In most machine learning applications, classification accuracy is not the
primary metric of interest. Binary classifiers which face class imbalance are
often evaluated by the $F_\beta$ score, area under the precision-recall curve,
Precision at K, and more. The maximization of many of these metrics can be
expressed as a constrained optimization problem, where the constraint is a
function of the classifier's predictions.
In this paper we propose a novel framework for learning with constraints that
can be expressed as a predicted positive rate (or negative rate) on a subset of
the training data. We explicitly model the threshold at which a classifier must
operate to satisfy the constraint, yielding a surrogate loss function which
avoids the complexity of constrained optimization. The method is model-agnostic
and only marginally more expensive than minimization of the unconstrained loss.
Experiments on a variety of benchmarks show competitive performance relative to
existing baselines.

本文提出了一种基于约束学习的新框架， 可以通过在训练数据的子集上预测正 / 负例率来解决二分类器中的类不平衡问题，并避免了复杂的约束优化问题。该方法与模型无关且仅支出少量计算代价。在各种基准测试上的实验显示了与现有基准相比具有具有竞争性的性能。