I want to know how L1 & L2 regularization works in Light GBM and how to interpret the feature importances.
Scenario is: I used LGBM Regressor with RandomizedSearchCV (cv=3, iterations=50) on a dataset of 400000 observations & 160 variables. In order to avoid overfitting/reguralize I provided below ranges for alpha/L1 & lambda/L2 parameters and the best values as per Randomized search are 1 & 0.5 respectively.
'reg_lambda': [0.5, 1, 3, 5, 10] 'reg_alpha': [0.5, 1, 3, 5, 10]
Now my question is about: Feature importance values with optimized values of reg_lambda=1 & reg_alpha=0.5 are very different from that without providing any input for reg_lambda & alpha. The regularized model considers only top 5-6 features important and makes importance values of other features as good as zero (Refer images). Is that a normal behaviour of L1/L2 regularization in LGBM?
Further explaining the LGBM output with L1/L2: The top 5 important features are same in both the cases (with/without regularization), however importance values after top 2 features has been shrunk significantly by the L1/L2 regularized model and after top 5 features the regularized model makes importance values as good as zero (Refer images of feature importance values in both cases).
Another related question I have is: How to interpret the importance values and when I run the LGBM model with Randomized search cv best parameters do I need to remove the features with low importance values & then run the model? OR should I run with all the features & the LGBM algorithm (with L1 & L2 regularization) will take care of low importance features and won't give them any weight or may be give minute weight when it makes predictions.
Any help will be highly appreciated.