Ridge and Lasso regression are powerful regularization techniques used to prevent overfitting in linear regression models. Standard linear regression can struggle when we have many features or when features are highly correlated with each other. The solution is to add penalty terms to the cost function that constrain the coefficient values, leading to more stable and generalizable models.
Ridge regression, also known as L2 regularization, adds a penalty term equal to lambda times the sum of squared coefficients to the mean squared error. This penalty shrinks the coefficients towards zero but never makes them exactly zero. Ridge regression is particularly effective at handling multicollinearity by shrinking correlated coefficients equally. The lambda parameter controls the strength of regularization - higher lambda values result in more shrinkage.
Lasso regression, or L1 regularization, adds a penalty equal to lambda times the sum of absolute values of coefficients. Unlike Ridge regression, Lasso can make coefficients exactly zero, effectively removing features from the model. This makes Lasso particularly valuable for feature selection, as it automatically identifies and eliminates unimportant variables. When lambda is large enough, some coefficients become zero, simplifying the model.
The key difference between Ridge and Lasso regression lies in how they handle coefficients. Ridge regression shrinks coefficients smoothly towards zero but never eliminates them completely, making it excellent for handling multicollinearity while keeping all features. Lasso regression, on the other hand, can set coefficients to exactly zero, effectively performing feature selection and creating sparse models. This makes Lasso ideal when you want to identify the most important features, though it may struggle with highly correlated features.
To summarize, Ridge and Lasso regression are powerful regularization techniques that add penalty terms to prevent overfitting. Ridge uses L2 penalty for smooth coefficient shrinkage and handles multicollinearity well. Lasso uses L1 penalty to perform automatic feature selection by setting coefficients to zero. The lambda parameter controls regularization strength in both methods. Choose Ridge when dealing with multicollinearity, and Lasso when you need feature selection.