Lasso and Elastic Net Regressions, Explained: A Visual Guide with Code Examples
REGRESSION ALGORITHM
Least Squares Regression, Explained: A Visual Guide with Code Examples for Beginners
Linear regression comes in different types: Least Squares methods form the foundation, from the classic Ordinary Least Squares (OLS) to Ridge regression with its regularization to prevent overfitting. Then there's Lasso regression, which takes a unique approach by automatically selecting important factors and ignoring others. Elastic Net combines the best of both worlds, mixing Lasso's feature selection with Ridge's ability to handle related features.
It's frustrating to see many articles treat these methods as if they're basically the same thing with minor tweaks. They make it seem like switching between them is as simple as changing a setting in your code, but each actually uses different approaches to solve their optimization problems!
While OLS and Ridge regression can be solved directly through matrix operations, Lasso and Elastic Net require a different approach – an iterative method called coordinate descent. Here, we'll explore how this algorithm works through clear visualizations. So, let's saddle up and lasso our way through the details!
Definition
Lasso Regression
LASSO (Least Absolute Shrinkage and Selection Operator) is a variation of Linear Regression that adds a penalty to the model. It uses a linear equation to predict numbers, just like Linear Regression. However, Lasso also has a way to reduce the importance of certain factors to zero, which makes it useful for two main tasks: making predictions and identifying the most important features.
Elastic Net Regression
Elastic Net Regression is a mix of Ridge and Lasso Regression that combines their penalty terms. The name "Elastic Net" comes from physics: just like an elastic net can stretch and still keep its shape, this method adapts to data while maintaining structure.
The model balances three goals: minimizing prediction errors, keeping the size of coefficients small (like Lasso), and preventing any coefficient from becoming too large (like Ridge). To use the model, you input your data's feature values into the linear equation, just like in standard Linear Regression.
The main advantage of Elastic Net is that when features are related, it tends to keep or remove them as a group instead of randomly picking one feature from the group.
