I have a model with only categorical features. The outcome is binary. I am training binary classifiers. Most of them are coded already as 0/1 . Some have increased cardinality (ie 4 categories). For my logistic-like models, I use Patsy, which introduces an intercept term and I have them one-hot-encoded for k-1 categories.
For decision tree-like models (adaboost, gradient boosting classifier,xgboost, etc), shall I include a separate column (1/0) for the reference category for any feature with ≥3 categories? Does it add more granularity or just overfits or decreases learning efficiency?