Misclassification excess risk bounds for PAC-Bayesian classification via convexified loss
This work addresses a gap in PAC-Bayesian theory for classification tasks, providing more direct risk bounds for practitioners, though it appears incremental as it builds on existing PAC-Bayesian frameworks.
The paper tackles the problem of deriving misclassification excess risk bounds for PAC-Bayesian classification when using convex surrogate losses, by leveraging PAC-Bayesian relative bounds in expectation instead of probability, and demonstrates this approach in several applications.
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.