  Cost-sensitive feature selection describes a feature selection problem, where
features raise individual costs for inclusion in a model. These costs allow to
incorporate disfavored aspects of features, e.g. failure rates of as measuring
device, or patient harm, in the model selection process. Random Forests define
a particularly challenging problem for feature selection, as features are
generally entangled in an ensemble of multiple trees, which makes a post hoc
removal of features infeasible. Feature selection methods therefore often
either focus on simple pre-filtering methods, or require many Random Forest
evaluations along their optimization path, which drastically increases the
computational complexity. To solve both issues, we propose Shallow Tree
Selection, a novel fast and multivariate feature selection method that selects
features from small tree structures. Additionally, we also adapt three standard
feature selection algorithms for cost-sensitive learning by introducing a
hyperparameter-controlled benefit-cost ratio criterion (BCR) for each method.
In an extensive simulation study, we assess this criterion, and compare the
proposed methods to multiple performance-based baseline alternatives on four
artificial data settings and seven real-world data settings. We show that all
methods using a hyperparameterized BCR criterion outperform the baseline
alternatives. In a direct comparison between the proposed methods, each method
indicates strengths in certain settings, but no one-fits-all solution exists.
On a global average, we could identify preferable choices among our BCR based
methods. Nevertheless, we conclude that a practical analysis should never rely
on a single method only, but always compare different approaches to obtain the
best results.
