Generalizing Gain Penalization for Feature Selection in Tree-based Models

We develop a new approach for feature selection via gain penalization in tree-based models. First, we show that previous methods do not perform sufficient regularization and often exhibit sub-optimal out-of-sample performance, especially when correlated features are present. Instead, we develop a new gain penalization idea that exhibits a general local-global regularization for tree-based models. The new method allows for full flexibility in the choice of feature-specific importance weights, while also applying a global penalization. We validate our method on both simulated and real data, exploring how the hyperparameters interact and we provide the implementation as an extension of the popular R package ranger.