# L1 and L2 Regularization

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# L1 and L2 Regularization Explained:

Both L1 and L2 regularization are techniques used in machine learning to prevent overfitting and improve the generalization ability of models. They achieve this by penalizing large parameter values, but do so in different ways:

**L1 Regularization (Lasso Regression):**

- Adds the absolute value of the magnitude of each coefficient (weight) as a penalty term to the loss function.
- Shrinks some coefficient values to zero, effectively sparsifying the model and selecting relevant features.
- More robust to outliers compared to L2, as absolute values are less sensitive to extreme values.
- Interpretability is improved as zero coefficients can indicate features irrelevant to the model.

**L2 Regularization (Ridge Regression):**

- Adds the squared magnitude of each coefficient as a penalty term to the loss function.
- Shrinks all coefficient values towards zero, but not necessarily to zero itself.
- Less affected by outliers compared to L1 as squares decrease the impact of extremes.
- Coefficients remain non-zero, making interpretation less straightforward.

Choosing Between L1 and L2:

- Feature selection: If feature selection is desired, L1 is preferred due to its sparsity-inducing property.
- Outlier sensitivity: If data contains outliers, L2 might be more stable due to its reduced sensitivity.
- Model complexity: L2 typically leads to less complex models, while L1 can result in simpler models with fewer features.
- Interpretability: Both methods can enhance interpretability to a certain extent, though L1’s feature selection makes it slightly more interpretable.

Hyperparameter Tuning:

Both methods require tuning the regularization parameter (lambda), which controls the strength of the penalty term. A higher lambda leads to stronger regularization and simpler models, but might hurt model accuracy. Finding the optimal lambda involves grid search, cross-validation, or other techniques.

Conclusion:

L1 and L2 regularization are valuable tools for preventing overfitting and improving model generalization. Understanding their differences and strengths is crucial for choosing the right technique and tuning parameters for optimal performance.

Additional Resources: