Decision Trees and Feature Selection

I understand CART as a Classification and Regression Tree, as just a Decision tree. Decision Trees are greedy and deterministic.

Random Forest is an ensemble of decision trees, so you will be using random trees ensembling to select features.

I am guessing, your question is not really descriptive about the situation, that since the decision tree is not pruned and uses all data it gives a good solution there is no need to take care of overfitting or pruning They normally achieve better in the train than Random Forest because they overfit easily.

Taking out features will just give the tree less information, so less power.

Does it mean that CART needs a large number of features to produce a good model?

Decision trees do good with a small number of features, it is not related.

Just to check, are you evaluating in the test set right?

A decision tree has implicit feature selection during the model building process. That is, when it is building the tree, it only does so by splitting on features that cause the greatest increase in node purity, so features that a feature selection method would have eliminated aren’t used in the model anyway.

This is different than say a random forest where each split is chosen on only a subset of features, so it is possible that a given split is chosen from only “bad” features. By performing feature selection you remove this possibility and improve performance in the forest