Proposition 2. Let X be some set andC be any collection of subsets ofX.

Under certain assumptions, frequently made for Bayes consistencyresults, we show that consistency in GeDTs and GeFs extend to any pattern of missing inputfeatures, ifmissing atrandom.

Thesemodels22 are very close to soft trees, to which we compare ourselves. In each case however, the models are enhanced with23 aneural network representation and suffer from alack of interpretability (one can even argue that these models are24 not tree modelsper se). The paper of Forsst & Hinton ([4]) considers aspecific variant of the soft tree model, with25 knowledge distillation. Combining both, as in PR-RF, reduces both bias and variance and leads to a method which significantly31 outperformsRF(Table5,AppendixA.4).32 Reviewer3.

Research on adversarial robustness is primarily focused on image and text data.

Decision trees are widely used in many settings where interpretable models are preferred orrequired.