# Why lasso yield a higher mse then ridge?

I do a rige and lasso regression on a train data set and get the lambdas via cross validation and evalute the prediction accuracy on a test data set.

After that i do the same procedure for the same data but adding polynomials to the power of 4 and interactions to the order of 2 (V1*V2)+(V1*V3) to the train and test data set.

At the end i get a smaller test mse with ridge for the model with interactions and polynomials compared to the model without interactions. That's a result that i would expect.

But for lasso I have a higher test mse compared to the model without interactions and polynomials. That's what i don't expected.

I don't understand why lasso performs worse than ridge and worse than a model with less explanatory variables?

• Please don't open a new question. Instead, edit the existing one. – Stephan Kolassa Jul 16 '18 at 15:54
• @StephanKolassa its a different question. The first one is about ols compared to ridge and lasso. This one is ridge compared to lasso and . And i also use different data setup – Dima Ku Jul 16 '18 at 15:56
• Thank you for clarifying. However, given that the two questions are very closely related, please include links next time. – Stephan Kolassa Jul 16 '18 at 15:58
• This sounds like an implementation issue. Are you using Elastic Net? – ERT Jul 16 '18 at 16:17
• no i just used ridge and lasso – Dima Ku Jul 16 '18 at 16:32