l1regularization

L1 regularization, also known as Lasso (Least Absolute Shrinkage and Selection Operator) regularization, is a technique used in machine learning to prevent overfitting by adding a penalty term to the cost function. This penalty is proportional to the absolute value of the magnitude of the coefficients.

The cost function with L1 regularization can be represented as: Cost = Original Cost + λ * Σ|w_i|, where Original Cost is the sum of squared errors or another appropriate loss function, w_i are the model's coefficients, and λ (lambda) is a hyperparameter that controls the strength of the regularization. A larger λ imposes a stronger penalty.

The key characteristic of L1 regularization is its ability to drive some coefficients exactly to zero. This feature makes L1 regularization a form of feature selection, as it effectively removes irrelevant or less important features from the model. This can lead to sparser models, which are often more interpretable and computationally efficient.

In contrast to L2 regularization (Ridge regression), which shrinks coefficients towards zero but rarely makes them exactly zero, L1 regularization's sparsity-inducing property is highly valued when dealing with high-dimensional datasets where many features might be redundant or noisy. The choice between L1 and L2 regularization often depends on the specific problem and the desired properties of the resulting model.