Abstract: Classification with rejection emerges as a learning paradigm which allows models to abstain from making predictions. The predominant approach is to alter the supervised learning pipeline by augmenting typical loss functions, letting model rejection incur a lower loss than an incorrect prediction.Instead, we propose a different distributional perspective, where we seek to find an idealized data distribution which maximizes a pretrained model's performance.This can be formalized via the optimization of a loss's risk with a $ \phi$-divergence regularization term.Through this idealized distribution, a rejection decision can be made by utilizing the density ratio between this distribution and the data distribution.We focus on the setting where our $ \phi $-divergences are specified by the family of $ \alpha $-divergence.Our framework is tested empirically over clean and noisy datasets.