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In some cases, however, it may be desirable to include an extremely large number of constraints.

The paper shows that the optimal rule for such metrics has the form of sign(P(y|x)-\delta^*), where \delta^* is a threshold that is metric dependent. This unified framework recovers many results for metrics studied in the literature. Authors devise 2 simple algorithms for estimating p(y|x) and the threshold delta^*. Bayes and statistical consistency of the proposed algorithms is then analyzed.

There are many natural models for noise.

Machine learning models developed from real-world data can inherit pre-existing bias in the dataset. When these models are used to inform decisions involving humans, it may exhibit similar discrimination against sensitive attributes (e.g., gender and race) [

Neural Networks can perform poorly when the training label distribution is heavily imbalanced, as well as when the testing data differs from the training distribution. In order to deal with shift in the testing label distribution, which imbalance causes, we motivate the problem from the perspective of an optimal Bayes classifier and derive a post-training prior rebalancing technique that can be solved through a KL-divergence based optimization. This method allows a flexible post-training hyper-parameter to be efficiently tuned on a validation set and effectively modify the classifier margin to deal with this imbalance. We further combine this method with existing likelihood shift methods, re-interpreting them from the same Bayesian perspective, and demonstrating that our method can deal with both problems in a unified way.