In practical applications of machine learning, it is often desirable to identify and abstain on examples where the models predictions are likely to be incorrect. Much of the prior work on this topic focused on out-of-distribution detection or performance metrics such as top-k accuracy. Comparatively little attention was given to metrics such as area-under-the-curve or Cohens Kappa, which are extremely relevant for imbalanced datasets. Abstention strategies aimed at top-k accuracy can produce poor results on these metrics when applied to imbalanced datasets, even when all examples are in-distribution. We propose a framework to address this gap. Our framework leverages the insight that calibrated probability estimates can be used as a proxy for the true class labels, thereby allowing us to estimate the change in an arbitrary metric if an example were abstained on. Using this framework, we derive computationally efficient metric-specific abstention algorithms for optimizing the sensitivity at a target specificity level, the area under the ROC, and the weighted Cohens Kappa. Because our method relies only on calibrated probability estimates, we further show that by leveraging recent work on domain adaptation under label shift, we can generalize to test-set distributions that may have a different class imbalance compared to the training set distribution. On various experiments involving medical imaging, natural language processing, computer vision and genomics, we demonstrate the effectiveness of our approach. Source code available at https://github.com/blindauth/abstention. Colab notebooks reproducing results available at https://github.com/blindauth/abstention_experiments.
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