Decision Tree Learning for Uncertain Clinical Measurements

Abstract: 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.