What is regularization in machine learning?

Theoretical Background: Regularization is a key concept in machine learning used to prevent overfitting, which occurs when a model learns the noise of the training data rather than the underlying pattern. Regularization techniques add a penalty term to the loss function to discourage the model from fitting too closely to the training data.

• L1 Regularization (Lasso): The penalty term is the sum of the absolute values of the coefficients ((\lambda \sum |w_i|)). This can lead to some coefficients becoming exactly zero, effectively performing feature selection.
• L2 Regularization (Ridge): The penalty term is the sum of the squares of the coefficients ((\lambda \sum w_i^2)). This tends to shrink the coefficients of correlated features together without making them exactly zero.

Practical Applications:

• L1 Regularization is useful in situations where you want a sparse model with fewer features. For example, in high-dimensional data such as text data where many features can be irrelevant.
• L2 Regularization is appropriate when you have multicollinearity among features. It helps to distribute the weights among the correlated features, reducing their variance.

Code Example: Here's a simple illustration using Python and Scikit-learn:

from sklearn.linear_model import Lasso, Ridge

# L1 Regularization
lasso = Lasso(alpha=0.1)
lasso.fit(X_train, y_train)

# L2 Regularization
ridge = Ridge(alpha=0.1)
ridge.fit(X_train, y_train)

Visual Representation:

graph LR
A[Cost Function without Regularization] -->|Add L1 Penalty| B[L1 Regularization]
A -->|Add L2 Penalty| C[L2 Regularization]

This diagram shows how regularization terms are added to the cost function to form L1 and L2 regularizations.

External References:

• Regularization in Machine Learning
• Understanding the difference between L1 and L2 Regularization

In conclusion, the choice between L1 and L2 depends on the specific problem and desired outcomes such as sparsity or dealing with multicollinearity.