  Classification algorithms in machine learning often assume a flat label
space. However, most real world data have dependencies between the labels,
which can often be captured by using a hierarchy. Utilizing this relation can
help develop a model capable of satisfying the dependencies and improving model
accuracy and interpretability. Further, as different levels in the hierarchy
correspond to different granularities, penalizing each label equally can be
detrimental to model learning. In this paper, we propose a loss function,
hierarchical curriculum loss, with two properties: (i) satisfy hierarchical
constraints present in the label space, and (ii) provide non-uniform weights to
labels based on their levels in the hierarchy, learned implicitly by the
training paradigm. We theoretically show that the proposed loss function is a
tighter bound of 0-1 loss compared to any other loss satisfying the
hierarchical constraints. We test our loss function on real world image data
sets, and show that it significantly substantially outperforms multiple
baselines.
