  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.
