  CXRs are a crucial and extraordinarily common diagnostic tool, leading to
heavy research for CAD solutions. However, both high classification accuracy
and meaningful model predictions that respect and incorporate clinical
taxonomies are crucial for CAD usability. To this end, we present a deep HMLC
approach for CXR CAD. Different than other hierarchical systems, we show that
first training the network to model conditional probability directly and then
refining it with unconditional probabilities is key in boosting performance. In
addition, we also formulate a numerically stable cross-entropy loss function
for unconditional probabilities that provides concrete performance
improvements. Finally, we demonstrate that HMLC can be an effective means to
manage missing or incomplete labels. To the best of our knowledge, we are the
first to apply HMLC to medical imaging CAD. We extensively evaluate our
approach on detecting abnormality labels from the CXR arm of the PLCO dataset,
which comprises over $198,000$ manually annotated CXRs. When using complete
labels, we report a mean AUC of 0.887, the highest yet reported for this
dataset. These results are supported by ancillary experiments on the PadChest
dataset, where we also report significant improvements, 1.2% and 4.1% in AUC
and AP, respectively over strong "flat" classifiers. Finally, we demonstrate
that our HMLC approach can much better handle incompletely labelled data. These
performance improvements, combined with the inherent usefulness of taxonomic
predictions, indicate that our approach represents a useful step forward for
CXR CAD.
