Lasso

What is L1 regularization, and how does it differ from other regularization techniques like L2 regularization? Explain the role of L1 regularization in the context of feature selection and model complexity. Discuss how L1 regularization affects the model's coefficients and its ability to perform automatic feature selection by encouraging sparsity. Additionally, highlight scenarios or types of datasets where L1 regularization might be more beneficial or less effective compared to other regularization methods.

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Regularization techniques like L1 and L2 are used to prevent overfitting in machine learning models by penalizing large coefficients.

L1 regularization, also known as Lasso regularization, adds a penalty term proportional to the absolute value of the coefficients of the features. It encourages sparsity by driving some coefficients to exactly zero, effectively performing feature selection by eliminating less important features. This feature selection capability makes L1 regularization particularly useful when dealing with datasets with a large number of features, as it helps to simplify models by focusing on the most relevant features. The resulting model simplification reduces overfitting.

On the other hand, L2 regularization, also known as Ridge regularization, adds a penalty term proportional to the square of the coefficients of the features. It doesn’t force coefficients to become exactly zero but instead shrinks them towards zero, making all features contribute to the model to some extent. L2 regularization is effective in handling multicollinearity and generally leads to more stable but less sparse models compared to L1 regularization.

Scenarios where L1 regularization might be more beneficial include:

High-dimensional datasets with many features: When dealing with datasets where feature space is large, L1 regularization helps in automatic feature selection, improving model interpretability and performance.
When feature sparsity is expected: In domains where it’s anticipated that only a few features are truly influential, L1 regularization can efficiently identify and focus on those features.

However, L1 regularization might be less effective in scenarios where:

All features are assumed to be important: If there’s a belief that most features are relevant and excluding any might cause loss of information, L1 might not be the best choice as it tends to set coefficients to zero.
The dataset has multicollinearity issues: L2 regularization is better suited for handling multicollinearity problems compared to L1 regularization.

In practice, a combination of L1 and L2 regularization, known as Elastic Net regularization, can be used to benefit from both techniques, leveraging the sparsity of L1 and the stability of L2.