I'm currently using XGBoost on a data-set with 21 features (selected from list of some 150 features), then one-hot coded them to obtain ~98 features. A few of these 98 features are somewhat redundant, for example: a variable (feature) $A$ also appears as $\frac{B}{A}$ and $\frac{C}{A}$.

My questions are :


How (If?) do Boosted Decision Trees handle multicollinearity? 
How would the existence of multicollinearity affect prediction if it is not handled?


From what I understand, the model is learning more than one tree and the final prediction is based on something like a "weighted sum" of the individual predictions. So if this is correct, then Boosted Decision Trees should be able to handle co-dependence between variables.

Also, on a related note - how does the variable importance object in XGBoost work?

Decision trees are by nature immune to multi-collinearity. For example, if you have 2 features which are 99% correlated, when deciding upon a split the tree will choose only one of them. Other models such as Logistic regression would use both the features.

Since boosted trees use individual decision trees, they also are unaffected by multi-collinearity. However, its a good practice to remove any redundant features from any dataset used for training, irrespective of the model's  algorithm. In your case since you're deriving new features, you could use this approach, evaluate each feature's importance and retain only the best features for your final model.

The importance matrix of an xgboost model is actually a data.table object with the first column listing the names of all the features actually used in the boosted trees. The second column is the Gain metric which implies the relative contribution of the corresponding feature to the model calculated by taking each feature's contribution for each tree in the model. A higher value of this metric when compared to another feature implies it is more important for generating a prediction.
