  Clinical decision requires reasoning in the presence of imperfect data. DTs
are a well-known decision support tool, owing to their interpretability,
fundamental in safety-critical contexts such as medical diagnosis. However,
learning DTs from uncertain data leads to poor generalization, and generating
predictions for uncertain data hinders prediction accuracy. Several methods
have suggested the potential of probabilistic decisions at the internal nodes
in making DTs robust to uncertainty. Some approaches only employ probabilistic
thresholds during evaluation. Others also consider the uncertainty in the
learning phase, at the expense of increased computational complexity or reduced
interpretability. The existing methods have not clarified the merit of a
probabilistic approach in the distinct phases of DT learning, nor when the
uncertainty is present in the training or the test data. We present a
probabilistic DT approach that models measurement uncertainty as a noise
distribution, independently realized: (1) when searching for the split
thresholds, (2) when splitting the training instances, and (3) when generating
predictions for unseen data. The soft training approaches (1, 2) achieved a
regularizing effect, leading to significant reductions in DT size, while
maintaining accuracy, for increased noise. Soft evaluation (3) showed no
benefit in handling noise.
