Should I use L1 or L2 regularization to fix overfitting in a high-dimensional dataset?

All answers to this question.

Since you mentioned that feature selection is a priority, L1 regularization (Lasso) is likely your best bet. Lasso has a unique property where it can shrink the coefficients of less important features all the way to zero, effectively acting as an automated feature selection tool. In a dataset with 500 features and only 2,000 rows, it's highly probable that many of those features are just noise. By zeroing them out, you simplify the model and improve generalization. L2 (Ridge), on the other hand, will keep all features but just minimize their impact, which might not be enough to stop the overfitting in such a sparse data environment.

   Answered 2025-02-16 by Jessica Walsh

Why not consider using Elastic Net instead of choosing just one? It combines both L1 and L2 penalties, which is often superior when you have highly correlated features. Have you checked the correlation matrix for your 500 features yet?

   Answered 2025-02-19 by Christopher Hayes

• Christopher, I actually haven't run a full correlation check yet because I was worried about the computational overhead on this specific instance. But your suggestion makes sense—if I have groups of correlated variables, Lasso might just pick one randomly, whereas Elastic Net would handle the group better. I'll try implementing Elastic Net with a cross-validation loop to find the optimal ratio between the L1 and L2 penalties to see if that stabilizes the test error.

     Commented 2025-02-21 by Robert Miller

L1 is definitely better for sparsity. If you have many irrelevant features, Lasso will clean up your model much faster than Ridge would. It makes the model way more interpretable too.

   Answered 2025-02-23 by Amanda Collins

• Spot on, Amanda. Interpretability is such an underrated benefit of L1. In high-dimensional spaces, knowing which 20 features actually matter is often more valuable than a slightly more accurate black-box model.

     Commented 2025-02-25 by Jessica Walsh