H$^2$EDL Improves Uncertainty Quantification in Hierarchical AI Classification

Fine-grained recognition tasks often involve classifying items within a hierarchical structure, where a model might be confident about a broad category but uncertain about its specific sub-classes. Existing methods struggle to capture this nuanced uncertainty effectively; some quantify total ignorance at the leaf level, while others propagate probabilities without a clear notion of evidence across the hierarchy. The H$^2$EDL model addresses this by observing that the taxonomic structure itself can serve as a "hyperdomain." By defining a local Dirichlet opinion for each branching node in the hierarchy, the model can induce every composite mass in a closed form, unifying fine-grained and intermediate concept uncertainty. This approach allows for a consistent representation of belief across different levels of the label tree. The model functions as a hierarchical classifier that maintains consistency and also defines a valid tree-structured hyper-opinion. The mass assigned to each node represents the belief that reaches that node without sufficient confidence to specialize further. Experiments on datasets like FGVC-Aircraft and DERM12345 show that H$^2$EDL approximately halves calibration error compared to cross-entropy baselines, with improvements more pronounced in deeper hierarchy levels and with larger training datasets.