Application of the representative measure approach to assess the
  reliability of decision trees in dealing with unseen vehicle collision data
Javier Perera-Lago Víctor Toscano-Durán Eduardo Paluzo-Hidalgo Sara Narteni Matteo Rucco
Machine learning algorithms are fundamental components of novel data-informed
Artificial Intelligence architecture. In this domain, the imperative role of
representative datasets is a cornerstone in shaping the trajectory of
artificial intelligence (AI) development. Representative datasets are needed to
train machine learning components properly. Proper training has multiple
impacts: it reduces the final model's complexity, power, and uncertainties. In
this paper, we investigate the reliability of the
$\varepsilon$-representativeness method to assess the dataset similarity from a
theoretical perspective for decision trees. We decided to focus on the family
of decision trees because it includes a wide variety of models known to be
explainable. Thus, in this paper, we provide a result guaranteeing that if two
datasets are related by $\varepsilon$-representativeness, i.e., both of them
have points closer than $\varepsilon$, then the predictions by the classic
decision tree are similar. Experimentally, we have also tested that
$\varepsilon$-representativeness presents a significant correlation with the
ordering of the feature importance. Moreover, we extend the results
experimentally in the context of unseen vehicle collision data for XGboost, a
machine-learning component widely adopted for dealing with tabular data.