Controlling Multiple Errors Simultaneously with a PAC-Bayes Bound
- URL: http://arxiv.org/abs/2202.05560v2
- Date: Thu, 22 Feb 2024 16:28:19 GMT
- Title: Controlling Multiple Errors Simultaneously with a PAC-Bayes Bound
- Authors: Reuben Adams and John Shawe-Taylor and Benjamin Guedj
- Abstract summary: We provide the first PAC-Bayes bound capable of providing rich information by bounding the Kullback-Leibler divergence between the empirical and true probabilities of a set of M error types.
Our bound is especially useful in cases where the severity of different mis-classifications may change over time.
- Score: 21.273964864852612
- License: http://creativecommons.org/licenses/by-nc-sa/4.0/
- Abstract: 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.
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