  Deep neural networks (DNNs) are notorious for making more mistakes for the
classes that have substantially fewer samples than the others during training.
Such class imbalance is ubiquitous in clinical applications and very crucial to
handle because the classes with fewer samples most often correspond to critical
cases (e.g., cancer) where misclassifications can have severe consequences. Not
to miss such cases, binary classifiers need to be operated at high True
Positive Rates (TPRs) by setting a higher threshold, but this comes at the cost
of very high False Positive Rates (FPRs) for problems with class imbalance.
Existing methods for learning under class imbalance most often do not take this
into account. We argue that prediction accuracy should be improved by
emphasizing reducing FPRs at high TPRs for problems where misclassification of
the positive, i.e. critical, class samples are associated with higher cost. To
this end, we pose the training of a DNN for binary classification as a
constrained optimization problem and introduce a novel constraint that can be
used with existing loss functions to enforce maximal area under the ROC curve
(AUC) through prioritizing FPR reduction at high TPR. We solve the resulting
constrained optimization problem using an Augmented Lagrangian method (ALM).
Going beyond binary, we also propose two possible extensions of the proposed
constraint for multi-class classification problems. We present experimental
results for image-based binary and multi-class classification applications
using an in-house medical imaging dataset, CIFAR10, and CIFAR100. Our results
demonstrate that the proposed method improves the baselines in majority of the
cases by attaining higher accuracy on critical classes while reducing the
misclassification rate for the non-critical class samples.
