L1 vs L2 Regularization vs Elastic Net: Key Differences Explained

**Regularization Simplified**

**Imagine you’re building a model to predict house prices using features like square footage, number of bedrooms, and age of the house.**

- **L1 Regularization (Lasso)**:

  - Suppose you have many features, some of which might not be very useful, like the color of the front door or the number of windows.

  - **L1 Regularization** will push the less important features (like color or number of windows) to zero, effectively removing them from the model.

  - This helps in simplifying the model by focusing only on the most relevant features.

- **L2 Regularization (Ridge)**:

  - Imagine you have important features like square footage and number of bedrooms, but they might be highly correlated.

  - **L2 Regularization** will reduce the influence of all features but won’t remove any of them.

  - It shrinks the coefficients of correlated features, ensuring they all contribute but in a more controlled way.

- **Elastic Net**:

  - If you want to use a combination of both approaches, you’d use **Elastic Net**.

  - It will both shrink the coefficients and potentially set some to zero, giving you a mix of feature selection and controlled regularization.

**Summary**: L1 Regularization (Lasso) is useful for feature selection by removing less important features, L2 Regularization (Ridge) is useful for controlling the influence of correlated features, and Elastic Net combines both techniques to balance between feature selection and regularization.