Misclassification excess risk bounds for PAC-Bayesian classification via convexified loss

• URL: http://arxiv.org/abs/2408.08675v1
• Date: Fri, 16 Aug 2024 11:41:06 GMT
• Title: Misclassification excess risk bounds for PAC-Bayesian classification via convexified loss
• Authors: The Tien Mai,
• Abstract summary: PAC-Bayesian bounds are a valuable tool for designing new learning algorithms in machine learning. In this paper we show how to leverage relative bounds in expectation rather than relying on PAC-Bayesian bounds in terms of generalization.
• Score: 0.0
• License: http://creativecommons.org/licenses/by-nc-sa/4.0/
• 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, it typically focus on providing generalization bounds with respect to a chosen loss function. 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.

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