Adams, Reuben; Shawe-Taylor, John; Guedj, Benjamin; (2024) Controlling Multiple Errors Simultaneously with a PAC-Bayes Bound. In: Globersons, Amir and Mackey, Lester and Belgrave, Danielle and Fan, Angela and Paquet, Ulrich and Tomczak, Jakub M and Zhang, Cheng, (eds.) Advances in Neural Information Processing Systems 37 (NeurIPS 2024). (pp. pp. 1-30). NeurIPS

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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 informationrich 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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