of the regularization parameter λ. A higher value of λ increases the regularization and reduces overfitting but may lead to an underfit model with reduced performance on the training data. The choice of λ is often determined through cross-validation or other tuning methods.

L2 regularization is commonly used in linear regression, logistic regression, and other linear models. It is particularly useful in situations where model stability, generalization, and handling multicollinearity (correlated features) are important.

Overall, L2 regularization provides a useful tool for controlling model complexity, improving generalization, and addressing multicollinearity issues in machine learning and statistical modeling tasks.