[2202.05560] Controlling A number of Errors Concurrently with a PAC-Bayes Sure


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Summary:Present PAC-Bayes generalisation bounds are restricted to scalar metrics of efficiency, such because the loss or error fee. Nonetheless, one ideally desires extra information-rich certificates that management all the distribution of doable outcomes, such because the distribution of the take a look at loss in regression, or the possibilities of various mis classifications. We offer the primary PAC-Bayes sure able to offering such wealthy info by bounding the Kullback-Leibler divergence between the empirical and true possibilities of a set of M error varieties, which might both be discretized loss values for regression, or the weather of the confusion matrix (or a partition thereof) for classification. We rework our sure right into a differentiable coaching goal. Our sure is particularly helpful in instances the place the severity of various mis-classifications could change over time; current PAC-Bayes bounds can solely sure a selected pre-decided weighting of the error varieties. In distinction our sure implicitly controls all uncountably many weightings concurrently.

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From: Reuben Adams [view email]
Fri, 11 Feb 2022 11:35:21 UTC (45 KB)
Thu, 22 Feb 2024 16:28:19 UTC (719 KB)

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