Regularization

Regularization

Regularization is a technique in machine learning used to prevent overfitting by adding extra constraints or penalties to a model during training.

Why Regularization is Important

Overfitting happens when a model learns noise and details from the training data, harming its ability to generalize on new data. Regularization discourages overly complex models by penalizing large or unnecessary model parameters.

Common Types of Regularization

1. L1 Regularization (Lasso)

• Adds the sum of the absolute values of coefficients as a penalty to the loss function.
• Encourages sparsity, meaning it can reduce some feature weights to zero, effectively performing feature selection.
• Loss function example:

$L=Los{s}_{original}+\lambda \sum _i|w_i|$

2. L2 Regularization (Ridge)

• Adds the sum of squared coefficients as a penalty.
• Penalizes large weights but does not force them to zero.
• Encourages smaller, more evenly distributed weights.
• Loss function example:

$L=Los{s}_{original}+\lambda \sum _i{w}_i^2$

3. Elastic Net

• Combines L1 and L2 penalties to balance sparsity and weight shrinkage.
• Useful when many correlated features exist.

How Regularization Works

By adding penalty terms, the model’s objective function becomes:

$\text{Objective}=\text{Original Loss}+\lambda \times \text{Penalty}$

Where $\lambda$ (lambda) controls the strength of regularization — higher values increase the penalty.

Benefits of Regularization

• Reduces overfitting.
• Improves model generalization on unseen data.
• Can perform feature selection (especially L1).
• Helps in models with many features or noisy data.

Example

In linear regression without regularization, the model might fit the training data perfectly but fail on test data (overfitting). Adding L2 regularization shrinks coefficients, leading to a simpler model that generalizes better.

Related Pages

• Overfitting
• Underfitting
• Bias-Variance Tradeoff
• Hyperparameter Tuning
• Model Evaluation Metrics

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