  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 (TPR) by setting a higher threshold but this comes at the cost
of very high False Positive Rates (FPR) 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 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). We solve the
resulting constrained optimization problem using an Augmented Lagrangian method
(ALM), where the constraint emphasizes reduction of FPR at high TPR. We present
experimental results for image-based classification applications using the
CIFAR10 and an in-house medical imaging dataset. Our results demonstrate that
the proposed method almost always improves the loss functions it is used with
by attaining lower FPR at high TPR and higher or equal AUC.
