Regularization

Regularization is a set of techniques used in statistical modeling and machine learning to prevent overfitting and improve the generalization ability of a model. Overfitting occurs when a model learns noise or irrelevant details in training data, leading to poor performance on unseen data. Regularization methods introduce additional constraints or penalties to the model's optimization process, encouraging simpler or more robust solutions.

Common forms of regularization include L1 and L2 regularization. L1 regularization, also known as Lasso, adds the absolute value of coefficients as a penalty, promoting sparsity by driving some coefficients to zero. L2 regularization, called Ridge, adds the squared magnitude of coefficients, encouraging smaller but non-zero coefficients. These penalties modify the loss function that the model seeks to minimize, effectively controlling model complexity.

Regularization is applicable across various algorithms, including linear regression, logistic regression, neural networks, and support vector machines. It is particularly valuable in high-dimensional settings where the number of features exceeds the number of observations, as it can help mitigate issues related to multicollinearity and overfitting.

In addition to L1 and L2, other regularization techniques include elastic net (a combination of L1 and L2), dropout (used in neural networks to randomly omit units during training), and early stopping (which halts training once performance on validation data begins to decline). By adding constraints or modifying the training process, regularization enhances the predictive robustness and interpretability of models, making it a fundamental practice in modern machine learning workflows.