What is regularization in machine learning?

Regularization is a technique used in machine learning to prevent overfitting and improve the generalization performance of models. Overfitting occurs when a model learns to fit the training data too closely, capturing noise or random fluctuations in the data rather than underlying patterns. Regularization methods introduce additional constraints or penalties to the model's objective function, discouraging overly complex models that may overfit the training data.

The primary goal of regularization is to find a balance between fitting the training data well and avoiding excessive complexity. By penalizing complexity, regularization encourages the model to generalize better to unseen data, leading to improved performance on validation or test datasets.

Two common regularization techniques used in machine learning are L1 regularization (Lasso) and L2 regularization (Ridge):

1. L1 Regularization (Lasso):L1 regularization adds a penalty term to the model's objective function that is proportional to the absolute values of the model's coefficients (weights).The penalty term encourages sparsity in the model, leading to some coefficients being exactly zero. This property makes L1 regularization useful for feature selection and automatic feature elimination.The regularization term is expressed as the sum of the absolute values of the model's coefficients: λ * ||w||?, where λ is the regularization parameter and ||w||? represents the L1 norm of the weight vector.
2. L2 Regularization (Ridge):L2 regularization adds a penalty term to the model's objective function that is proportional to the squared values of the model's coefficients (weights).The penalty term encourages smaller but non-zero values for all coefficients, effectively reducing their magnitudes and preventing them from becoming too large.The regularization term is expressed as the sum of the squared values of the model's coefficients: λ * ||w||?2, where λ is the regularization parameter and ||w||? represents the L2 norm (Euclidean norm) of the weight vector.

Both L1 and L2 regularization methods involve tuning a hyperparameter λ (lambda) that controls the strength of regularization. Higher values of λ result in stronger regularization, leading to simpler models with reduced risk of overfitting but potentially higher bias.

Regularization is a crucial tool for improving the performance and robustness of machine learning models, particularly when dealing with high-dimensional data or limited training samples. It helps strike a balance between model complexity and generalization ability, leading to more reliable predictions on unseen data.

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