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.
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?