Ridge Regression vs Lasso Regression
Last Updated :
03 Mar, 2025
Ridge and Lasso Regression are two popular techniques in machine learning used for regularizing linear models to avoid overfitting and improve predictive performance. Both methods add a penalty term to the model’s cost function to constrain the coefficients, but they differ in how they apply this penalty.
- Ridge Regression, also known as L2 regularization, adds the squared magnitude of the coefficients as a penalty.
- On the other hand, Lasso Regression, or L1 regularization, introduces a penalty based on the absolute value of the coefficients.
In this article, we will discuss about both the techniques including differences between them in detail.
What is Ridge Regression or (L2 Regularization) Method?
Ridge regression, also known as L2 regularization, is a technique used in linear regression to prevent overfitting by adding a penalty term to the loss function. This penalty is proportional to the square of the magnitude of the coefficients (weights).
Ridge Regression is a version of linear regression that includes a penalty to prevent the model from overfitting, especially when there are many predictors or not enough data.
The standard loss function (mean squared error) is modified to include a regularization term:
Loss = \text{MSE} + \lambda \sum_{i=1}^{n} w_i^2
Here, λ is the regularization parameter that controls the strength of the penalty, and wi are the coefficients.
What is Lasso Regression or (L1 Regularization) Method?
Lasso regression, also known as L1 regularization, is a linear regression technique that adds a penalty to the loss function to prevent overfitting. This penalty is based on the absolute values of the coefficients.
Lasso regression is a version of linear regression including a penalty equal to the absolute value of the coefficient magnitude. By encouraging sparsity, this L1 regularization term reduces overfitting and helps some coefficients to be absolutely zero, hence facilitating feature selection.
The standard loss function (mean squared error) is modified to include a regularization term:
Loss = \text{MSE} + \lambda \sum_{i=1}^{n} |w_i|
Here, λ is the regularization parameter that controls the strength of the penalty, and wi are the coefficients.
Difference between Ridge Regression and Lasso Regression
The key differences between ridge and lasso regression are discussed below:
| Characteristic | Ridge Regression | Lasso Regression |
|---|
| Regularization Type | Applies L2 regularization, adding a penalty term proportional to the square of the coefficients | Applies L1 regularization, adding a penalty term proportional to the absolute value of the coefficients. |
| Feature Selection | Does not perform feature selection. All predictors are retained, although their coefficients are reduced in size to minimize overfitting | Performs automatic feature selection. Less important predictors are completely excluded by setting their coefficients to zero. |
| When to use | Best suited for situations where all predictors are potentially relevant, and the goal is to reduce overfitting rather than eliminate features | Ideal when you suspect that only a subset of predictors is important, and the model should focus on those while ignoring the irrelevant ones. |
| Output model | Produces a model that includes all features, but their coefficients are smaller in magnitude to prevent overfitting | Produces a model that is simpler, retaining only the most significant features and ignoring the rest by setting their coefficients to zero. |
| Impact on Prediction | Reduces the magnitude of coefficients, shrinking them towards zero, but does not set any coefficients exactly to zero. All predictors remain in the model | Shrinks some coefficients to exactly zero, effectively removing their influence from the model. This leads to a simpler model with fewer features |
| Computation | Generally faster as it doesn’t involve feature selection | May be slower due to the feature selection process |
Example Use Case | Use when you have many predictors, all contributing to the outcome (e.g., predicting house prices where all features like size, location, etc., matter) | Use when you believe only some predictors are truly important (e.g., genetic studies where only a few genes out of thousands are relevant). |
When to Use Ridge Regression?
Ridge Regression is most suitable when all predictors are expected to contribute to the outcome and none should be excluded from the model. It reduces overfitting by shrinking the coefficients, ensuring they don’t become too large, while still keeping all the predictors in the model.
For example, when predicting house prices, features like size, number of bedrooms, location, and year built are all likely relevant. Ridge Regression ensures these features remain in the model but with reduced influence to create a balanced and robust prediction.
When to Use Lasso Regression?
Lasso Regression is ideal when you suspect that only a few predictors are truly important, and the rest may add noise or redundancy. It performs automatic feature selection by shrinking the coefficients of less important predictors to zero, effectively removing them from the model.
For example, in genetic research, where thousands of genes are analyzed for their effect on a disease, Lasso Regression helps by identifying only the most impactful genes and ignoring the irrelevant ones, leading to a simpler and more interpretable model.