Controlling Multiple Errors Simultaneously with a PAC-Bayes Bound
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2022
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| _version_ | 1866910731495014400 |
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| author | Adams, Reuben Shawe-Taylor, John Guedj, Benjamin |
| author_facet | Adams, Reuben Shawe-Taylor, John Guedj, Benjamin |
| contents | Current PAC-Bayes generalisation bounds are restricted to scalar metrics of performance, such as the loss or error rate. However, one ideally wants more information-rich certificates that control the entire distribution of possible outcomes, such as the distribution of the test loss in regression, or the probabilities of different mis-classifications. We provide the first PAC-Bayes bound capable of providing such rich information by bounding the Kullback-Leibler divergence between the empirical and true probabilities of a set of $M$ error types, which can either be discretized loss values for regression, or the elements of the confusion matrix (or a partition thereof) for classification. We transform our bound into a differentiable training objective. Our bound is especially useful in cases where the severity of different mis-classifications may change over time; existing PAC-Bayes bounds can only bound a particular pre-decided weighting of the error types. In contrast our bound implicitly controls all uncountably many weightings simultaneously. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2202_05560 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Controlling Multiple Errors Simultaneously with a PAC-Bayes Bound Adams, Reuben Shawe-Taylor, John Guedj, Benjamin Machine Learning Statistics Theory Current PAC-Bayes generalisation bounds are restricted to scalar metrics of performance, such as the loss or error rate. However, one ideally wants more information-rich certificates that control the entire distribution of possible outcomes, such as the distribution of the test loss in regression, or the probabilities of different mis-classifications. We provide the first PAC-Bayes bound capable of providing such rich information by bounding the Kullback-Leibler divergence between the empirical and true probabilities of a set of $M$ error types, which can either be discretized loss values for regression, or the elements of the confusion matrix (or a partition thereof) for classification. We transform our bound into a differentiable training objective. Our bound is especially useful in cases where the severity of different mis-classifications may change over time; existing PAC-Bayes bounds can only bound a particular pre-decided weighting of the error types. In contrast our bound implicitly controls all uncountably many weightings simultaneously. |
| title | Controlling Multiple Errors Simultaneously with a PAC-Bayes Bound |
| topic | Machine Learning Statistics Theory |
| url | https://arxiv.org/abs/2202.05560 |