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| Format: | Preprint |
| Published: |
2025
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| Online Access: | https://arxiv.org/abs/2505.05273 |
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| _version_ | 1866908354145681408 |
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| author | Soen, Alexander |
| author_facet | Soen, Alexander |
| contents | Learning to reject provide a learning paradigm which allows for our models to abstain from making predictions. One way to learn the rejector is to learn an ideal marginal distribution (w.r.t. the input domain) - which characterizes a hypothetical best marginal distribution - and compares it to the true marginal distribution via a density ratio. In this paper, we consider learning a joint ideal distribution over both inputs and labels; and develop a link between rejection and thresholding different statistical divergences. We further find that when one considers a variant of the log-loss, the rejector obtained by considering the joint ideal distribution corresponds to the thresholding of the skewed Bhattacharyya divergence between class-probabilities. This is in contrast to the marginal case - that is equivalent to a typical characterization of optimal rejection, Chow's Rule - which corresponds to a thresholding of the Kullback-Leibler divergence. In general, we find that rejecting via a Bhattacharyya divergence is less aggressive than Chow's Rule. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_05273 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Connection Between Learning to Reject and Bhattacharyya Divergences Soen, Alexander Machine Learning Information Theory Learning to reject provide a learning paradigm which allows for our models to abstain from making predictions. One way to learn the rejector is to learn an ideal marginal distribution (w.r.t. the input domain) - which characterizes a hypothetical best marginal distribution - and compares it to the true marginal distribution via a density ratio. In this paper, we consider learning a joint ideal distribution over both inputs and labels; and develop a link between rejection and thresholding different statistical divergences. We further find that when one considers a variant of the log-loss, the rejector obtained by considering the joint ideal distribution corresponds to the thresholding of the skewed Bhattacharyya divergence between class-probabilities. This is in contrast to the marginal case - that is equivalent to a typical characterization of optimal rejection, Chow's Rule - which corresponds to a thresholding of the Kullback-Leibler divergence. In general, we find that rejecting via a Bhattacharyya divergence is less aggressive than Chow's Rule. |
| title | A Connection Between Learning to Reject and Bhattacharyya Divergences |
| topic | Machine Learning Information Theory |
| url | https://arxiv.org/abs/2505.05273 |