How Does Ridge Regression Differ from Lasso?

TL;DR

Ridge regression penalizes the sum of squares of coefficients, effectively shrinking them towards zero, while Lasso applies a penalty to the absolute values, allowing some coefficients to become exactly zero. This video explores both regression techniques and demonstrates how to use the glimnet package in RStudio for model selection and performance evaluation through cross-validation.

Transcript

okay so yeah we're going to do our final session in the in the model selection um uh chapter and we're going to look at Ridge regression and lassu and once again we're using our markdown in in our studio that will help us create a nice document at the end of the session and as you as we've seen it's just as simple as as having a script but it's bet... Read More

Key Insights

• 📦 The glimnet package in RStudio provides efficient tools for fitting Ridge and Lasso models.
• 0️⃣ Ridge regression shrinks coefficients towards zero, while Lasso selects some coefficients to be exactly zero.
• 🆘 The plot method in glimnet helps visualize the effect of the penalty on coefficients.

Questions & Answers

Q: What is the difference between Ridge regression and Lasso model selection?

Ridge regression penalizes the sum of squares of coefficients, while Lasso penalizes the absolute values of coefficients. This difference makes Lasso capable of shrinking some coefficients to exactly zero, allowing variable selection.

Q: How does the glimnet package in RStudio help with Ridge and Lasso models?

The glimnet package provides functions for fitting Ridge and Lasso models, as well as other models in between. It allows fitting models for different loss functions, such as logistic regressions and ordinary regressions.

Q: What is the purpose of the plot method in the glimnet package?

The plot method in the glimnet package allows visualizing the coefficients of the fitted models as a function of the log of Lambda. This helps understand the effect of the penalty on the coefficients.

Q: How does cross-validation help in selecting the best model?

Cross-validation, specifically k-fold cross-validation, helps estimate the performance of different models. By choosing the model with the lowest mean squared error within one standard error, overfitting can be minimized.

Summary & Key Takeaways

• The session introduces Ridge regression and Lasso model selection using the glimnet package in RStudio.

• Ridge regression applies a penalty to the sum of squares of coefficients, while Lasso penalizes the absolute values of coefficients.

• The session demonstrates the use of plots and cross-validation to select the best model based on mean squared error.