  In many studies, we want to determine the influence of certain features on a
dependent variable. More specifically, we are interested in the strength of the
influence -- i.e., is the feature relevant? -- and, if so, how the feature
influences the dependent variable. Recently, data-driven approaches such as
\emph{random forest regression} have found their way into applications
(Boulesteix et al., 2012). These models allow to directly derive measures of
feature importance, which are a natural indicator of the strength of the
influence. For the relevant features, the correlation or rank correlation
between the feature and the dependent variable has typically been used to
determine the nature of the influence. More recent methods, some of which can
also measure interactions between features, are based on a modeling approach.
In particular, when machine learning models are used, SHAP scores are a recent
and prominent method to determine these trends (Lundberg et al., 2017).
  In this paper, we introduce a novel notion of feature importance based on the
well-studied Gram-Schmidt decorrelation method. Furthermore, we propose two
estimators for identifying trends in the data using random forest regression,
the so-called absolute and relative transversal rate. We empirically compare
the properties of our estimators with those of well-established estimators on a
variety of synthetic and real-world datasets.
