Misclassification excess risk bounds for PAC-Bayesian classification via convexified loss
Abstract: PAC-Bayesian bounds have proven to be a valuable tool for deriving generalization bounds and for designing new learning algorithms in machine learning. However, they typically focus on providing generalization bounds with respect to a chosen loss function. In this study, we concentrate on the problem of PAC-Bayesian classification, specifically referring to the PAC-Bayesian method for binary classification. In classification tasks, due to the non-convex nature of the 0-1 loss, a convex surrogate loss is often used, and thus current PAC-Bayesian bounds are primarily specified for this convex surrogate. This work shifts its focus to providing misclassification excess risk bounds for PAC-Bayesian classification when using a convex surrogate loss. Our key ingredient here is to leverage PAC-Bayesian relative bounds in expectation rather than relying on PAC-Bayesian bounds in probability. We demonstrate our approach in several important applications.
Submission Length: Regular submission (no more than 12 pages of main content)
Changes Since Last Submission: Corrected some texts and added some references required by reviewers.
Assigned Action Editor: ~Daniel_M_Roy1
Submission Number: 3196
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