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For the lasso (linear regression with L1 regularization) with a fixed value of λ, it is necessary to use cross–validation to select the best optimization algorithm.

I know for a fact that we can use cross validation to find optimal value of λ, but is it neccesary to use cross validation in case λ is fixed?

Any thoughts please?

Hardik
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1 Answers1

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Cross Validation isn't about if your Regularization Parameter is Fixed or not. Its more related to the R^2 metric.

Lets say you consider 100 records and divide your data into 5 sub-datasets , means each sub-data contains 20 records. Now out of 5 sub-datas , there are 5 different ways to assign anyone of the sub-data as Cross-Validation (CV) Data.

For all these 5 scenarios, we can find out the R^2, and then find out the Average R^2. This way, you can have a comparison of your R-score with the Average R-score.

Sohil Sharma
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